Lesson 12: The Force of Friction

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Consult not your fears but your hopes and dreams. Think not about your frustrations, but about your unfulfilled potential. Concern yourself not with what you tried and failed in, but with what is still possible for you to do.

Pope John XXIII

Friction is a force that opposes motion. It works to slow down moving objects, and to prevent stationary objects from moving in the first place. Friction is caused by bumps on the surfaces of objects that get caught as they are pulled across other surfaces.

When we look at a magnified view of the surfaces of the box and the ground, we can see that they are actually quite rough. When the box is given a push in any direction, the two surfaces catch on each other and the box will slow down until it stops.

Reducing Friction

Friction is often a nuisance because it converts kinetic energy (motion) into heat; just try rubbing your hands together very rapidly for a few seconds. There are several things that can be done to reduce the amount of friction acting on surfaces:

1. Smooth surfaces offer much less friction; consider a play ground slide or the top of a shuffleboard table.
2. Using oil to lubricate the surfaces allows them to slide along each other more easily.
3. Rolling an object across another causes much less friction than sliding.
4. Friction with the air, or air resistance, can be reduced by streamlining the shape of the object.

Kinetic Friction

There are two kinds of friction that we need to consider: kinetic friction and static friction.

Kinetic friction occurs when one object is sliding across the other. Examples of kinetic friction include pulling a toboggan across the snow, pushing a box across the floor, or slamming on the brakes of a car that does not have an antilock braking system and skidding to a stop. In each of these situations, friction slows, or stops, an object by converting the energy of motion into heat energy.

Disc brakes on modern cars use friction to slow the car down. A metal disc, or rotor, passes through a set of brake pads. When the driver steps on the brake pedal, hydraulic pressure causes the brake pads to pinch the rotor. Friction between the brake pads and the rotor slows the car down by converting the car’s kinetic energy into heat. Braking systems in some hybrid cars convert kinetic energy into chemical energy that is stored in batteries. This stored energy can be used later to move the car with an electric engine.

Two things will affect the amount of friction acting – the weight of the object and the actual surfaces that are in contact. There will be much more friction acting between Velcro and carpet than between waxed skis and snow. We need to account for both of these factors mathematically.

Equation for Kinetic Friction

Where,

= the force of friction (N)
= the normal force (N)
= the coefficient of kinetic friction (no units)

We use the Greek letter m u (symbol μ pronounced me-ew) to symbolize the coefficient of kinetic friction. This value generally varies between 0 and 1. If there is no friction acting between surfaces, = 0. If there is a lot of friction acting, then will be much closer to 1. Like pi (π), µ is also a unitless quantity; we usually refer to such quantities as proportionality constants.

Example 1

What is the force of friction () acting on a 20 kg box that is being pushed across the floor at a constant speed if the coefficient of kinetic friction (μ_k) between the two objects is 0.35?

Since friction opposes motion, the force of friction and the direction of motion must be in opposite directions; see diagram.

Given:

= 0.35

g = 9.8 N/kg

Required:

F_f = ?

Solution:

The box is on a horizontal surface and FN and Fg are the only two vertical forces acting, so we know that they must be equal.

Therefore,

F_N = F_g
F_N = mg
F_N = (20 kg)(9.8 N/kg)
F_N = 196 N
F_f = F_N
F_f = (0.35)(196 N)
F_f = 68.6 N
The force of friction between the box and the floor is 68.6 N .

Static Friction

Static friction acts up until the point when the object begins to move, the point at which kinetic friction begins acting. In order to start an object moving, you must first overcome static friction. Generally speaking, it takes more force to start an object moving than it does to keep it moving. This is why the coefficient of static friction for two surfaces is generally larger than the coefficient of kinetic friction.

Equation for Static Friction

Where,

= the force of friction (N)

= the normal force (N)

= the coefficient of static friction (no units)

The “less than or equal to” sign in the equation tells us that  is the maximum amount of static friction that can be acting. If more force is applied to the object than, it will start to move and we will have a kinetic friction problem.

Enrichment

You can find the some typical coefficients of friction for various materials online. Enter the phrase “coefficient of friction reference table” into an internet search engine such as Google or Yahoo.

Practice Questions

1. Michelle is taking her little sister Sally for a toboggan ride. Sally and the toboggan have a combined mass of 40 kg. The coefficient of static friction between the toboggan and the snow is 0.25 and the coefficient of kinetic friction is 0.18.
   1. What force must Michelle apply in order to get the toboggan moving?
   2. Describe the frictional force and the motion of the toboggan if Michelle only applies a force of 70 N?
   3. Once the toboggan starts to move, how much force does Michelle need to apply to keep it going at a constant speed?
   4. Describe the frictional force and the motion of the toboggan if Michelle applies a force greater than the one calculated in question 3.

Answer

Given:g = 9.8 N/kgµs = 0.25µk = 0.18m = 40 kg

1.

Required: F_f = ?

Solution:

F_g = mg

F_g =(40 kg)(9.8 N/kg)

F_g = 392 N

Since F_N and F_g are the only two vertical forces and the toboggan is on a horizontal surface,

F_N = F_g

F_N = 392 N

F_f ≤ µ_sF_N

F_f ≤ (0.25)(392 N)

F_f ≤ 98 N

In order to get the toboggan to start moving, Michelle must apply a force of at least 98 N in order to overcome the static friction.

2. Remember that F_f ≤ 98 N gives us the maximum value for the force of friction. We can have less than this acting. If Michelle only applies a force of 70 N, then that is not enough to overcome the force of static friction and the toboggan will not move. However, there will still have to be 70 N of friction acting between the ground and the toboggan to balance Michelle’s applied force.

3. Now that the toboggan has started to move, Michelle only needs to apply enough force to overcome the force of kinetic friction.

F_f = µ_kF_N

F_f = (0.18)(392 N)

F_f = 70.6 N

In order to keep the toboggan moving at a constant speed, Michelle must apply a force of 70.6 N.

4. If Michelle applies a force greater than 70.6 N, the toboggan will begin to accelerate and the force of friction will remain the same. Kinetic friction is not dependent on the speed of the object.