A 6.0-kg box is raised a distance of 3.0m from rest by a vertical applied force of 80 N. Find (a) the work done on the box by the applied force, (b) the work done on the box by gravity, and (c) the final kinetic energy of the box.
work= work done on gravity + KE gained
80*3=6g*3+KE
To find the work done on the box by the applied force, we can use the formula:
Work = Force × Distance
Given that the applied force is 80 N and the distance is 3.0 m, we can substitute these values into the formula:
Work = 80 N × 3.0 m = 240 J
Therefore, the work done on the box by the applied force is 240 Joules (J).
To find the work done on the box by gravity, we need to determine the gravitational force acting on the box. The formula for gravitational force is:
Force = Mass × Acceleration due to gravity
Given that the mass of the box is 6.0 kg and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the gravitational force:
Force = 6.0 kg × 9.8 m/s^2 = 58.8 N
Now, we can use the same formula as above to find the work done by gravity. Since the box is raised vertically, the distance over which gravity acts is the same as the distance the box is raised, which is 3.0 m:
Work = 58.8 N × 3.0 m = 176.4 J
Therefore, the work done on the box by gravity is 176.4 Joules (J).
To find the final kinetic energy of the box, we can use the formula:
Kinetic Energy = (1/2) × Mass × Velocity^2
Since the box is initially at rest, the initial kinetic energy is zero. Since there are no other forces or work done on the box apart from the applied force and gravity, the total work done on the box equals the change in kinetic energy. Therefore, the final kinetic energy is equal to the total work done on the box:
Final Kinetic Energy = Work by applied force + Work by gravity
Final Kinetic Energy = 240 J + 176.4 J
Final Kinetic Energy = 416.4 J
Therefore, the final kinetic energy of the box is 416.4 Joules (J).
To find the answers to these questions, we need to apply some basic principles from physics. Let's break down each question and explain how to get the answer:
(a) The work done on an object can be calculated using the formula:
Work = Force * Distance * cos(theta)
In this case, the applied force is 80 N, and the distance the box is raised is 3.0 m. However, we are not given the angle (theta) between the applied force and the displacement. Assuming the force is applied vertically upwards and the displacement is also vertical, the angle between them is 0 degrees. In this case, cos(0) = 1.
So, the work done on the box by the applied force would be:
Work = 80 N * 3.0 m * cos(0) = 240 J
(b) The work done on the box by gravity can be calculated using the formula:
Work = Force_gravity * Vertical Distance * cos(theta)
The gravitational force on the box can be calculated using the formula:
Force_gravity = mass * gravity
Given that the mass of the box is 6.0 kg and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the gravitational force:
Force_gravity = 6.0 kg * 9.8 m/s^2 = 58.8 N
Since the displacement is vertical, the angle (theta) between the gravitational force and the displacement is 180 degrees. In this case, cos(180) = -1.
So, the work done on the box by gravity would be:
Work = -58.8 N * 3.0 m * cos(180) = -176.4 J (negative because the gravitational force is acting in the opposite direction of the displacement)
(c) The work-energy principle states that the work done on an object equals the change in its kinetic energy:
Work_net = Change in kinetic energy
In this case, the net work is the sum of the work done by the applied force and the work done by gravity:
Work_net = Work_applied + Work_gravity
Final Kinetic Energy = Initial Kinetic Energy + Work_net
However, we need the initial kinetic energy of the box. Since the box is at rest initially, it has no initial kinetic energy (Initial Kinetic Energy = 0).
So, the Final Kinetic Energy = 0 + Work_net = 240 J + (-176.4 J) = 63.6 J
Therefore, the final kinetic energy of the box is 63.6 Joules.