Purpose: To use the ballistic pendulum to determine the initial velocity of a projectile using conservation of momentum and conservation of energy.
Equipment: Ballistic pendulum, carbon paper, meter stick, clamp, box, triple beam balance, plumb.
Introduction: In this experiment a steel ball will be shot into the bob of a pendulum and the height, h, to which the pendulum bob moves, as shown in Figure 1, will determine the initial velocity, V, of the bob after it receives the moving ball. If we equate the kinetic energy of the bob and ball at the bottom to the potential energy of the bob and ball at the height, h, that they are raised to, we get:
( K.E ) bottom = ( P.E)top
½ ( M + m ) V² = ( M + m ) g.h
where M is the mass of the pendulum and m is the mass of the ball. Solving for V we get:
V = √ 2gh ……………. ( 1 )
Using conservation of momentum we know the momentum before impact (collision) should be the same as the momentum after impact. Therefore:
Pi = Pf
or
mv0 = ( M + m) V …………… ( 2 )
where v0 is the initial velocity of the ball before impact. By using equations (1) and (2) we can therefore find the initial velocity, v0, of the ball.
We can also determine the initial velocity of the ball by shooting the ball as above but this time allowing the ball to miss the pendulum bob and travel horizontally under the influence of gravity. In this case we simply have a projectile problem where we can measure the distance traveled horizontally and vertically (see Figure 2 from the ballistic pendulum at http://www.hartnell.edu/physics/labs4a.htm) and then determine the initial velocity, v0, of the ball.
M + m Starting with equations:
∆x = voxt + ½axt² ……………… ( 3 )
∆y = voyt + ½ayt²
……………… ( 4 )
You should be able to derive the initial velocity of the ball in the horizontal direction (assuming that
∆x and ∆y are known). Include this derivation in your lab report.
Procedure:
Part I Determination of Initial Velocity from Conservation of Energy
1. Set the apparatus near one edge of the table as shown in figure 2. Make sure that the base is accurately horizontal, as shown by a level. Clamp the frame to the table. To make the gun ready for shooting, rest the pendulum on the rack, put the ball in position on the end of the rod and, holding the base with one hand, pull back on the ball with the other until the collar on the rod engages the trigger. This compresses the spring a definite amount, and the ball is given the same initial velocity every time the gun is shot.
2. Release the pendulum from the rack and allow it to hang freely. When the pendulum is at rest, pull the trigger, thereby propelling the ball into the pendulum bob with a definite velocity. This causes the pendulum to swing from a vertical position to an inclined position with the pawl engaged in some particular tooth of the rack.
3. Shoot the ball into the cylinder about nine times, recording each point on the rack at which the pendulum comes to rest. This in general will not be exactly the same for all cases but may vary by several teeth of the rack. The mean of these observations gives the mean highest position of the pendulum. Raise the pendulum until its pawl is engaged in the tooth corresponding most closely to the mean value and measure h1, the elevation above the surface of the base of the index point for the center of gravity. Next release the pendulum and allow it to hang in its lower most position and measure h2. The difference between these two values gives h, the vertical distance through which the center of gravity of the system is raised after shooting the ball. Record h:
4. Carefully remove the pendulum from its support. Weigh and record the masses of the pendulum and of the ball. Replace the pendulum and carefully adjust the thumb screw.
5. From these data calculate the initial velocity v using equations (1) and (2). Part II Determination of Initial Velocity from Measurements of Range and Fall
1. To obtain the data for this part of the experiment the pendulum is positioned up on the rack so that it will not interfere with the free flight of the ball. One observer should watch carefully to determine the point at which the ball strikes the floor. The measurements in this part of the experiment are made with reference to this point and the point of departure of the ball. Clamp the frame to the table, as it is important that the apparatus not be moved until the measurements have been completed. A piece of paper taped to the floor at the proper place and covered with carbon paper will help in the exact determination of the spot at which the ball strikes the floor.
Note: Use caution in shooting the gun.
2. Shoot the ball a number of times, noting each time the point at which it strikes the floor. Determine, relative to the edge of the paper, the average position of impact of the ball. Determine the distances ∆x using this average position on the floor. From the the values of ∆x and ∆y calculate v0 by the use of equations (3) and (4). Make careful sketches in your lab report that clearly show all of the distances involved.
