PHYSC 4A: Principles of Physics

Lab 6: Friction

Purpose

The purpose of this lab is to determine the coefficients of static and kinetic friction for wood onwood, and to observe the effects of friction on the motion of objects.

Theory

A force of friction is present whenever two surfaces are in contact. There are two varieties -static friction which is present when one is trying to move an object which is in contact witha surface, and kinetic friction which is present when the object is in motion along the surface.The magnitude of the static frictional force satisfies the inequality

fs sFN ; (1)

where FN is the normal force, and s is called the coefficient of static friction. The value of sdepends on the surfaces involved, and the maximum static frictional force that can act on anobject is fmaxs = sFN . When the object is just about to move from rest, the static friction forceis maximum. Once the object is moving, the force of kinetic friction takes over. The kineticfriction force is proportional to the normal force, with

fk = kFN ; (2)

where k is called the coefficient of kinetic friction. The value of k is less than the value of s.

Consider a block of mass M on a horizontal surface, attached by a string and pulley to ahanging mass m. Newtons equation of motion for masses M and m are

T fs = 0; FN = Mg; T mg = 0: (3)

Eliminating T , we find fs = mg. However, when the mass M is just about to slide, we havefs = sFN . Therefore,

mg = sMg: (4)

Hence, the coefficient of static friction is given by

s =m

M: (5)

If the block is moving with constant velocity, we have

k =m

M: (6)

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Consider now a block of massM on a surface which is elevated at an angle to the horizontal.The weight of the block will cause it to slide down the incline, as soon as the maximum staticfrictional force is overcome. The angle of slippage can be determined from Newtons laws.When the block is just about to slip, we have

fs = Mg sin ; FN = Mg cos : (7)

Therefore,

s = tan s; (8)

where s is the angle at which the block just begins to slip.

Equipment

Block of wood String Pulley Friction boardWeight hangerWeights Glider sail Timing photogates.

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Procedure: Part 1 - Determination of s

1: Measure the mass of the block of wood. Set the block on a level wood surface, and use astring to attach it to a weight hanger.

2: Add an additional 1kg mass on top of the block. The mass of the block plus this 1kg isdenoted by M .

3: Now start adding mass in small increments to the weight hanger, until the block just be-gins to slide. Record the value of the hanging mass m. Use (5) to determine the coefficient ofstatic friction.

4: Repeat this procedure three times.

5: Repeat this procedure with masses of 0:8kg and 0:6kg on top of the block.

6: Record the data in a table as follows. Calculate the average value of s, and determinethe percentage error.

Table 1: Determination of s

M(kg) m(kg) s

Procedure: Part 2 - Determination of k

1: Recall that the coefficient of kinetic friction is less than the coefficient of static friction. Thus,if we give the block a slight nudge, we can make it travel at constant velocity. The hangingmass required to do this is less that the mass obtained in Part 1.

2: Add an additional 1kg mass on top of the block. The mass of the block plus this 1kg isdenoted by M .

3: Now a mass to the weight hanger which is less than the mass required in Part 1. Recordthis value as m.

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4: Give the block a slight nudge and try to ensure that it is moving at constant velocity. Youneed to determine this by inspection.

5: Use (6) to determine the coefficient of kinetic friction.

6: Repeat this procedure three times.

7: Repeat this procedure with masses of 0:8kg and 0:6kg on top of the block.

8: Record the data in a table as follows. Calculate the average value of k, and computethe percentage error.

Table 2: Determination of k

M(kg) m(kg) k

Procedure: Part 3 - Motion on an Incline

1: Remove the hanging mass from the block, and add an additional 0:5kg mass on top ofthe block.

2: Gradually elevate the board at increasing angles relative to the horizontal. Measure theangle when the block just begins to slide.

3: Use (8) to determine the coefficient of static friction.

4: Repeat this procedure three times.

5: Repeat this procedure with masses of 0:4kg and 0:3kg on top of the block.

6: Calculate the average value of s, and determine the percentage error.

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