PHYS 31, SCU Physics Dept.

, Spring 2024 Name:

Lab Section: Lab Partners:

Lab 6: Friction
There are two types of friction: kinetic and static. Kinetic friction is the friction between surfaces in relative
motion. When an object slides across another surface, microscopic bumps and defects tend to impede and resist the
motion. Experimentally, it is observed that the force of kinetic friction is proportional to the normal force FN acting
between the surfaces in contact with one another: if you increase the normal force, the surfaces are crushed more
together, increasing the effective contact area and thus increasing the frictional force. Mathematically, we can write
the force of kinetic friction as
Fk = µk FN (1)
The coefficient of kinetic friction µk is a dimensionless quantity that depends on the properties of the two surfaces.
µk ranges from 0.01 for very smooth surfaces to 1.5 for very rough surfaces.
Static friction describes the frictional forces between the surfaces of two objects that are at rest with respect
to each other. The static friction between the two surfaces is described by the coefficient of static friction µs .
Experimentally, is it found that the maximum value for the static frictional force is proportional to the normal force
between the two surfaces. Thus, the static frictional force Fs is

Fs ≤ µs FN (2)
Since the objects are at rest with one another,molecular bonds are easier to form making the object harder to
move and so greater force is needed to start motion when to keep the object in motion. Therefore µs is generally
greater than µk . Graphically, this is shown in Figure 1: As you increase the applied force F , the static friction force
increases linearly until the applied force F equals µs FN . After this point the object “breaks away” and the friction
force falls to the kinetic friction value.

fr

fr = μsFN

kinetic
static

0 F

no
sliding
motion

Figure 1: (a) Force of friction (fr) as a function of an external force (F) applied to an object that is initially at rest.

Experimental Objectives
The purpose of this lab is to determine the relationship between frictional forces and the normal force on an
object, to calculate the kinetic and static coefficients of friction between a plastic cart and paper, and gain a
practical understanding of static and kinetic friction.

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Part 1: Static Friction
Through force measurements using the force sensor we will determine the static coefficient of friction µs .
Connect the force sensor to the plastic friction cart. With no force acting on the sensor, press the “Tare” (zero)
button before taking any measurements. Open the “Force vs. time” graph to view the applied force. Remember
to always check the zero of the sensor before taking measurements and reset it if needed.

1. Place 500 g in the cart. Slowly and carefully pull the cart as it rests on the paper while monitoring the force
value on the computer. Make sure the string and the force sensor are parallel to the table at all
times.
Sketch the force vs time graph below. Identify the regions of static and kinetic friction on your graph and
record the minimum force needed to the cart to start moving.

Fmin =

2. Repeat this procedure (except for the sketching) with 4 different additional masses (in 100 gram increments)
in the cart (keeping the initial 500 g in the cart). In a table, record the total mass, calculated normal force
and minimum force needed for the cart to start moving for each of the 5 different masses.

3. Make a plot of the minimum force required for the cart to move versus the normal force of the cart. Draw a line
of best fit through your data points. Calculate the slope and explain here what it represents (Hint: Equation
2).

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 4. Next, you will study how the frictional force behaves when the applied force Fpull is not parallel to the surface.
With 500g in the cart, pull on it at an angle 45◦ below the horizontal.
Record the magnitude of the minimum force needed to move the cart from rest. Sketch a free body diagram
and then, using your data, calculate the normal force (FN ) acting on the cart, the horizontal component of
Fpull , and µs .

Fpull = FN = Fpullx =
µs = .

How does this friction coefficient compare with the one calculated previously? What did you expect?

Part 2: Kinetic Friction

To study the kinetic friction and calculate the coefficient of kinetic friction, we will use the pulley system shown
in Figure 2(a). Looking at the free body diagrams of our system (Figure 2(b)), we can write Newton’s Second Law
for the two masses as
m1 a = T − f r (3)

m2 a = m2 g − T (4)
Here we have assumed that the accelerations of the two masses are the same by neglecting any frictional effects on
the pulley, making the tension in the string uniform. The kinetic frictional force f r is given by

f r = µk FN = µk m1 g (5)

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 m1 a
FN

T a
T
fr m1 m2
a
m2
W1 W2

(a) (b)

Figure 2: (a) Pulley system used to calculate µk . (b) Free body diagrams for the cart-pulley system. Wi is the
weight of the object and “fr” is the frictional force.

1. Show that Eqs. 3-5 can be combined to give this expression for the (common) acceleration of the masses:

(m2 − µk m1 )g
a= (6)
m1 + m2

2. Attach the friction cart to the hanging mass (m2 ) that’s strung over a pulley. Set the hanging mass to 50 g
and put 100 g in the plastic cart (for stability). Place the motion sensor on the table such that it can record
the motion of the friction cart. You will release the system from rest and, using the motion sensor, measure
the velocity of the cart as a function of time.

3. Determine the acceleration of the mass system from the velocity graph. Use this experimental acceleration,
along with its theoretical expression (Eqn. 6), to calculate µk . Perform at least 2 trials to verify the consistency
of your measurements and calculate the average coefficient of friction based on the average acceleration.
µkave =

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4. A different experimental approach will now be used to determine the coefficient of kinetic friction: cart moving
with a constant velocity (a = 0). This allows us to write a simple expression relating the friction force and the
applied pull force:
Fpull = µk mg. (7)

Monitor the velocity of the cart (using the motion sensor) and the force value simultaneously. Practice pulling
the cart, with 100g in it, at a constant velocity and, when happy with the result, record the force value needed
to pull the cart at a constant velocity. Repeat this with 200g in the cart. Make a data table consisting of the
weight of the cart, the applied pull force and calculated coefficient of kinetic friction.

Calculate the average coefficient of kinetic friction and compare with the value obtained previously. What are
some sources of error?
µkave =

Compare your average coefficient of kinetic friction with your average coefficient of static friction. Did you
expect these experimental findings? Explain.