Force of Limiting Friction and Normal Reaction Experiment

Aim

To study the relation between force of limiting friction and normal reaction and to find the coefficient of friction between surface of a moving block and that of a horizontal surface.

Apparatus and material required

A wooden block with a hook, a horizontal plane with a glass or laminated table top (the table top itself may be used as a horizontal plane), a frictionless pulley which can be fixed at the edge of the horizontal table/plane, spirit level, a scale, pan, thread or string, spring balance, weight box and five masses of 100 g each.

Terms and Definitions

Friction: The tendency to oppose the relative motion between two surfaces in contact is called friction.

Static Friction:It is the frictional force acting between two solid surfaces in contact at rest but having a tendency to move (slide) with respect to each other.

Limiting Friction:It is the maximum value of force of static friction when one body is at the verge of sliding with respect to the other body in contact.

Kinetic (or Dynamic) Friction: It is the frictional force acting between two solid surfaces in contact when they are in relative motion.

Principle

The maximum force of static friction, i.e., limiting friction, FL, between two dry, clean and unlubricated solid surfaces is found to obey the following empirical laws:

• The limiting friction is directly proportional to the normal reaction, R, which is given by the total weight W of the body (Fig. E 7.1). The line of action is same for both W and R for horizontal surface,
• FL∝R⇒F_L = μ_LR
• i.e μ_L = F_L/R
• Thus, the ratio of the magnitude of the limiting friction, F_L, to the magnitude of the normal force, R, is a constant known as the coefficient of limiting friction (μ_L) for the given pair of surfaces in contact.
• The limiting friction depends upon the nature of surfaces in contact and is nearly independent of the surface area of contact over wide limits so long as normal reaction remains constant.

Note that F_L=μ L_R is an equation of a straight line passing through the origin. Thus, the slope of the straight-line graph between Fl (along Yaxis) and R (along Xaxis) will give the value of coefficient of limiting friction μ_L.

In this experiment, the relationship between the limiting friction and normal reaction is studied for a wooden block. The wooden block is made to slide over a horizontal surface (say glass or a laminated surface) (Fig. E 7.2).

Procedure

1. Find the range and least count of the spring balance.
2. Measure the mass (M) of the given wooden block with hooks on its sides and the scale pan (m) with the help of the spring balance.
3. Place the glass (or a laminated sheet) on a table and make it horizontal, if required, by inserting a few sheets of paper or cardboard below it. To ensure that the table-top surface is horizontal use a spirit level. Take care that the top surface must be clean and dry.
4. Fix a frictionless pulley on one edge of table-top as shown in Fig. E 7.2. Lubricate the pulley if need be.
5. Tie one end of a string of suitable length (in accordance with the size and the height of the table) to a scale pan and tie its other end to the hook of the wooden block.
6. Place the wooden block on the horizontal plane and pass the string over the pulley (Fig. E7.2). Ensure that the portion of the string between pulley and the wooden block is horizontal. This can be done by adjusting the height of the pulley to the level of hook of block.
7. Put some mass (q) on the scale pan. Tap the table-top gently with your finger. Check whether the wooden block starts moving.
8. Keep on increasing the mass (q) on the scale pan till the wooden block just starts moving on gently tapping the glass top. Record the total mass kept on the scale pan in Table E 7.1.
9. Place some known mass (say p ) on the top of wooden block and adjust the mass (q') on the scale pan so that the wooden block alongwith mass p just begins to slide on gently tapping the table top. Record the values of p' and q'in Table E 7.1
10. Repeat step 9 for three or four more values of p and record the corresponding values of q in Table E 7.1. A minimum of five observations may be required for plotting a graph between F_L and R.

Observations

1. Range of spring balance = ... to ... g
2. Least count of spring balance = ... g
3. Mass of the scale pan, (m) = ... g
4. Mass of the wooden block (M) = ... g
5. Acceleration due to gravity (g) at the place of experiment= ... m/s ²
6. Range of spring balance = ... to ... g

Table E 7.1: Variation of Limiting Friction with Normal

Graph

Plot a graph between the limiting friction (F_L) and normal force (R) between the wooden block and the horizontal surface, taking the limiting friction FL along the y-axis and normal force R along the xaxis. Draw a line to join all the points marked on it (Fig. E 7.3). Some points may not lie on the straightline graph and may be on either side of it. Extend the straight line backwards to check whether the graph passes through the origin. The slope of this straight-line graph gives the coefficient of limiting friction (μ_L) between the wooden block and the horizontal surface. To find the slope of straight line, choose two points A and B that are far apart from each other on the straight line as shown in Fig. E 7.3. Draw a line parallel to x-axis through point A and another line parallel to y-axis through point B. Let point Z be the point of intersection of these two lines. Then, the slope μ_L of straight line graph AB would be

μ_L = F_L/R = BZ/AZ

Result

1. Surface of the table should be horizontal and dust free.
2. Thread connecting wooden block and pulley should be horizontal.
3. Friction of the pulley should be reduced by proper oiling.
4. Table top should always be tapped gently.

Sources of Error

1. Always put the mass at the centre of wooden block.
2. Surface must be dust free and dry.
3. The thread must be unstretchable and unspun.