3. Find the percentage difference between the values of v0 determined by the two methods in parts I and II. Try to analyze, the probable errors of the two methods and estimate which one should give the more accurate result.
Note: Before leaving the apparatus, put the ball on its peg and be sure that the spring gun is released.
Conclusions:
I learned that the conservation of energy theorem applies accurately when all external and internal forces are taken into consideration such as friction and centripetal force. Considering dK = W and dK = -Ug, W = -Ug. K = .5(mv^2) and Ug = mgh. Since dK = Kf - Ki, we have that W = Kf - Ki = Ug = -mgh.
Sources of error are strictly through human error.
Sunday, December 16, 2012
Centripetal Force
Purpose: To verify Newton’s second law of motion for the case of uniform circular
motion.
Equipment: Centripetal force apparatus, metric scale, vernier caliper, stop watch,
slotted weight set, weight hanger, triple beam balance.
Introduction:
The centripetal force apparatus is designed to rotate a known mass trough
a circular path of known radius. By timing the motion for a definite
number of revolutions and knowing the total distance that the mass has
traveled, the velocity can be calculated. Thus the centripetal force, F,
necessary to cause the mass to follow its circular path can be
determined from Newton’s second law.
r
Where m is the mass, v is the velocity, and r is the radius of the circular
path.
Here we have used the fact that for uniform circular motion, the
acceleration, a, is given by:
Procedure:
1. For each trial the position of the horizontal crossarm and the vertical indicator
post must be such that the mass hangs freely over the post when the spring is
detached. After making this adjustment, connect the spring to the mass and
practice aligning the bottom of the hanging mass with the indicator post while
rotating the assembly.
2. Measure the time for 50 revolutions of the apparatus. Keep the velocity as
constant as possible by keeping the pointer on the bottom of the mass aligned with
the indicator post. A white sheet of paper placed as a background behind the
apparatus can be helpful in getting the alignment as close as possible. Using the
same mass and radius, measure the time for three different trials. Record all data
in a neat excel table (see 6).
3. Using the average time obtained above, calculate the velocity of the mass. From
this calculate the centripetal force exerted on the mass during its motion.
F = (mv^2)/r
a(c) = (v^2)/r
4. Independently determine the centripetal force by attaching a hanging weight to
the mass until it once again is positioned over the indicator post (this time at rest).
Since the spring is being stretched by the same amount as when the apparatus was
rotating, the force stretching the spring should be the same in each case.
a. Calculate this force and compare with the centripetal force obtained
in part 3 by finding the percent difference.
b. Draw a force diagram for the hanging weight and draw a force
diagram for the spring attached to the hanging mass:
5. Add 100 g to the mass and repeat steps 2, 3 and 4 above.
6. The following data should be calculated and recorded in your excel table:
a. Mass and radius for each trial.
b. Average number of revolutions/sec (frequency) for each trial.
c. Linear speed for each trial.
d. Calculated and measured centripetal force for each trial and their percent
difference.
Conclusions:
I learned that in order to calculate the centripetal force of an object undergoing circular motion, the formula F = (mv^2)/r must be used where m = mass, v = linear velocity (tangential), and r = radius. I also learned that when extra mass is added to the system but centripetal force and the radius are constant, then the deciding factor must be that the velocity depreciated, that is, the velocity decreased to account for equilibrium on both sides of the equation.
Possible sources of error are of course resultant from human interference and quite possibly significant figure usage during calculations.
motion.
Equipment: Centripetal force apparatus, metric scale, vernier caliper, stop watch,
slotted weight set, weight hanger, triple beam balance.
Introduction:
The centripetal force apparatus is designed to rotate a known mass trough
a circular path of known radius. By timing the motion for a definite
number of revolutions and knowing the total distance that the mass has
traveled, the velocity can be calculated. Thus the centripetal force, F,
necessary to cause the mass to follow its circular path can be
determined from Newton’s second law.
r
Where m is the mass, v is the velocity, and r is the radius of the circular
path.
Here we have used the fact that for uniform circular motion, the
acceleration, a, is given by:
Procedure:
1. For each trial the position of the horizontal crossarm and the vertical indicator
post must be such that the mass hangs freely over the post when the spring is
detached. After making this adjustment, connect the spring to the mass and
practice aligning the bottom of the hanging mass with the indicator post while
rotating the assembly.
