Question

The above box of mass 47 kg is sliding down a frictionless incline that makes an angle of 34° with the horizontal.

Solve the gravitational force into its x and y components along the rotated coordinate system.
Find the value of the Normal force.
What is the acceleration of the box?
A. To find the acceleration, you need more information.
B. The acceleration is 9.8 m/s².
C. The acceleration is 5 m/s².
D. The acceleration is 3 m/s².

Answer 1

To solve this problem, resolve the gravitational force acting on the box into its x and y components along the inclined plane. The normal force can be calculated using the component of gravity perpendicular to the incline. The acceleration of the box can be determined using the force and mass.

Step-by-step explanation:

To solve this problem, we need to resolve the gravitational force acting on the box into its x and y components along the inclined plane.

The gravitational force can be resolved into two components:

• The component perpendicular to the incline (N): N = mg cos(θ)
• The component parallel to the incline (F): F = mg sin(θ)

The normal force (N) is equal to the component of gravity perpendicular to the incline, so N = 47 kg * 9.8 m/s² * cos(34°).

The acceleration of the box can be determined using the equation a = F/m, where F is the force parallel to the incline and m is the mass of the box. Therefore, the acceleration of the box is 5 m/s² (option C).