An 52.0 N box of clothes is pulled 7.3 m up a 30.0° ramp by a force of 103 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.
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To calculate the change in the box's kinetic energy, we need to consider the work done by the force along the ramp and the work done against the friction force. The change in kinetic energy can be obtained by subtracting the work done against friction from the work done by the force along the ramp.
1. First, let's calculate the work done by the force along the ramp. The work done by a force can be calculated using the formula: work = force * distance * cos(theta), where theta is the angle between the force and the displacement. In this case, the force is 103 N, the distance is 7.3 m, and the angle theta is 30 degrees.
work = 103 N * 7.3 m * cos(30°)
work = 103 N * 7.3 m * √(3)/2
work = 1020.522 J (rounded to three decimal places)
2. Next, let's calculate the work done against friction. The work done against friction is given by the formula: work = friction force * distance. The friction force can be calculated using the formula: friction force = coefficient of friction * normal force. In this case, the coefficient of friction is 0.22, and the normal force is equal to the weight of the box, which is 52.0 N.
friction force = 0.22 * 52.0 N
friction force = 11.44 N (rounded to two decimal places)
work = friction force * distance
work = 11.44 N * 7.3 m
work = 83.392 J (rounded to three decimal places)
3. Finally, let's calculate the change in kinetic energy. Since the change in kinetic energy is the difference between the work done by the force along the ramp and the work done against friction, we can calculate it as:
change in kinetic energy = work by force - work against friction
change in kinetic energy = 1020.522 J - 83.392 J
change in kinetic energy = 937.130 J (rounded to three decimal places)
Therefore, the change in the box's kinetic energy is 937.130 J.