2. Measure the time for 50 revolutions of the apparatus. Keep the velocity as
constant as possible by keeping the pointer on the bottom of the mass aligned with
the indicator post. A white sheet of paper placed as a background behind the
apparatus can be helpful in getting the alignment as close as possible. Using the
same mass and radius, measure the time for three different trials. Record all data
in a neat excel table (see 6).
3. Using the average time obtained above, calculate the velocity of the mass. From
this calculate the centripetal force exerted on the mass during its motion.
F = (mv^2)/r
a(c) = (v^2)/r
4. Independently determine the centripetal force by attaching a hanging weight to
the mass until it once again is positioned over the indicator post (this time at rest).
Since the spring is being stretched by the same amount as when the apparatus was
rotating, the force stretching the spring should be the same in each case.
a. Calculate this force and compare with the centripetal force obtained
in part 3 by finding the percent difference.
b. Draw a force diagram for the hanging weight and draw a force
diagram for the spring attached to the hanging mass:
5. Add 100 g to the mass and repeat steps 2, 3 and 4 above.
6. The following data should be calculated and recorded in your excel table:
a. Mass and radius for each trial.
b. Average number of revolutions/sec (frequency) for each trial.
c. Linear speed for each trial.
d. Calculated and measured centripetal force for each trial and their percent
difference.
Conclusions:
I learned that in order to calculate the centripetal force of an object undergoing circular motion, the formula F = (mv^2)/r must be used where m = mass, v = linear velocity (tangential), and r = radius. I also learned that when extra mass is added to the system but centripetal force and the radius are constant, then the deciding factor must be that the velocity depreciated, that is, the velocity decreased to account for equilibrium on both sides of the equation.
Possible sources of error are of course resultant from human interference and quite possibly significant figure usage during calculations.
Projectile Simulation
Purpose: 1. To gain a better understanding of motion in two dimensions by working a projectile
problem
2. To gain experience using a computer simulation of a physical problem
Equipment Needed: windows based computer with Interactive Physics software
Introduction: The computer will be used to create a simulation of a rubber ball being thrown through a
window on the side of a building. The computer, of course, uses the laws of physics
(previously programmed into the computer) to simulate the motion. In a similar way, we
can use the laws of physics to do the calculations ourselves and predict the correct initial
velocity needed and thus check the accuracy of our simulation. The only other means of
verifying any simulation (and the best!) is doing the actual experiment, but depending on
the situation this may be difficult and/or costly.
By adjusting the initial velocity of the ball we can use the computer to repeat the
experiment over and over again until we achieve the desired result (getting the ball
through the window). The ball's initial velocity is controlled by using the slider bars for
Vx and Vy or by simply typing in values in the boxes below each slider. Be sure that the
simulation has been reset before making any changes. The components, Vx and Vy, of
the ball's velocity are displayed by digital meters. Vectors attached to the ball indicate
the ball's velocity as well as the x and y components of the velocity.
Procedure:
1. Turn on the computer and load the Interactive Physics software located within the Physics Apps
folder. Select File/Open and double click on FLYBALL file.
2. Set the initial velocity of the ball by adjusting the sliders for Vx and Vy and observe the initial
velocity vector attached to the ball change as you adjust the sliders. Run the simulation and observe
the motion of the ball. Watch the velocity vector and its components as they change throughout the
motion.
Repeat the simulation with a different initial velocity until the ball goes through the center of the
window. Record V0x, V0y, and the total elapsed time. Also locate the initial position of the ball by
moving the mouse until the cursor on the center of the ball. Read the values for x and y in the
coordinate boxes in the lower left portion of the screen. In a similar manner, determine the
coordinates of the center of the window. Make a motion diagram showing all relevant variables.
Using your motion equations, calculate what the time of flight should be and compare with the
simulation time.
V0x
V0y
∆t
x0
y0
xf
yf3. Using the player controls, step the motion back to where your projectile is at the very top of its path.
Record the values for Vx, Vy, and t at this point. From your initial velocity, calculate what the time
should be at the top. How does your calculated time compare with the simulation’s time?
