A child does 350 J of work while pulling a box from the ground up to his tree house with a rope. The tree house is above the ground. What is the mass of the box?
To find the mass of the box, we need to use the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy.
In this case, the work done by the child pulling the box up is 350 J. However, since the box is moving vertically against gravity, we need to account for both the work done against gravity and the work done to overcome the vertical displacement.
The work done against gravity can be calculated using the formula:
Work = force × distance × cos(θ)
Where:
- Force is the weight of the box, which is equal to mass × acceleration due to gravity (9.8 m/s²).
- Distance is the vertical displacement of the box, which is the height of the tree house.
- θ is the angle between the force and the displacement (which is 0 degrees for vertical motion).
Since the child is pulling the box vertically upwards, we can assume that the angle between the force and displacement is 0 degrees, so cos(θ) = 1.
The work done to overcome the vertical displacement can be calculated as:
Work = force × distance
Where:
- The force is the weight of the box (mass × acceleration due to gravity).
- The distance is the vertical displacement, which is the height of the tree house.
Equating the total work done to the sum of these two components:
350 J = (mass × acceleration due to gravity × height) + (mass × acceleration due to gravity × height)
Now we can solve for the mass of the box:
350 J = 2 × mass × acceleration due to gravity × height
Rearranging the equation:
mass = 350 J / (2 × acceleration due to gravity × height)
Substituting the value of acceleration due to gravity (9.8 m/s²) and the known height, you can calculate the mass of the box.