Question

What force must be applied to a 100.0-kg crate on a frictionless plane inclined at 30° to cause an acceleration of 2.0 m/s² up the plane?

a) 57.7 N
b) 100 N
c) 200 N
d) 346.4 N

Answer 1

To find the force required to accelerate a 100.0-kg crate up a frictionless plane inclined at 30°, use the formula F = ma. The force required is 100 N.

Step-by-step explanation:

To find the force required to accelerate a 100.0-kg crate up a frictionless plane inclined at 30°, we can use the formula F = ma, where F is the force, m is the mass, and a is the acceleration.

First, we need to find the component of the acceleration that is parallel to the incline. This can be done using the formula a_parallel = a * sin(θ), where θ is the angle of the incline.

In this case, the acceleration is 2.0 m/s² and the angle of the incline is 30°. So, the parallel acceleration is 2.0 m/s² * sin(30°) = 2.0 m/s² * 0.5 = 1.0 m/s².

Finally, we can calculate the force required using F = ma. F = 100.0 kg * 1.0 m/s² = 100 N.