Ramps and Inclines

Some physics problems include defining forces and motion of objects in a ramp or incline. To work on these kind of problems, the following must be done.

1. Represent all the forces acting on the object on a ramp using the Free-Body Diagram. Use a box or a dot to represent an object and arrows representing the forces acting on the object with the head pointing at the direction of the force.
2. Apply Newton’s laws of motion and the concept of forces to solve problems of objects on the ramp.
3. Label all necessary components in the FBD.

Example 1.

An object is at rest in a ramp inclined at $$30^\circ$$ from the ground. What are the forces that act on the object?

FBD:

Example 2.

A $$150-kg$$ box is pushed towards the truck. If the ramp is inclined $$60^\circ$$ from the ground, how much force is applied to make the box moving at $$1.5\;m/s^2$$?

Given:

$$m= 150\;kg\\ \text{angle}=60^\circ\\ a=1.5\;m/s^2$$

Solution:

To solve for the force exerted on the box, we will use the Newton’s second law of motion $$F=ma$$.

$$F=(150\;kg)(1.5\;m/s^2)=225\;N$$