4. Run the simulation using a ball speed of V0x = 6.00 m/s and V0y = 8.02 m/s. Record the horizontal
and vertical components of the velocity at various times (using the player controls), completing a
table like the one shown below. Be careful to record the sign (positive or negative) in all cases.
Time (s) Vx (m/s) Vy (m/s)
0.0 6.0 8.02
0.2
0.4
0.6
0.8
1.0
1.2
1.4
5. Using the data from the table, plot the horizontal and vertical components of the velocity, Vx and Vy,
versus time on a single graph in Graphical Analysis. Use different symbols to mark the data points
for the two velocity components. You should observe that one component of velocity changes while
the other is constant. Explain. What should the slope for each curve be?
6. Fit the graphs and find the slopes of the lines. Did they agree with your expectations? Explain.
Print a copy of the graphs for everyone in the group. 7. The horizontal and vertical positions of a projectile in free fall are given by
x = x0 + V0xt + ½axt
2
y = y0 + V0yt + ½ayt
2
Solve each of these equations algebraically for V0x and V0y.
8. Using the results from part 7, calculate V0x and V0y
for a time of flight of 1.6 s and then run the
simulation. Verify that the ball does go through the center of the window for your calculated values
of V0x and V0y . Repeat for a time of flight of 1.33 s and 0.5 s. Sketch the shape of each trajectory
and discuss the differences in the trajectories. What determines the amount of time the projectile
spends in the air?
9. Calculate the initial speed (magnitude of the velocity) and direction (angle above the horizontal) for
each of the three simulations discussed in part 8. Put the results from parts 8 and 9 in a table.
V0 θ
Conclusions:
The purpose of the projectile simulation lab was to estimate the trajectory an object would take to undergo a predetermined behavior and by mechanics of kinematics, we were to ascertain the velcocities of the x and y directions to make the object fulfil the desired behavior given initial and final positions as well as acceleration. Before this lab, I was completely confused as to how a
"split-up" kinematic equations were related and afterward I was able to relate them by solving for certain variables and interpolating them into the other equation, much like one of the rocket problems discussed during the course of the semester.
problem
2. To gain experience using a computer simulation of a physical problem
Equipment Needed: windows based computer with Interactive Physics software
Introduction: The computer will be used to create a simulation of a rubber ball being thrown through a
window on the side of a building. The computer, of course, uses the laws of physics
(previously programmed into the computer) to simulate the motion. In a similar way, we
can use the laws of physics to do the calculations ourselves and predict the correct initial
velocity needed and thus check the accuracy of our simulation. The only other means of
verifying any simulation (and the best!) is doing the actual experiment, but depending on
the situation this may be difficult and/or costly.
By adjusting the initial velocity of the ball we can use the computer to repeat the
experiment over and over again until we achieve the desired result (getting the ball
through the window). The ball's initial velocity is controlled by using the slider bars for
Vx and Vy or by simply typing in values in the boxes below each slider. Be sure that the
simulation has been reset before making any changes. The components, Vx and Vy, of
the ball's velocity are displayed by digital meters. Vectors attached to the ball indicate
the ball's velocity as well as the x and y components of the velocity.
Procedure:
1. Turn on the computer and load the Interactive Physics software located within the Physics Apps
folder. Select File/Open and double click on FLYBALL file.
2. Set the initial velocity of the ball by adjusting the sliders for Vx and Vy and observe the initial
velocity vector attached to the ball change as you adjust the sliders. Run the simulation and observe
the motion of the ball. Watch the velocity vector and its components as they change throughout the
motion.
Repeat the simulation with a different initial velocity until the ball goes through the center of the
window. Record V0x, V0y, and the total elapsed time. Also locate the initial position of the ball by
moving the mouse until the cursor on the center of the ball. Read the values for x and y in the
coordinate boxes in the lower left portion of the screen. In a similar manner, determine the
coordinates of the center of the window. Make a motion diagram showing all relevant variables.
Using your motion equations, calculate what the time of flight should be and compare with the
simulation time.
V0x
V0y
∆t
x0
y0
xf
yf3. Using the player controls, step the motion back to where your projectile is at the very top of its path.
Record the values for Vx, Vy, and t at this point. From your initial velocity, calculate what the time
should be at the top. How does your calculated time compare with the simulation’s time?
