Download Experiment 5U: Kinetic Friction

September 2016
Experiment 5U: Kinetic Friction
Purpose
The purpose of this experiment is to study how kinetic friction depends on the type of surface
and the weight of the sliding object and to calculate the coefficient of kinetic friction μk.
Apparatus
Track with feet and end stop, super pulley with clamp, photogate head, photogate bracket,
friction block with string, PASCO 850 universal interface, mass and hanger set, level, dial
balance (on the side).
Theory
If an object, resting on a horizontal surface is pulled by a horizontal force F (Fig 1), the
surface will exert a force of friction fs (force of static friction) which exactly balances F until F
reaches a critical value Fcrit. Fcrit is the maximum value of the static force of friction fmax.
Until this point, the net force is zero and the object remains at rest. Above this point the net force
is not zero and the object will move. Experiments show that fmax is proportional to the normal
force N:
fmax = Fcrit = s N = s Mg
where s is the coefficient of static friction, N is the normal force = Mg.
Once the object is moving, the frictional force is called the force of kinetic friction fk:
f k = k N
where k is the coefficient of kinetic friction. The force of kinetic friction is constant regardless
of the speed of the object. If the frictional force fk is less than fmax, the motion can still be
maintained even though the force F is less than Fcrit.
27a
Experiment 5U
In this experiment, a block of mass M is placed on a level surface. A string connects the block to
a mass m hanging over a pulley. Gravity exerts a force on mass m which is transferred to block
M through the tension in the string. When released, the block will slide across the surface as the
hanging mass falls. Both masses will be moving with the same acceleration a. Figure 2 shows
the free-body diagrams for both masses.
Applying Newton’s Second Law:
fk
For m:
mg – T = ma
(1)
For M:
T – fk = Ma
N = Mg
fk = μkN
(2)
(3)
(4)
Figure 2
By combining equations (1) & (2), we
can solve for fk :
fk = mg – (M + m)a
(5)
We can find the acceleration due to gravity by measuring v and t. A graph of velocity versus
time produces a straight line. Its slope is Δv/Δt = the acceleration a. Inserting this value in
Equation (5), and the values of g, m and M, we can calculate fk.
Preliminary Setup
1. Install the feet on the track and level it.
2. Mount the pulley with clamp at one end of the track as
shown in Figure 3.
3. Mount the end stop a short distance before the pulley.
4. Put the photogate on the photogate bracket and mount
the bracket on the track so it is horizontal. (It is shown
tipped up slightly for clarity in Figure 3 but yours should
be completely flat.)
5. Position the bracket and photogate so that the spokes of
the pulley will interrupt the photogate beam as the pulley turns.
6. Connect the interface to the computer and turn them both on. Plug the photogate into digital
input 1 of the 850 Universal Interface.
7. Open the “Exp5U Kinetic Friction” Capstone file on your desktop.
27b
Experiment 5U
Procedure
1. Measure the mass of the friction block and record it as Mblock in Table 1. (Include units.)
2. Place the friction block on the track with the wide wood side facing down. Push the other end
of the string through the hole of the end stop and attach a hanger to it. Put the string over the
pulley. Move the block near the pulley and adjust the pulley height so the string is parallel to the
track.
3. Put enough mass on the hanger so that the friction block will begin to slide on the track
without an initial push.
4. Pull the block back until the hanging mass is just below the pulley. Note the position of the
block so you can start each trial at the same place.
5. Click “Record” to begin data recording and then release the block. Click “Stop” to end data
recording before the block reaches the end stop. Try to catch the block with your hand before it
strikes the end stop.
6. You will see a graph of Speed vs Time on your computer. If the graph is a straight line, then
click the “Scale to Fit” icon (the icon on the top left) on the graph toolbar. If the graph is NOT a
straight line, then add a little more mass to the hanger and redo the run. Record the total hanging
mass m in Table 1 (don't forget to include the mass of the hanger).
7. Click the black triangle by the “Curve Fit” icon (the icon on the top right) and select “Linear”.
The slope of the Speed vs Time plot is the acceleration of the block. Enter it in the a1 column of
Table 1.
8. Repeat the run once more, entering the acceleration in the a2 column of Table 1. The pulley
may need to be readjusted so the string is still parallel to the track. Enter this result as a2.
9. Calculate aaverage, the average of a1 and a2, and enter it in Table 1.
Table 1
Wood
side
down
Felt
side
down
M
Mblock
Mextra
m
(block + extra)
(units?) (units?)
(units?)
(units?)
-0.05
0.1
-0.05
0.1
27c
a1
(units?)
a2
(units?)
aaverage
(units?)
Experiment 5U
10. Add an extra 50 g of mass on top of the friction block and repeat steps 3-9.
11. Replace the 50 g mass with a 100 g mass and repeat the steps 3-9.
12. Repeat steps 2-11 but with the wide felt side of the friction block facing down on the track.
Before You Leave:
Exit the program.
DO NOT SAVE YOUR CHANGES. Click “Discard” when the window pops up.
Lab Report
Complete Table 2 using data from Table 1. Use Equation (5) to calculate fk and then
Equation (4) to calculate μk. Remember to label quantities with the correct units.
Table 2
M
(units?)
m
(units?)
aaverage
(units?)
fk
(units?)
N
(units?)
μk
(units?)
avg μk
(units?)
Wood
side
down
Felt
side
down
Question #1 What happens to the friction force between a sliding object and its surface if the
objects weight increases? Why?
Question #2
A block of mass m1 = 2 kg on a horizontal
surface is connected to a mass m2 = 4 kg that
hangs vertically as shown in the figure. The
two blocks are connected by a string of
negligible mass passing over a frictionless
pulley. The coefficient of kinetic friction
between m1 and the horizontal surface is 0.27.
Equations (1)-(5) may help you solve these
questions.
a) What is the acceleration of the hanging
mass?
b) Determine the tension in the cord.
27d