Question

A crate slides down a ramp that makes a 20∘ angle with the ground. To keep the crate moving at a steady speed, Paige pushes back on it with a 76 N horizontal force. Part A How much work does Paige do on the crate as it slides 4.0 m down the ramp? Express your answer with the appropriate units.

Answer 1

Paige does 285.64 J of work on the crate as it slides 4.0 m down the ramp.

Step-by-step explanation:

To calculate the work done by Paige on the crate as it slides down the ramp, we need to calculate the component of Paige's force that is in the direction of motion. Since the ramp makes a 20∘ angle with the ground, the component of Paige's force in the direction of motion is given by Fcosθ, where F is the force applied by Paige and θ is the angle of the ramp. Therefore, the work done by Paige is equal to the component of Paige's force multiplied by the distance the crate slides down the ramp.

Using the given values, we have a horizontal force of 76 N and a distance of 4.0 m. The angle of the ramp is 20∘. Calculating the component of the force in the direction of motion, we get: 76 N * cos(20∘) = 71.41 N.

Now, we can calculate the work done by Paige: Work = Force * Distance = 71.41 N * 4.0 m = 285.64 J (joules).