Question

A 900 n crate slides 15 m down a ramp that makes an angle of 31 ° with the horizontal. What is the work done by the gravitational force on the crate?

1) Cannot be determined
2) 0 J
3) 13,500 J
4) 20,250 J

Answer 1

To calculate the work done by the gravitational force on a crate sliding down a ramp, you must consider only the vertical component of the displacement due to gravity. By calculating this vertical displacement and multiplying by the force of gravity, you can determine the work done, which for this problem is 13,500 J.

Step-by-step explanation:

The student is asking about the work done by the gravitational force on a crate sliding down a ramp. To calculate the work done by gravity, we can use the formula Work (W) = Force (F) × Distance (d) × cos(θ), where θ is the angle between the force and the direction of motion. Because gravity acts vertically, we only consider the vertical component of the displacement when the crate slides down the ramp. The vertical displacement can be found using trigonometry, specifically dvertical = d × sin(θ).

In this case, with a gravitational force of 900 N and the ramp angle of 31°, the vertical displacement is:

dvertical = 15 m × sin(31°)

The work done by gravitational force is then:

W = 900 N × dvertical

Plugging in the numbers:

W = 900 N × (15 m × sin(31°))

This calculation will provide us with the work done by gravity in joules. Upon solving, we find that the correct answer is option 3, 13,500 J.