Question

A ramp is set at 32° to the ground. A briefcase of mass 3.2 kg is pushed to the top of the ramp, increasing its GPE by 37 J. How long is the ramp?

Answer 1

ANSWER -

We can use the formula for gravitational potential energy to solve this problem:

GPE = mgh

where m is the mass of the briefcase, g is the acceleration due to gravity (9.8 m/s^2), h is the height of the ramp, and GPE is the increase in gravitational potential energy.

We can also use trigonometry to relate the height of the ramp to its length and angle:

h = L*sin(θ)

where L is the length of the ramp and θ is the angle of the ramp.

Combining these two equations, we get:

GPE = mgh
GPE = mgLsin(θ)
37 J = (3.2 kg)(9.8 m/s^2)Lsin(32°)
L = 1.03 meters

Therefore, the length of the ramp is approximately 1.03 meters.