4. Run the simulation using a ball speed of V0x = 6.00 m/s and V0y = 8.02 m/s. Record the horizontal
and vertical components of the velocity at various times (using the player controls), completing a
table like the one shown below. Be careful to record the sign (positive or negative) in all cases.
Time (s) Vx (m/s) Vy (m/s)
0.0 6.0 8.02
0.2
0.4
0.6
0.8
1.0
1.2
1.4
5. Using the data from the table, plot the horizontal and vertical components of the velocity, Vx and Vy,
versus time on a single graph in Graphical Analysis. Use different symbols to mark the data points
for the two velocity components. You should observe that one component of velocity changes while
the other is constant. Explain. What should the slope for each curve be?
6. Fit the graphs and find the slopes of the lines. Did they agree with your expectations? Explain.
Print a copy of the graphs for everyone in the group. 7. The horizontal and vertical positions of a projectile in free fall are given by
x = x0 + V0xt + ½axt
2
y = y0 + V0yt + ½ayt
2
Solve each of these equations algebraically for V0x and V0y.
8. Using the results from part 7, calculate V0x and V0y
for a time of flight of 1.6 s and then run the
simulation. Verify that the ball does go through the center of the window for your calculated values
of V0x and V0y . Repeat for a time of flight of 1.33 s and 0.5 s. Sketch the shape of each trajectory
and discuss the differences in the trajectories. What determines the amount of time the projectile
spends in the air?
9. Calculate the initial speed (magnitude of the velocity) and direction (angle above the horizontal) for
each of the three simulations discussed in part 8. Put the results from parts 8 and 9 in a table.
V0 θ
Conclusions:
The purpose of the projectile simulation lab was to estimate the trajectory an object would take to undergo a predetermined behavior and by mechanics of kinematics, we were to ascertain the velcocities of the x and y directions to make the object fulfil the desired behavior given initial and final positions as well as acceleration. Before this lab, I was completely confused as to how a
"split-up" kinematic equations were related and afterward I was able to relate them by solving for certain variables and interpolating them into the other equation, much like one of the rocket problems discussed during the course of the semester.
Hooke’s Law and the Simple Harmonic Motion of a Spring
Hooke’s Law and the Simple Harmonic Motion of a Spring
Purpose: To determine the force constant of a spring and to study the motion of a spring and mass
when vibrating under influence of gravity.
Equipment: Spring, masses, weight hanger, meter stick, support stand with clamps, motion detector,
LabPro interface, wire basket.
Introduction: When a spring is stretched a distance x from its equilibrium position, it will exert a restoring
force directly proportional to this distance. We write this restoring force, F, as:
1) F = -kx
where k is the spring constant and depends on the stiffness of the spring. The minus
sign remind us that the direction of the force is opposite to the displacement.
Equation 1 is valid for most springs and is called Hooke’s Law.
If a mass is attached to a spring that is hung vertically, and the mass is pulled down
and released, the spring and the mass will oscillate about the original point of
equilibrium. Using Newton’s second law and some calculus we can show that the
motion is periodic (repeats itself over and over) and has period, T (in sec), given by
2) T =
4
where m is the mass supported by the spring.
table
table clamp
spring
hanging
mass
support rods
π
2
k
m
Procedure:
1. Hang the spring on the support rod, as shown in the diagram, and measure the position of the lower end
of the spring. Place 350 gm mass on the spring and observe its position. Now attach, in turn, masses of
450, 550, 650, 750, 850, 950, 1050 gm and measure how far the spring is stretched for each of these
masses.
2. Make a plot of the downward force applied to the spring (y-axis) versus the displacement of the spring (xaxis). Remembering Equation 1, determine the force constant, k.
3. Start up the Logger Pro software by clicking on its icon in the Physics Apps folder. From the program
click on Open/Mechanics/Hooke’s Law to open the file for this experiment. A graph of linear position
vs time should appear. Place the motion detector on the floor beneath the hanging mass. Place the wire
basket over the motion detector to protect it from any accidentally dropped masses. Once again place the
350 gm mass on the spring and pull the mass downward until the spring has been stretched 10 cm.
Release the mass and observe the subsequent motion. Start collecting data by clicking on the Collect
button. The time scale on your graph should allow for at least five cycles of the motion to be seen. Press
the “x=” button and determine the time for five cycles. From this number calculate the period of motion.
