Physics

To find the change in gravitational potential energy as the mass slides down the frictionless incline, we need to use the relationship between the height the object has fallen and its acceleration.

 

Gravitational Potential Energy

The change in gravitational potential energy () is given by:

 

Where:

is the mass of the object,

is the acceleration due to gravity,

is the change in height.

 

Height Fallen

To find , we need to consider the motion of the object along the incline.

 

The distance traveled along the incline after time can be found using the equation for uniformly accelerated motion:

 

Where:

is the distance traveled along the incline,

is the acceleration along the incline,

is the time.

 

The acceleration along the incline is given by:

 

Thus, the distance traveled along the incline is: