Download Work –Energy

Work – Energy
Introduction to Physics 105
6/98
Name _____________________Conf________
Partner’s Name ________________________
Equipment
cart, track, hanger and masses, photogate, card, cushion, pulley, meter stick, lab
jack, spring, lab stand, string
Purpose: Investigate work and energy relationships by doing three different
experiments.
Data:
Show your work in the Data and Calculations space. Attach additional work
and graphs to lab. Include all steps, labels and remember your units.
Definitions
Gravitational Potential Energy = mgh
Kinetic Energy 
1 2
mv
2
Potential Energy of a Spring 
Percent Difference 
1 2
kx
2
xy
 100
y
Total Mechanical Energy, E
E = PE + KE
Part 1
m
g
h
m
v
k
x
x
y
mass
acceleration due to gravity
height above reference level
mass
speed
spring constant
spring stretch
second value
first value(most reliable value)
PE = Potential Energy
KE = Kinetic Energy
Gravitational Potential Energy
Purpose
In this experiment you will compare the gravitational potential energy stored in a
hanging mass to the kinetic energy that the system receives.
Procedure
1.
Set up the equipment as shown in Figure 1 on a level track.
cart
photogate
timer
M
card
20 g
track
mass - m
cushion
Figure 1
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h
Work – Energy
6/98
2.
Place a total (mass + hanger) of 20 g on a the end of a string . This is mhanger.
Record in the space below.
3.
Determine the mass of the cart and the card. This is mcart. Record below.
4.
Determine the mass of the system. Msystem = mcart + mhanger. Record below.
5.
Pull the cart back so that the hanging mass is approximately 30 cm above the
cushion. Measure the exact height to at least one decimal place. This is height h.
Record below.
6.
Compute the initial potential energy of the mass relative to the cushion.
Remember : PE = mhanger g h Show calculations and record below.
7.
Let the mass drop and measure the final velocity of the system using a photogate
timer (velocity = [card length]/time). Compute the final kinetic energy of the
system, using Msystem. The cart should go through the photogate just after the mass
hits the cushion. Show calculations and record below.
8.
Calculate the percent difference between the initial potential energy of the mass
(mhanger) and the final kinetic energy of the system (Msystem).
9.
Is total mechanical energy conserved? If not do your results suggest that energy
was lost to friction? Explain.
Data and Calculations
mcart=
(kg)
Msystem=mcart+mhanger=
h=
PE = mhanger g h =
Card length =
(kg)
(meter)
(Joule)
Time =
(sec)
Speed =
(m/s)
1
2
KE  mv2 =
% difference =
Clark College Physics Dept
(meter)
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(Joule)
Work – Energy
Part 2
6/98
Potential and Kinetic Energy
Purpose
In this experiment you will compare the gravitational potential energy stored in the
cart to the kinetic energy that the cart receives by changing heights.
Procedure
1.
Set up the equipment as shown in Figure 2, on a inclined track. Note that the
string from part 1 has been removed. Measure the height of the cart above the
table at positions 1 and 2. h1 = _______ h2 = ________
Photogate
timer
1
2
Figure 2
2. Measure the mass of the cart and compute the potential energy (PE) of the cart at
each of the two positions. Clearly label data and show calculations here.
Position 1
Position 2
PE=M g h (J)
1
KE  mv2 (J)
2
Total Energy (J)
3.
Place the cart at position 1 and release it from rest. Use the photogate timer to
calculate the velocity of the cart at position 2. Remember : v = x / t, where x = length of
the card and t = time from the photogate.
Position 1
Position 2
*********
Time, t(s)
Card length, x (m)
*********
0.0
Speed, x/t (m/s)
1
4.
What is the kinetic energy KE  mv2 of the cart at positions 1 and 2? Record in
the table above.
2
5.
Calculate the TOTAL mechanical energy, E = KE + PE of the cart at positions 1
and 2, and record in the table above. Is total mechanical energy conserved? Explain.
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Work – Energy
Part 3
6/98
Stored Energy
Purpose
In this experiment you will compare the potential energy stored in a spring to the
kinetic energy that the cart receives when pulled by the spring.
Procedure
1.
Find the spring constant as explained below.
Set the spring in the lab stand as shown.
Measure the spring’s initial length (L0)
when no force is applied.
Apply a force of 1.96 N to the spring by spring
hanging a 200 g mass on the end of the
spring.
L0 =
cm
Measure the length of the stretched spring.
Calculate the stretch (L – L0) for this
force.
Put your values in the table below.
Force (N)
Lo (m)
Figure 3
Length (m)
Stretch (L-Lo
For an ideal spring the stretch is directly proportional to the applied force. That is
F = k(stretch)= kx.
This relation between stretch and force is called Hooke's Law. The spring
constant (k) can be calculated by dividing the force by the stretch. Do this to
calculate k.
k=F/x=________________
Spring Constant, k=_____________________
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Work – Energy
2.
6/98
Make sure that the track is level. Place a cart on the track and attached it to a
spring as shown. Make sure that the photogate timer is to the right of the card
when the spring is unstretched and that there is enough string between the end of
the track and the spring so the cart can easily glide through the photogate after the
spring gets to its unstretched position. Pull the cart back stretching the spring.
Measure the total spring stretch, x.
cart
M
photogate
timer
card
track
30 cm of
string
stretched spring
Figure 4
3.
x=
4.
Calculate the potential energy stored in the spring when it is stretched.
(m)
k=
(N/m) Spring PE  1 kx 2
2
PE=
(J)
Position the photogate timer so you can measure the velocity of the cart right after
the spring becomes unstretched.
Unstretched position
Time, t (s)
Card length, x (m)
Speed, x/t (m/s)
5.
Calculate the kinetic energy of the cart.
1
KE  mv2
2
6.
Unstretched position
(J)
Compare the initial potential energy stored in the spring with the kinetic energy of
the cart.
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Work – Energy
6/98
Questions
1.
If the photogate timer ran slow. That is, measured too short a time, would the
kinetic energy measured using the timer be too high or too low?
2.
If there were friction in Part 3, would the potential energy be greater than or less
than the kinetic energy?
Clark College Physics Dept
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