Download Lab 6: Work-Energy Theorem

LAB 6
Work–Energy Theorem
OBJECTIVES
1. To study the interplay between the work done on an object and its change in kinetic
energy.
2. Predict and compare how the work done on an object changes its kinetic energy.
EQUIPMENT
Dynamics track, force sensor, photogate pulley sensor, photogate timers, simple
pendulum, supports, masses, steel balls, string.
THEORY
The Work-Energy theorem states that if net force is applied to an object a distance, the
work done changes the kinetic energy of the object such that
W  F  d  K  K 2  K1  21 mv 22  21 mv12
PROCEDURE
Part 1: Work-Energy Theorem applied to a Cart-Mass System
a. Hang a mass over a pulley to provide a constant force to the cart. How big is that
force? Hint: it’s not equal to mhangingg. Predict the work WT done on the cart by the
string using the fact that it traveled a distance d.
b. Using a motion sensor (set Capstone to measure velocity to 3 significant figures) to
measure the cart’s maximum velocity. Repeat ten times, determine vexpt and σv, and
record your data a table. At this point, you should measure the mass of the cart and
hanging mass.
c. From the velocity vexpt, determine the change in kinetic energy ∆Kexpt of the cart.
d. Propagate the velocity error σv to the change in kinetic energy error σK using σK =
2∆Kexpt σv / vexpt. Plot a 2 σK-distribution curve for your data.
e. Is the predicted work WT consistent with a 2 σK-distribution curve from your data?
That is, are the quantities WT and ∆Kexpt as predicted by the work-energy theorem?
Explain.
f. The work done by friction W f was not accounted for in this experiment. Here is the
way to estimate this work.
 Give the cart a light push while recording its speed and position (no hanging
mass).
 Measure the deceleration due to friction and then calculate the force of friction
using N2L.
 Now estimate the work done by friction W f in the original experiment and
recalculate the net work done on the cart from (1a).
 Does the net work done Wnet,thy = W T – W f on the cart fall within the 2 σKdistribution curve from your data?
Part 2: Work-Energy Theorem applied to the Simple Pendulum with a Peg
When the bob of a simple pendulum of length L is released from rest from a
horizontal position, it swings down and the string will hit a thin peg located a
distance d below the support. Using the work-energy theorem, predict the
minimum length of d such that the bob just swings completely around in a
circle.
a. Experimentally locate the peg’s location such that the bob is able to just
swings completely around in a circle – this is your measured peg’s
location. Have everyone in your lab group measure this once and
average these values to determine dexpt.
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b. Predicting dthy using the Work-Energy theorem
 Write an expression for the net work done on the pendulum’s bob such that the
work done on the bob from point A is able to swing completely around in a circle
at point C. Hint: W AB increases the ∆K while W BC decreases ∆K.
 Using the centripetal acceleration from N2L, predict the minimum velocity vthy
required for the bob to just swing completely around in a circle. In other words,
apply Newton’s condition for circular motion at point C.
 Combine the calculations from (2b) and (2c) using the work-energy theorem,
and predict the minimum value of dthy.
c. Compare the experimental measured dexpt with the predicted dthy using a percent
difference. How do they compare? Is the work-energy theorem consistent within
experimental errors? Explain.
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