For problems that involve an object accelerating along an inclined plane, how can the weight be used to determine the force component that causes motion?

For problems that involve an object accelerating along an inclined plane, the weight can be used to determine the x and y force component that causes the motion by using the formula:

The force component along the x direction is equal to weight of the object multiplies by sin of angle of inclination of the ramp. Fx=wsin(a). while force component along the y direction is equal to weight of the object multiplies by cos of angle of inclination of the ramp, Fy = wcos(a).

component of the weight of the block is accelerating the block along the inclined plane

Explanation:

When an object is sliding on the inclined plane such either in upward or downward direction

then the component of the weight along the inclined plane and perpendicular to inclined plane is given as

along the inclined plane

perpendicular to inclined plane

now the normal force due to inclined plane is counter balanced by the component of the weight

So it is given as

while the other component of the weight of the block is accelerating the block along the inclined plane

so we have