Question

Bicycle caliper brakes consist of rubber pads mounted in rigid metal "shoes." The normal force applied by a bicycle caliper brake pad to the wheel rim is about 1.0×10^2

N. The contact area of the brake pad is approximately 4.0 cm×0.80 cm, with the long dimension parallel to the rim's rotation. The pad is 1.0 cm thick. The coefficient of kinetic friction between the rubber pad and the aluminum rim is 0.50.

Answer 1

The force applied by a bicycle caliper brake pad to the wheel rim can be calculated using the equation F = μN, where F is the force, μ is the coefficient of kinetic friction, and N is the normal force.

Step-by-step explanation:

The force applied by a bicycle caliper brake pad to the wheel rim can be calculated using the equation:

F = μN

where F is the force, μ is the coefficient of kinetic friction, and N is the normal force. In this case, the coefficient of kinetic friction is 0.50, and the normal force is 1.0 x 10^2 N. Therefore, the force applied by the brake pad is:

F = 0.50 x 1.0 x 10^2 N = 5.0 x 10^1 N

Answer 2

The frictional force, which is the braking force exerted by the pads on the rim, is 50 N.

To calculate the frictional force exerted by the bicycle caliper brake pads on the wheel rim, we can follow these steps:

1. Determine the Normal Force
`(\( F_N \))`: The normal force is provided as
`\( 1.0 * 10^2 \) N.`

2. Calculate the Frictional Force
`(\( F_f \))` : The frictional force can be calculated using the coefficient of kinetic friction
`(\( \mu_k \))` and the normal force. The formula is:

`\[ F_f = \mu_k \cdot F_N \]`

3. Calculate the Braking Force: The frictional force is the force that provides the braking action on the wheel rim.

Given:

- The coefficient of kinetic friction
`(\( \mu_k \))` is 0.50.

- The normal force
`(\( F_N \)) is \( 1.0 * 10^2 \)` N.

Using the formula:

`\[ F_f = 0.50 \cdot 1.0 * 10^2 \, \text{N} = 50 \, \text{N} \]`

So, the frictional force, which is the braking force exerted by the pads on the rim, is 50 N.

This is the force that will slow down the rotation of the wheel as the brakes are applied. The contact area and the thickness of the pad are not needed to calculate the frictional force, as it depends solely on the normal force and the coefficient of kinetic friction.