Question

If a 37-kg crate is placed on an inclined ramp, and when the angle the ramp makes with the horizontal is increased to 30°, the crate begins to slide. What angle does the crate begin to slide if its mass is doubled?

a. 15°
b. 30°
c. 45°
d. 60°

Answer 1

The angle at which a crate begins to slide on an inclined plane is independent of its mass, so if a 37-kg crate starts sliding at a 30° angle, a 74-kg crate will also begin to slide at the same angle, which is 30°.

Step-by-step explanation:

When a crate begins to slide down an incline, it does so because the component of its weight parallel to the surface of the ramp exceeds the maximum static friction force holding it in place. The mass of the crate does not affect the angle at which it begins to slide, because both the force due to gravity and the frictional force are proportional to the mass, and thus the mass cancels out when calculating the ratio that determines the angle. Therefore, if a 37-kg crate begins to slide at a 30° angle, doubling the mass to 74 kg will not change the angle at which it begins to slide. The answer is b. 30°.