What is the Work Done on a Car by Gravity on an Inclined Plane?

[dance_sg]

Homework Statement

A car of mass 1500 kg rolls down a hill for a distance of 150 m as shown.
If the road makes an angle of 15º with the horizontal, how much work is done on the car by the force of gravity?

Homework Equations

ep=mgh, w=fd, f=ma

The Attempt at a Solution

i really have no idea. am i trying to find acceleration(gravity)?

 

[kuruman]

You need a better expression for work than the one you have put down. The definition of work is not force times distance. Check your textbook.

 

[jgens]

Well, there are two ways to do this problem. The first uses the definition of work: What you need to do is find the component of the force acting along the car's plane of motion and then use W = F * d. The second way uses the definition of gravitational potential energy: The GPE at a point is the amount of work necessary to lift an object against a gravitational field to a specific height (the amount of work done against gravity).

 

[dance_sg]

"What you need to do is find the component of the force acting along the car's plane of motion"

---> how do i do that?

 

[jgens]

Perhaps you should try the approach using potential energy . . .

Alright, assuming that the hill is essentially an inclined plane, draw your freebody diagram and orient one of your coordinate axes in the direction of the normal force. Now, since force is a vector component, you now need to resolve the gravitational force into its "vertical" and "horizontal" components using trigonometry (the vertical component is opposite the direction of the normal force and the horizontal component is perpendicular to both).

 

[tiny-tim]

"What you need to do is find the component of the force acting along the car's plane of motion"

---> how do i do that?

i] what is the force?
ii] what is the angle?
iii] what is the vector formula for work done?