Question

Suppose a 2.15 kg crate is placed on a slope that makes an angle of 32.0° with the horizontal. Find the acceleration of the crate along the slope, assuming the slope to be frictionless. If a force of 15.6 N upward along the slope is applied to the crate, what would its acceleration be?

Answer 1

The acceleration of a 2.15 kg crate on a frictionless 32° incline is calculated by dividing the gravitational force component parallel to the slope by the crate's mass. An opposing 15.6 N force changes the net force and therefore the acceleration, which is found with the same method.

Step-by-step explanation:

To find the acceleration of the 2.15 kg crate on a frictionless slope angled at 32.0° with the horizontal, we can use Newton's second law. The only force causing acceleration along the slope is the component of gravity parallel to the slope. This force can be calculated using F = m × g × sin(θ), where m is the mass of the crate, g is the acceleration due to gravity (9.8 m/s²), and θ is the angle of the incline.

For the 2.15 kg crate, the parallel component of the gravitational force is 2.15 kg × 9.8 m/s² × sin(32.0°). To find the acceleration, we divide this force by the mass of the crate, as per the formula a = F/m.

If a force of 15.6 N is applied upward along the slope, this force acts against the component of gravity. The net force on the crate is the applied force minus the parallel component of gravity. The acceleration can again be calculated by dividing this net force by the mass of the crate.