Record your data. Repeat this for the other masses used in part 1. Create a data table which gives
average T and m values.
4. Using the data for the last trial (with m = 1050 g), fit the data to a sinusoidal function using the
Analyze/Curve Fit option. Determine the period and the amplitude from your function. Compare the
period with the value obtained in part 3.
5. Make a plot of T2 (y-axis) vs m (x-axis).
Conclusion:
The whole point of Hooke's Law in this experiment was to understand the conservation of momentum, potential gravitational energy, potential spring energy, and the conservation of energy with regards to projectile motion. Since Hooke's Law is F=-kx where k is the spring constant and x is the displacement of the spring due to compression or extension, it's understood that the force is in the opposite direction of the displacement because of the signs in the equation.
Inelastic Collision
INELASTIC COLLISIONS
Purpose:
To analyze the motion of two low friction carts during an inelastic collision and verify that the law of
conservation of linear momentum is obeyed.
Equipment:
Computer with Logger Pro software, lab pro, motion detector, horizontal track, two carts, 500 g
masses(3), triple beam balance, bubble level
Introduction:
This experiment uses the carts and track as shown in the figure. If we regard the system of the two
carts as an isolated system, the momentum of this system will be conserved. If the two carts have
a perfectly inelastic collision, that is, stick together after the collision, the law of conservation of
momentum says
Pi = Pf
m1v1 + m2v2 = (m1 + m2)V
where v1 and v2 are the velocities before the collision and V is the velocity of the combined mass
after the collision.
Procedure:
1. Set up the apparatus as shown in Figure 1. Use the bubble level to verify that the track is as
level as possible. Record the mass of each cart. Connect the lab pro to the computer and the
motion detector to the lab pro. On the computer, start the Logger Pro software, open the
Mechanics folder and the Graphlab file.
2. First, check to see that the motion detector is working properly by clicking the Collect button to
start collecting data. Move the cart nearest the detector back and forth a few times while
observing the position vs time graph being drawn by the computer. Does it provide a
reasonable graph of the motion of the cart? Remember to be aware of unwanted reflections
caused by objects in between the motion detector and the cart. Also, position the carts so that
their velcro pads are facing each other. This will insure that they will stick together after the
collision.
TABLE
carts
computer
motion
detector
track m1 m2
v13. With the second cart (m2) at rest give the first cart (m1) a moderate push away from the motion
detector and towards m2. Observe the position vs time graph before and after the collision.
What should these graphs look like? Draw an example:
The slope of the position vs. time graph directly before and directly after the collision give the
velocity directly before and directly after the collision. To avoid the problem of dealing with
friction forces (Remember, we are assuming the system is isolated.), we will find the velocity of
the carts at the instant before and after the collision.
Is this a good approximation? Why or why not?
For the velocity before the collision, select a very small range of data points just before the
collision. Avoid the portion of the curve which represents the collision. Choose
Analyze/Linear Fit. Record the slope (velocity) of this line. Repeat for a very small range of
data points just after the collision. Record this slope (velocity) as well.
4. Repeat for two more collisions. Calculate the momentum of the system the instant before and
after the collision for each trial and find the percent difference. Put your results in an Excel data
table. Show sample calculations here:
5. Place an extra 500 g on the second cart and repeat steps 3 and 4. Sketch one representative
graph showing the position vs time for a typical collision. (What do velocity vs. time and
acceleration vs. time look like?6. Remove the 500 g from the second cart and place it on the first cart. Repeat steps 3 and 4.
7. Find the average of all of the percent differences found above. This average represents your
verification of the law of conservation of linear momentum. How well is the law obeyed based
on the results of your experiment? Explain.
8. For each of the nine trials above calculate the kinetic energy of the system before and after the
collision. Find the percent kinetic energy lost during each collision. Put this information in a
separate data table. Show sample calculations here:
9. Do a theoretical calculation for ΔK/K in a perfectly inelastic collision for the three situations:
1. a mass, m, colliding with an identical mass, m, initially at rest.
2. a mass, 2m, colliding with a mass, m, initially at rest.
3. a mass, m, colliding with a mass, 2m, initially at rest.
