A box of mass 15.0kg is released on a 32° incline , on a it accelerated down the incline at 0.30m/s² . The frictional force impending its motion ?

To find the frictional force impeding the motion of the box, we first need to calculate the net force acting on the box along the incline.

The net force along the incline can be calculated using the equation:

Net force = Mass * Acceleration

Net force = 15.0kg * 0.30m/s²
Net force = 4.5 N

Next, we need to calculate the component of the gravitational force acting along the incline. This can be calculated using the equation:

Component of gravitational force along incline = Mass * Acceleration due to gravity * sin(θ)

where θ is the angle of the incline (32°) and the acceleration due to gravity is 9.81 m/s².

Component of gravitational force along incline = 15.0kg * 9.81m/s² * sin(32°)
Component of gravitational force along incline = 75.0 N

Since the box is accelerating down the incline, the frictional force is acting in the opposite direction to the net force. Therefore, the frictional force can be calculated as:

Frictional force = Component of gravitational force along incline - Net force

Frictional force = 75.0 N - 4.5 N
Frictional force = 70.5 N

Therefore, the frictional force impeding the motion of the box is 70.5 N.