A force of 310 N is applied horizontally to a crate in order to displace the crate 45.0 m across a level floor at a constant velocity. As a result of this work, the crate's internal energy is increased by an amount equal to 12 percent of the crate's initial internal energy. Calculate the initial internal energy of the crate. (Disregard the work done on the floor, and assume that all work goes into the crate.)
To calculate the initial internal energy, we need to first find the work done on the crate. We can find the work done by using the equation:
W = Fd
Where W is the work done, F is the applied force, and d is the displacement.
W = 310 N × 45.0 m = 13950 J
From the problem statement, we know that the increase in the internal energy is 12 percent of the initial internal energy.
ΔE = 0.12 × E_initial
We can equate this to the work done:
13950 J = 0.12 × E_initial
Now, we can solve for the initial internal energy:
E_initial = 13950 J / 0.12 = 116250 J
So the initial internal energy of the crate is 116250 J.
To calculate the initial internal energy of the crate, we need to first find the work done on the crate and then use the equation relating work and internal energy.
1. Find the work done on the crate:
Work Done = Force x Distance
Given:
Force = 310 N
Distance = 45.0 m
Work Done = 310 N x 45.0 m = 13950 N·m or Joules
2. Find the initial internal energy of the crate:
The work done on the crate is equal to the change in internal energy.
Change in Internal Energy = Work Done
Let's assume the initial internal energy of the crate is U.
Change in Internal Energy = U x 12/100
13950 = U x 12/100
Rearranging the equation:
U = 13950 x 100/12
U = 116250
Therefore, the initial internal energy of the crate is 116250 Joules.
To calculate the initial internal energy of the crate, we need to understand the relationship between work, force, and displacement.
The work done on an object can be calculated using the formula: work = force x displacement x cos(theta), where theta is the angle between the force and the displacement.
In this case, the force (F) is 310 N and the displacement (d) is 45.0 m. We are also told that the crate is displaced at a constant velocity, which means there is no net force acting on the crate in the direction of displacement. Therefore, the angle (theta) between the force and displacement is 0 degrees, and the cos(0) is 1.
Using the formula, we can calculate the work done on the crate:
work = 310 N x 45.0 m x cos(0) = 13950 J
We are also told that the work done on the crate increases its internal energy by an amount equal to 12% of its initial internal energy. Let's represent the initial internal energy as 'U'.
Therefore, the work done on the crate is equal to 12% of its initial internal energy:
13950 J = 0.12 * U
Dividing both sides by 0.12, we get:
U = 13950 J / 0.12 ≈ 116250 J
Therefore, the initial internal energy of the crate is approximately 116250 Joules.