Question

A box with a weight of 20 newtons rest at a bottom of a ramp and is pushed to the end of the ramp with a force of 40 newtons. This ramp is an incline of 15 meters long. What is the maximum height of the ramp. (Hint: Lesson 6) (Show your work)

Answer 1

The maximum height of the ramp is 29.4 meters.

Step-by-step explanation:

To find the maximum height of the ramp, we can use the concept of work. The work done on an object can be calculated as the product of the force applied and the distance over which the force is applied. In this case, the force of 40 newtons is applied over a distance of 15 meters.

The work done on the box is therefore

40 newtons * 15 meters = 600 joules.

The work done on the box is equal to the change in its potential energy, given by the equation

PE = mgh,

where m is the mass of the box, g is the acceleration due to gravity, and h is the height. In this case, the weight of the box is equal to its mass times gravity, so 20 newtons = m * 9.8 m/s^2.

Solving for m, we find

m = 20 newtons / 9.8 m/s^2 = 2.04 kilograms.

Substituting the values into the equation,

600 joules = 2.04 kilograms * 9.8 m/s^2 * h.

Solving for h, we find

h = 29.4 meters.