Conclusions:
I learned that when a perfectly inelastic collision occurs, momentum is conserved. When momentum is conserved, the change in momentum is 0. For this to occur, the initial momentum must be equal to the final momentum [m1*v1 = (m1+m2)*v2]. The only way this is possible is for the velocity of the combined masses must decrease to compensate for the additional weight. If momentum is conserved, there must have been some ΔK because the velocity is going to be squared and therefore if momentum is negative, the resulting velocity had to be negative which is negated by squaring the velocity, therefore kinetic energy has to always be positive (that does not mean that you can't have a negative ΔK because ΔK = K(final)-K(initial)).
Human Power
Objective: To determine the power output of a person.
Equipment: Two meter sticks, stopwatch, kilogram bathroom scale
Power is defined to be the rate at which work is done or equivalently, the rate at which energy is converted from one form to another. In this experiment you will do some work by climbing from the first floor of the science building to the second floor. By measuring the vertical height climbed and knowing your mass, the change in your gravitational potential energy can be found with the formula: ∆ PE = mgh (where m is the mass, g the acceleration of gravity, and h is the vertical height gained) Your power output can be determined by Power = ∆ PE/∆t (where ∆t is the time to climb the vertical height h.)
Procedure:
1. Determine your mass by weighing on the kilogram bathroom scale. Record your mass in kg..
2. Measure the vertical distance between the ground floor and the second floor for the science building. This can most easily be done by using two meter long meter sticks held end to end in the stairwell at the west end of the building. Make a careful sketch of the stairwell area that explains the method used to determine this height.
3. Designate a record keeper and a timer for the class. At the command of the timing person, run or walk (whatever you feel comfortable doing) up the stairs from the ground floor to the second floor. Be sure that your name and time are recorded by the record keeper.
4. After everyone in the class has completed one trip up the stairs, repeat for one more trial.
5. Return to class and calculate your personal power output in watts using the data collected from each of your climbing trip up the stairs. Obtain the average power output from the two trials.
6. Put your average power on the board and then calculate the average power for the entire class once everyone has reported their numbers on the board.
7. Determine your average power output in units of horsepower.
Questions:
Is it okay to use your hands and arms on the hand-railing to assist you in your climb up the stairs? Explain why or why not.
No, it is not acceptable to use your hands and arms to propel yourself up the flight of stairs because then it is not your power alone that is allowing your vertical position displacement to occur. Although it is true that it takes energy to pull yourself up, you are still transferring kinetic energy into potential energy by contacting the rail of the stairwell.
Discuss some of the problems with the accuracy of this experiment.
This experiment is not fully accurate in that the recording of the change in time by stopwatch controlled by a human has the potential to be off due to observation, optical illusion, and preconceived notions of space-time orientation.
Equipment: Two meter sticks, stopwatch, kilogram bathroom scale
Power is defined to be the rate at which work is done or equivalently, the rate at which energy is converted from one form to another. In this experiment you will do some work by climbing from the first floor of the science building to the second floor. By measuring the vertical height climbed and knowing your mass, the change in your gravitational potential energy can be found with the formula: ∆ PE = mgh (where m is the mass, g the acceleration of gravity, and h is the vertical height gained) Your power output can be determined by Power = ∆ PE/∆t (where ∆t is the time to climb the vertical height h.)
Procedure:
1. Determine your mass by weighing on the kilogram bathroom scale. Record your mass in kg..
2. Measure the vertical distance between the ground floor and the second floor for the science building. This can most easily be done by using two meter long meter sticks held end to end in the stairwell at the west end of the building. Make a careful sketch of the stairwell area that explains the method used to determine this height.
3. Designate a record keeper and a timer for the class. At the command of the timing person, run or walk (whatever you feel comfortable doing) up the stairs from the ground floor to the second floor. Be sure that your name and time are recorded by the record keeper.
4. After everyone in the class has completed one trip up the stairs, repeat for one more trial.
5. Return to class and calculate your personal power output in watts using the data collected from each of your climbing trip up the stairs. Obtain the average power output from the two trials.
6. Put your average power on the board and then calculate the average power for the entire class once everyone has reported their numbers on the board.
7. Determine your average power output in units of horsepower.
Questions:
Is it okay to use your hands and arms on the hand-railing to assist you in your climb up the stairs? Explain why or why not.
