Question

A 30kg box sits on an incline that is situated at 20 degrees from the horizontal. What is the minimum force a person must apply to the box to keep it from sliding down the incline? (Friction is negligible)

Answer 1

To keep a 30 kg box from sliding down a 20-degree incline, calculate the gravitational force component acting along the incline using the formula F = m · g · sin(θ), resulting in a force of approximately 100.68 N.

Step-by-step explanation:

The subject in question is Physics, and it involves understanding how forces work on objects on an incline when friction is negligible. Given a 30kg box on a 20-degree incline, we need to calculate the minimum force required to prevent it from sliding down the incline. The force needed to keep the object stationary will be equal to the component of the weight of the object acting down the slope. This can be calculated using Newton's second law and the formula for the weight component along the incline: F = m · g · sin(θ), where m is the mass of the box, g is the acceleration due to gravity (9.8 m/s²), and θ is the angle of the incline.

Here's how to calculate it:

1. Identify the mass of the box (30 kg) and the angle of the incline (20 degrees).
2. Calculate the gravitational force component acting along the incline: F = 30 kg × 9.8 m/s² × sin(20).
3. Compute the sin(20°) which is approximately 0.342.
4. Now multiply to find the force: F = 30 kg × 9.8 m/s² × 0.342 ≈ 100.68 N. This is the minimum force required to prevent the box from slipping.