One day while moving boxes you get tired and decide to use a rocket instead. You attach a small rocket of negligible mass to a 74.2 kg box. When you turn the rocket on, it provides a constant thrust of 271 N, and the sbox begins sliding across the pavement. If the magnitude of acceleration of the box is 1.72 m/s2, what is the coefficient of kinetic friction between the soapbox and pavement?

Question

One day while moving boxes you get tired and decide to use a rocket instead. You attach a small rocket of negligible mass to a 74.2 kg box. When you turn the rocket on, it provides a constant thrust of 271 N, and the sbox begins sliding across the pavement. If the magnitude of acceleration of the box is 1.72 m/s2, what is the coefficient of kinetic friction between the soapbox and pavement?

Answer 1

resistive friction force = mu m g = mu (74.2)(9.81) = 728 mu

so
271 - 728 mu = 74.2 (1.72)
solve for mu

Answer 2

To find the coefficient of kinetic friction between the soapbox and the pavement, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration.

The net force acting on the soapbox is the difference between the applied force (thrust from the rocket) and the frictional force opposing its motion. Mathematically, we can represent this as:

net force = applied force - frictional force

Given that the applied force is equal to the thrust of the rocket (271 N) and the acceleration of the soapbox (1.72 m/s^2), we can rewrite the equation as:

271 N - frictional force = (74.2 kg) * (1.72 m/s^2)

Now, let's determine the frictional force. The frictional force can be calculated using the equation:

frictional force = coefficient of kinetic friction * normal force

The normal force is the force exerted by a surface to support the weight of an object resting on it. In this case, the normal force is equal to the weight of the soapbox (mass * gravitational acceleration). Thus, the normal force is:

normal force = (74.2 kg) * (9.8 m/s^2) = 726.76 N

Now, let's substitute the values into the equation:

271 N - (coefficient of kinetic friction) * 726.76 N = (74.2 kg) * (1.72 m/s^2)

Simplifying the equation by rearranging the terms, we have:

(coefficient of kinetic friction) * 726.76 N = 271 N - (74.2 kg) * (1.72 m/s^2)

Now, divide both sides of the equation by 726.76 N to isolate the coefficient of kinetic friction:

coefficient of kinetic friction = [271 N - (74.2 kg) * (1.72 m/s^2)] / 726.76 N

Solving this equation will give you the coefficient of kinetic friction between the soapbox and the pavement.