No, it is not acceptable to use your hands and arms to propel yourself up the flight of stairs because then it is not your power alone that is allowing your vertical position displacement to occur. Although it is true that it takes energy to pull yourself up, you are still transferring kinetic energy into potential energy by contacting the rail of the stairwell.
Discuss some of the problems with the accuracy of this experiment.
This experiment is not fully accurate in that the recording of the change in time by stopwatch controlled by a human has the potential to be off due to observation, optical illusion, and preconceived notions of space-time orientation.
Acceleration of Gravity
Objectives:
- To determine the acceleration of gravity for a freely falling object.
- To gain experience using the computer as a data collector.
Materials:
- Windows based computer
- LabPro interface
- LoggerPro software
- Motion detector
- Rubber ball
- Wire basket
Procedure:
- Gather the necessary materials and then proceed to connect the LabPro to the computer and the motion detector to the DIG/SONIC2 port on the LabPro. Turn on the computer and load the LoggerPro software by double clicking on its icon located within the PhysicsApps folder. A file named graphlab will be used to set up the computer for collecting the data needed for this experiment. To open this file, select File, Open, and then open the mechanics folder. When this folder opens, open the graphlab file.
- Upon opening the file, you should see a blank position vs. time graph. The y-axis (position axis) should be from 0m to 4m while the x-axis (time axis) should be from 0s to 4s. These values can be changed by pointing the mouse at the upper and lower limits on either scale and clicking on the number to be changed. Enter in the desired numbers and push the Enter key.
- Place the motion detector on the floor, facing upward, and place the wire basket (inverted) over the motion detector to protection the detector from the impact of the falling ball. Check to see that the motion detector is working properly by holding the rubber ball about 1m above the detector. Click the Collect button to begin taking data and then move your hand up and down a few times in order to verify that the graph of the motion is consistent with the actual motion of your hand. After 4s the computer will stop taking data and will be ready for another trial. If the equipment does not seem to be working properly, seek assistance from the instructor.
- Give the ball a gentle toss straight up from a point about 1 meter above the detector. The ball should rise 1 or 2 m above where your hand released the ball. Ideally your toss should result in the ball going straight up and down directly above the detector. It will take a few tries to perfect your toss. Be aware of what your hands are doing after the toss as they may interfere with the path of the ultrasonic waves as they travel from the detector to the ball and back. Take your time and practice until you can get a position-time graph that has a nice parabolic shape.
- Select the data in the interval that corresponds to the ball in freefall by clicking and dragging the mouse across the parabolic portion of the graph. Release the mouse button at the end of this data range. Any later data analysis done by the program will use only the data from this range. Choose Analyze/Curve Fit from the menu at the top of the window. Choose a quadratic function [t^2+ b t + c] and let the computer find the values of a, b, and c that best fit the data. If the fitted curve matches the data curve, select Try Fit. Click on OK if the fit looks good. A box should appear on the graph that contains the values of a, b, and c. Use unit analysis to give a physical interpretation and the proper units for each of these quantities. Find the acceleration, g_exp, of the ball from this data and calculate the percent difference between this value and the accepted value, g_acc, (9.80 m/s2).
- Look at a graph of velocity vs time for this motion by double clicking on the y-axis label and select “velocity” and deselect “position”. Examine this graph carefully. Explain (relate them to the actual motion of the ball) the regions where the velocity is negative, positive, and where it reaches zero. Determine the slope from a linear curve fit to the data. Use unit analysis to find the values of m and b that best fit the data. Give a physical interpretation and the proper units for each of these quantities. Find the acceleration of the ball, g_exp, from this data and calculate the percent difference between this value and the accepted value, g_acc. Put together an excel spreadsheet for your data. Finally, select Experiment, then Store Latest Run to prepare for the next trial.
- Repeat steps 4 - 6 for at least five more trials. Obtain an average value for the acceleration of gravity and a percent difference between this value and the accepted value.
- Obtain a printout of one representative graph for position vs time and velocity vs. time and include this in your lab report. Put both graphs on a single page.
Conclusion:
The purpose of this lab was to discover through observation and measurement the constant we know to be gravity (g) of roughly -9.8 m/s^2. Human error is the source of any discrepancies in data. Considering I worked by myself, I do not think I did so poorly. Shout out to Tito for helping me set it up.
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