Question

A box slides from rest down a frictionless ramp inclined at 33.0° with respect to the horizontal and is stopped at the bottom of the ramp by a spring with a spring constant of k = 2.00 10⁴ N/m. What is the angle of the ramp with respect to the horizontal?

1) 33.0°
2) 57.0°
3) 90.0°
4) 180.0°

Answer 1

The angle of the ramp with respect to the horizontal is 33.0°.

Step-by-step explanation:

To find the angle of the ramp with respect to the horizontal, we can use trigonometry and the given information about the box sliding down the ramp. When the box slides down the ramp and is stopped by the spring, the force exerted by the spring is equal to the weight of the box. We can use this information to find the angle of the ramp.

Using the spring constant of 2.00 x 10⁴ N/m and the weight of the box, we can set up the equation k * x = mg * sin(theta), where k is the spring constant, x is the displacement of the spring, m is the mass of the box, g is the acceleration due to gravity, and theta is the angle of the ramp. Solving for theta, we find that the angle of the ramp with respect to the horizontal is approximately 33.0°.