Final answer:
To find the coefficient of kinetic friction between the box and the surface, we can use the equation friction force = coefficient of kinetic friction * normal force. The normal force is equal to the weight of the box, so we can calculate it using the equation normal force = mass * gravity. In this case, the friction force is equal to the force that brings the box to a stop, which can be calculated using the equation friction force = mass * acceleration. Substituting these values into the equation, we can solve for the coefficient of kinetic friction.The option d is the correct answer .
Step-by-step explanation:
To find the coefficient of kinetic friction between the box and the surface, we can use the equation: friction force = coefficient of kinetic friction * normal force. The normal force is equal to the weight of the box, so we can calculate it using the equation: normal force = mass * gravity. In this case, the friction force is equal to the force that brings the box to a stop, which can be calculated using the equation: friction force = mass * acceleration. Substituting these values into the equation, we can solve for the coefficient of kinetic friction.
Given:
- Mass of the box (m) = 10 kg
- Initial velocity (v) = 2 m/s
- Distance traveled before stopping (d) = 4 m
To find the acceleration:
- Use the equation: d = (v^2 - u^2) / (2a) where d is the distance, v is the final velocity, u is the initial velocity, and a is the acceleration.
- Solve for a: a = (v^2 - u^2) / (2d)
- Substitute the given values: a = (0 - 2^2) / (2 * 4)
- Simplify: a = -0.5 m/s^2
To find the normal force:
- Use the equation: Normal force = mass * gravity
- Substitute the given values: Normal force = 10 kg * 9.8 m/s^2
- Simplify: Normal force = 98 N
To find the friction force:
- Use the equation: friction force = mass * acceleration
- Substitute the given values: friction force = 10 kg * (-0.5 m/s^2)
- Simplify: friction force = -5 N
To find the coefficient of kinetic friction:
- Use the equation: friction force = coefficient of kinetic friction * normal force
- Substitute the known values: -5 N = coefficient of kinetic friction * 98 N
- Solve for the coefficient of kinetic friction: coefficient of kinetic friction = -5 N / 98 N
- Convert to positive value: coefficient of kinetic friction = 0.051
Therefore, the coefficient of kinetic friction between the box and the surface is approximately 0.051.