Experiment 5: Inclines and Circular Motion
Part 1: Coefficient of friction of an incline.
You will find μs for a block on a board. The board is attached by a hinge to a base with a large
protractor on it. The board is tipped steeper and steeper until the maximum friction is reached, then
the block slides away. This angle is recorded. The maximum friction force and corresponding
normal force are then calculated the angle. Since friction is at its maximum, f < μsn becomes f = μsn
and μs is calculated from this.
1. The board and block need to be smooth and fairly clean. Please do not put tape or pencil marks
on them.
2. Measure the mass of the wooden block. Calculate its weight.
3. Place the block on the board. Gently tip the board steeper and
steeper. Record the angle where the block slides.
4. Repeat several times to determine a range of uncertainty.
5. Calculate the coefficient of friction which corresponds to your average angle:
a. Draw a free body diagram of the block on the incline, just before it slid.
b. Resolve the forces into components parallel and perpendicular to the incline.
c. Use ΣFx = 0 and ΣFy = 0 to obtain the friction force and the normal force from the weight of
the block.
d. Solve for μ from f = μsn.
(Don't expect it to necessarily match the textbook value. μ can vary due to several factors such as
the type of wood, smoothness, and so forth.)
Part 2: Centripetal Force
Your objective is to verify the formula for centripetal force. A
rubber stopper, mass m, is at one end of a string, and a
counterweight, mass m', is at the other. In between, the string passes
through a tube which you hold while twirling the stopper in a circle.
You know the centripetal force on the stopper from the
counterweight hanging on the string: Gravity pulls on the
counterweight, the counterweight pulls on the string, and the string
pulls on the stopper. (This assumes that no other force is added to the string as it passes through the
tube.) You will separately find mv2/r to see if it matches the known force: You get m by putting the
stopper on a balance. You get r by measuring the apparatus with a meter stick. You get v by
counting the number of revolutions the stopper makes in a minute.
Procedure: Use at least 150 grams for m'. Twirl the stopper in a horizontal circle above your head,
at the right speed so that the string does not slip up or down through the tube. A piece of tape on the
string, maybe half an inch below the tube, makes it easier to watch its movement. Do not interfere
with free movement of the string: Touch only the tube, not the string itself, and do not let the tape
touch the bottom of the tube. Because of friction, there will be a range of speeds where the tape
stays put. Use the slowest speed where the tape does not begin to sink. It is also important that you
move your hand in as small a circle as possible. Twirl it from the wrist, not the elbow.
After some practice, count N, the number of revolutions the stopper makes in one minute. Then, lay
the apparatus on the table with the same size gap between the tube and the tape, and measure r, the
radius of the path of the stopper's center. Record the masses of the stopper, m, and the
counterweight, m'.
Calculations: In your calculations, have all distances in meters, mass in kilograms, and time in
seconds. This will make force come out in newtons.
Compute the stopper's speed: The distance covered during each revolution is the circumference of
the circular path, 2πr. So, in N revolutions, the total distance covered is N(2πr). Speed is distance ÷
time; calculate the speed from the fact that the stopper covers this much distance in 60 sec.
Compute the quantity mv2/r. Also, compute the weight of m', which equals the centripetal force.
The value from the formula has a 20% uncertainty; the weight of the counterweight has an
uncertainty which is quite small. If your two values do not agree, and you've made no mistakes in
your calculations, then your twirler probably hasn't quite perfected his or her technique. Ask the
instructor for suggestions, and double-check your data.
Did you succeed in verifying that Fc = m v2/r?
PHY 121
Report on Experiment 5: Inclines and Circular Motion
Part 1:
mass of block: _____________
angle of friction: minimum angle = __________ maximum angle = __________
θ = __________ + __________
Show calculation of coefficient of friction:
Part 2:
m=
m' =
N=
r=
Compute v of cork:
mv2 =
r
m'g =