A horizontal force of magnitude F = 116 N is used to push a box of mass m = 9 kg from rest a distance d = 13 m?
1)How much work is done by the force on the box?
WF =
2) How much work is done on the box by the gravitational force during this same displacement?
Wg =
3) How much work is done by the normal force of the slope on the box during this displacement?
WN =
4) How fast is the box moving after this displacement?
v =
sorry Please disregard this post
To solve these problems, we need to understand the concepts of work and energy.
1) The work done by a force is defined as the product of the magnitude of the force and the displacement of the object in the direction of the force. In this case, the horizontal force of magnitude F = 116 N is acting on the box, and it moves a distance d = 13 m. Therefore, the work done by the force on the box is given by the formula:
WF = F * d = 116 N * 13 m = 1508 N·m (or joules)
2) The gravitational force is acting vertically downwards on the box. However, since the displacement is horizontal, the gravitational force does not do any work on the box during this displacement. Therefore, the work done on the box by the gravitational force (Wg) is zero.
Wg = 0 joules
3) The normal force acts perpendicular to the surface of the slope and does not do any work in the horizontal direction. Therefore, the work done by the normal force of the slope (WN) is also zero.
WN = 0 joules
4) To determine the final speed of the box after the displacement, we can use the work-energy theorem. The work done on an object is equal to the change in its kinetic energy.
The initial velocity of the box is zero since it starts from rest. The work done by the force on the box (WF) is equal to the change in kinetic energy (ΔKE). Thus, we can write:
WF = ΔKE
Using the formula for work done (WF = F * d) and the formula for kinetic energy (KE = 1/2 * m * v^2), we can rearrange the equation to solve for v (final velocity):
F * d = 1/2 * m * v^2
Substituting the given values:
116 N * 13 m = 1/2 * 9 kg * v^2
Simplifying:
1508 N·m = 4.5 kg * v^2
Dividing both sides by 4.5 kg:
v^2 = 1508 N·m / 4.5 kg
v^2 = 334.2 m²/s²
Taking the square root of both sides:
v ≈ √334.2 m²/s²
v ≈ 18.28 m/s
Therefore, the box is moving with a final speed of 18.28 m/s after this displacement.