A 10 kg box starts from rest and is then pulled horizontally 27 meters across the ground by a rope. The rope has a force of 100N applied to it and forms an angle of 50 degree to the ground. The coefficient of kinetic friction is 0.50 for this surface.
(a)How much work is done by the applied force?
(b)How much work is done by friction?
(c) How much work is done by gravity?
(d)How much work is done by the normal force?
(e)What;s the total work done on the box?
(f)what is the change in potential energy of the box?
(i)What is the change in potential energy of the box?
(j)how long did it take for the box to travel 18 meters?
(k) what is the total power?
M*g = 10 * 9.8 = 98 N. = Wt. of box.
a. Work = F*d = 100*Cosw50 * 27 =
b. Fn = 98-100*sin50 =
Fk = u*Fn.
Work = Fk*d =
d. Work = Fn*d
To solve this problem, we need to understand the concepts of work, friction, gravity, normal force, potential energy, and power. Let's break down each question and explain how to find the answers.
(a) How much work is done by the applied force?
Work is defined as the product of force and displacement in the direction of the force. The formula is given by:
Work = force × displacement × cos(θ)
In this case, the force (F) applied by the rope is 100 N, and the displacement (d) is 27 meters. The angle (θ) between the force and displacement is given as 50 degrees. Substituting these values into the formula, we get:
Work = 100 N × 27 m × cos(50°)
Calculating this expression will give you the work done by the applied force.
(b) How much work is done by friction?
Frictional work can be calculated by multiplying the force of friction (f) by the displacement (d), but considering the negative sign to represent the opposing direction of the force. The formula is given by:
Work = - force of friction × displacement
To find the force of friction, we need to multiply the coefficient of kinetic friction (μ) with the normal force (N). The normal force can be calculated by multiplying the mass (m) of the box with the acceleration due to gravity (g). The formula is given by:
Force of friction = μ × N = μ × (m × g)
In this case, the mass (m) of the box is 10 kg, the acceleration due to gravity (g) is approximately 9.8 m/s², and the coefficient of kinetic friction (μ) is given as 0.50. Using these values, we can calculate the force of friction and then find the work done by friction.
(c) How much work is done by gravity?
The work done by gravity can be calculated using the formula:
Work = force × displacement × cos(θ)
In this case, the force of gravity (mg) acts vertically downward, but the displacement occurs horizontally. Therefore, the angle (θ) between the force and displacement is 90 degrees, and cos(90°) = 0. So, the work done by gravity in this case is zero.
(d) How much work is done by the 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 box is being pulled horizontally, so the normal force does not perform any work. Therefore, the work done by the normal force is zero.
(e) What is the total work done on the box?
To find the total work done on the box, we need to sum up the work done by the applied force, work done by friction, work done by gravity, and work done by the normal force.
Total work = Work by applied force + Work by friction + Work by gravity + Work by normal force
Since the work done by gravity and the normal force is zero in this case, the total work done on the box is equal to the sum of the work done by the applied force and the work done by friction.
(f) What is the change in potential energy of the box?
The change in potential energy of an object is given by the formula:
Change in potential energy = m × g × change in height
However, in this question, no vertical motion or change in height is mentioned. Therefore, the change in potential energy of the box is also zero.
(i) What is the change in kinetic energy of the box?
The change in kinetic energy is given by the formula:
Change in kinetic energy = Work done by applied force + Work done by friction
So, to find the change in kinetic energy, we need to sum up the work done by the applied force and the work done by friction.
(j) How long did it take for the box to travel 18 meters?
To find the time taken by the box to travel a given distance, we need to know the speed or velocity of the box. However, this information is not provided in the question. Therefore, we cannot determine the time taken without additional information.
(k) What is the total power?
Power is defined as the rate at which work is done or energy is transferred. It can be calculated using the formula:
Power = Work / Time
However, in this question, we do not have the information about the time taken for the box to be pulled. Therefore, we cannot determine the total power without additional information.