An 56.0 N box of clothes is pulled 5.2 m up a 30.0° ramp by a force of 104 N that points along the ramp. If the coefficient of kinetic friction between the box and the ramp is 0.22, calculate the change in the box's kinetic energy.
To calculate the change in the box's kinetic energy, we need to find the work done on the box and the frictional work done.
1. First, let's find the work done on the box by the force pulling it up the ramp. The work done is given by the formula:
Work = Force * Distance * cos(θ)
where Force is the parallel component of the force (104 N) along the ramp, Distance is the displacement (5.2 m), and θ is the angle between the force and the direction of motion (30°).
Plugging in the values, we have:
Work = 104 N * 5.2 m * cos(30°)
2. Next, let's find the frictional force acting on the box. The frictional force is given by:
Frictional Force = coefficient of kinetic friction * Normal Force
The normal force can be calculated by finding the perpendicular component of the weight of the box. The weight of the box is given by:
Weight = mass * gravitational acceleration
Given that the weight is 56.0 N, we can calculate the normal force as:
Normal Force = Weight * cos(θ)
Lastly, we can find the frictional force:
Frictional Force = coefficient of kinetic friction * Normal Force
Plugging in the given values, we have:
Frictional Force = 0.22 * (56.0 N * cos(30°))
3. The work done against friction is given by:
Work against Friction = Frictional Force * Distance
Plugging in the values, we have:
Work against Friction = Frictional Force * 5.2 m
4. Now, we can calculate the change in kinetic energy by subtracting the work done against friction from the work done on the box:
Change in Kinetic Energy = Work - Work against Friction
Plugging in the previously calculated values, we can find the answer.