11 PHYSICS 3. Activity: Rolling Friction

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🔬 3. Activity: Rolling Friction

Aim: To determine the force of limiting friction for rolling of a roller on a horizontal plane.

Principle:

When an object rolls on a surface, the point of contact between the object and the surface is instantaneously at rest. However, due to slight deformation of both the rolling object and the surface, a small area of contact is formed rather than a single point. This deformation leads to a resistance to rolling motion known as rolling friction. Rolling friction is generally much smaller than static or kinetic (sliding) friction. The force of limiting rolling friction is the maximum rolling friction that needs to be overcome to initiate or sustain rolling motion without slipping.

Apparatus:

1. Roller: A cylindrical object (e.g., a hollow metal cylinder, a wooden dowel, or a disc that can roll). Ensure it has a uniform shape and mass distribution.

2. Horizontal Plane: A smooth, flat, rigid surface (e.g., a polished wooden plank, a glass sheet, or a marble slab).

3. Spring Balance: Two spring balances (one with low range for horizontal force, one for weight if roller weight is unknown).

4. String/Thread: A thin, strong thread.

5. Pulley: A frictionless pulley fixed at the edge of the horizontal plane.

6. Weight Pan/Hanger: To add known weights.

7. Standard Weights: Various known weights (e.g., 50g, 100g, 200g).

8. Measuring Scale/Ruler: To measure distances if needed for additional calculations (though not strictly for determining the force of friction directly in this setup).

Experimental Setup:

1. Place the horizontal plane on a sturdy table, ensuring it is perfectly level.

2. Fix the frictionless pulley at one edge of the horizontal plane such that the string can pass over it smoothly.

3. Tie one end of the string to the center of the roller.

4. Pass the string over the pulley.

5. Attach a weight pan/hanger to the other end of the string.

6. Place the roller on the horizontal plane.

7. Optionally, a spring balance can be attached directly to the roller to pull it horizontally, or weights can be added to the hanger to apply a controlled force. For limiting friction, the latter (adding weights) is often more precise for determining the minimum force needed to just start rolling.

Procedure:

1. Measure the weight of the roller (W): Use a spring balance or weighing scale to determine the mass (m) of the roller, then calculate its weight W = m g(where g = 9.8 m/s2. Record this as the normal force (N) acting on the roller if the plane is horizontal.

2. Initial Setup: Place the roller on the horizontal plane. Ensure the string is taut and horizontal from the roller to the pulley, and then vertically down to the weight pan.

3. Apply Force Gradually: Start adding small, known weights to the weight pan, one by one.

4. Observe Motion: Carefully observe the roller. At some point, as weights are added, the roller will just begin to roll. The force applied at this exact moment is the force of limiting rolling friction.

5. Record Force: The total weight in the pan (including the weight of the pan itself) that just initiates the rolling motion is the limiting rolling friction (Fr).

6. Repeat and Average: Repeat steps 3-5 at least three to five times. This helps to minimize experimental error and get a more reliable average value.

7. Vary Normal Force (Optional but Recommended for detailed study): To observe how rolling friction depends on normal force, add additional known weights on top of the roller itself. This increases the total normal force (N = W{roller}} + W{added on roller}). Then repeat steps 3-6. This will allow you to determine the coefficient of rolling friction later.

Data Table:

Sr. No.	Weight of Roller (WR​) (N)	Additional Weight on Roller (WA​) (N)	Total Normal Force (N=WR​+WA​) (N)	Applied Force (Weights in Pan) just causing Rolling (Fr​) (N)
1.	(e.g., 2.5)	0	2.5
2.	(e.g., 2.5)	0	2.5
3.	(e.g., 2.5)	0	2.5
Average			2.5	Avg. Fr
4.	(e.g., 2.5)	(e.g., 1.0)	3.5
5.	(e.g., 2.5)	(e.g., 1.0)	3.5
6.	(e.g., 2.5)	(e.g., 1.0)	3.5
Average			3.5	Avg. Fr

(Note: Units can be in grams/kilograms for mass and converted to Newtons for force by multiplying by 'g'. Ensure consistency.)

Calculations:

1. Calculate Weight of Roller (Normal Force):

   If mass of roller m = 250 g = 0.25kg

   W=  mg = 0.25 kg x 9.8  m/s2 = 2.45 N 

2. Calculate Applied Force (Fr):

3. If the weight pan has mass m = 20g and added weights m = 80 g to just start rolling.

   Total mass in pan = 20g+80g =100g

   Fr = 0.1 x 9.8 = 9.8 N

4. Average the Fr values for each specific Normal Force (N).

   For example, if for N = 2.45  N the readings for Fr were 0.98 N, 1.02 N, 0.95  N

   Average Fr = (0.98 + 1.02 + 0.95) / 3 = 2.95 / 3 = 0.98N

5. Calculate the Coefficient of Rolling Friction 

   So, Coefficient of Rolling Friction 

   Using the example above:  = 0.98N / 2.45  N = 0.4

   (Note: This value is quite high for typical rolling friction, which is usually much smaller. This example is illustrative.)

   Plotting Fr vs.N will give a straight line passing through the origin, and the slope of this line will be Coefficient of Rolling Friction 

6. = Fr / N.

Result:

The force of limiting rolling friction for the given roller on the horizontal plane, when the normal force is equal to the weight of the roller ($N = [Average Weight of Roller]$ N), is determined to be Coefficient of Rolling Friction 

(If varying normal force)

It is observed that the force of limiting rolling friction increases with an increase in the normal force.

The average coefficient of rolling friction  for this system is found to be

• Ensure the horizontal plane is perfectly level to prevent the roller from moving due to gravity.

• The pulley should be as frictionless as possible to accurately transfer the applied force.

• The string should be thin, strong, and parallel to the horizontal plane to avoid vertical components of force.

• Add weights to the pan very gently and incrementally to accurately determine the point where rolling just begins.

• Ensure the roller is clean and free of any debris that could affect its rolling motion.

• Repeat readings and take an average to minimize random errors.

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