Download Lab 7 Work Energy

Lab 7 Work and Kinetic Energy!
Objective
We will compare results obtained from Newton’s second law to results obtained using the workenergy theorem.
Equipment
Cart, track, smart pulley, force sensor, motion sensor, masses and string.
Description
In this lab we will measure the acceleration due to gravity using the following system of connected
masses.
cart
morion
sensor
vi
vf
∆x
hanging mass
vi
∆x
vf
Newton’s Law
Using Newton’s second law, the acceleration and tension are given by the following. We can find
the acceleration due to gravity by measuring the acceleration of the objects.
a=
m
g
M +m
⇒ g =a
M +m
m
Work-Energy Theorem
The work-energy theorem states the total energy put into the system of objects is manifested in
the kinetic energy change of the system.
Wtotal = ΔK
The energy put into the system comes from gravity acting on the hanging mass. This is the left
side of the equation below. The change in the kinetic energy is shown on the right.
1
1
(M + m) 2
mgΔx = M(v f2 − vi2 ) + m(v f2 − vi2 ) ⇒ g =
(v f − vi2 )
2
2
2mΔx
We can find the acceleration due to gravity by measuring the displacement and the initial and final
speeds.
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Experiment
Measure the following masses. Use 50 g for the hanging mass.
cart (kg)
hanging mass (kg)
Make sure the track is level by placing the cart at various locations to see if it moves by itself.
Also, make sure the string from the cart to the pulley is horizontal. Set the motion sensor to
collect data at 50 Hz. Set the motion sensor to use the narrow beam.
Raise the hanging mass as high as possible, start the data recording, then release until the
hanging mass hits the floor.
If your velocity data is noisy (not smooth and linear), rinse and repeat.
Analysis: Newton’s Second Law
Use the slope of the velocity data to find the acceleration of the system while falling. Use this
acceleration to find the value of the acceleration due to gravity. Compare your result to the
expected value.
Analysis: Work-Energy Theorem
Select two times in your data as the initial and final states. The initial time should be just after
release and the final time should be before the hanging weight hits the ground. Record the
following values at these two times.
initial position (m) final position (m) initial speed (m/s) final speed (m/s)
Calculate the acceleration due to gravity using the work-energy theorem. Compare your result to
the expected value.
Analysis: Energy Loss
Calculate the amount of energy that is lost throughout this process. The energy loss is defined as
the total work done to the system (energy in) minus the kinetic energy gained from this work
(energy out). Where did the lost energy go? List the ways that this experiment can lose energy?
Conclusion
Present your two experimental values of “g” and their relative errors.
Do the result from the two experiments match?
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