Problem 9 - College Physics

Question

A 0.50 -kg shuffleboard puck slides a distance of \(3.0 \mathrm{~m}\) on the board. If the coefficient of kinetic friction between the puck and the board is \(0.15,\) what work is done by the force of friction?

Step-by-Step Solution

Answer

The work done by friction is -2.205 J.

Step 1: Understanding the Problem

To solve this problem, we need to calculate the work done by the force of friction as a shuffleboard puck slides across the board. The work done by friction can be calculated using the formula for work: \[ W = F_d \times d \times \cos(\theta) \] where \( W \) is the work, \( F_d \) is the force of friction, \( d \) is the distance, and \( \theta \) is the angle between the force and direction of motion. Since friction opposes the direction of motion, \( \theta = 180^\circ \).

Step 2: Calculate the Force of Friction

First, find the force of friction \( F_d \) using the formula: \[ F_d = \mu_k \times N \] where \( \mu_k = 0.15 \) is the coefficient of kinetic friction and \( N = m \times g \) is the normal force. Here, \( m = 0.50 \) kg and \( g = 9.8 \) m/s², so: \[ F_d = 0.15 \times (0.50 \times 9.8) = 0.735 \text{ N} \]

Step 3: Calculate the Work Done by Friction

Work done by the force of friction is calculated by substituting the force, distance, and angle into the work formula: \[ W = F_d \times d \times \cos(180^\circ) \] Since \( \cos(180^\circ) = -1 \), the formula adjusts to: \[ W = 0.735 \text{ N} \times 3.0 \text{ m} \times (-1) = -2.205 \text{ J} \] The negative sign indicates that friction is doing work against the direction of motion.

Key Concepts

Kinetic Friction

Kinetic friction is a force that opposes the motion of two surfaces sliding past each other. It plays a crucial role in many everyday activities, from driving a car to sliding objects across a surface. When two surfaces are in motion relative to each other, kinetic friction resists this motion, making it a force to be managed and considered in physics problems.
In the context of the shuffleboard exercise, the puck slides over the board, creating kinetic friction that works against its motion. This friction relies on two main factors:

• The roughness of the surfaces in contact (quantified by the coefficient of kinetic friction, \( \mu_k \)).
• The force pressing the surfaces together, known as the normal force.

In our problem, the coefficient of kinetic friction is 0.15, and it influences how easily the puck slides, determining the force of friction that opposes its motion.

Normal Force

The normal force is the force exerted by a surface to support the weight of an object resting on it. It acts perpendicular or "normal" to the surface. When dealing with horizontal surfaces, like in our shuffleboard exercise, the normal force balances out the gravitational force acting on the object.
The normal force can be calculated as:

• \( N = m \times g \)

where \( m \) is the mass of the object and \( g \) is the acceleration due to gravity. In this case:

• \( m = 0.50 \) kg
• \( g = 9.8 \) m/s²

Thus, the normal force for the puck is \( 4.9 \) N. This force is essential for determining the force of friction, since friction is directly proportional to the normal force through the coefficient of kinetic friction. The combination of these forces affects how the puck slows and eventually stops due to the work done against its motion.

Force of Friction

The force of friction is a resisting force that acts in the opposite direction to the movement of objects moving across a surface. In physics problems like our shuffleboard exercise, understanding how to calculate the force of friction is essential. The force of friction, for kinetic interactions, is calculated using the formula:

• \( F_d = \mu_k \times N \)

where \( \mu_k \) is the coefficient of kinetic friction and \( N \) is the normal force. From our problem, we have:

• \( \mu_k = 0.15 \)
• Normal force, \( N = 0.50 \times 9.8 = 4.9 \) N

Thus, the force of friction \( F_d \) comes out to be \( 0.735 \) N.
This force is essential as it is used to calculate the work done by friction, which can tell us how much energy the puck loses due to friction as it travels over the shuffleboard. The frictional work done, in this case, is negative, indicating the loss of energy in the system as the puck comes to rest.