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

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Homework Help Overview

The problem involves calculating the work done on a car by gravity as it rolls down an inclined plane. The car has a mass of 1500 kg and travels a distance of 150 m down a hill inclined at an angle of 15º.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss different definitions of work and suggest finding the gravitational force component along the incline. Questions arise about how to resolve forces and the appropriate formulas for calculating work.

Discussion Status

Some participants have provided guidance on using gravitational potential energy and resolving forces into components. Multiple approaches are being explored, but there is no explicit consensus on the best method to proceed.

Contextual Notes

Participants are questioning the definitions and components involved in calculating work, indicating a need for clarification on the physics concepts at play. There is also an emphasis on drawing free-body diagrams and using trigonometry to resolve forces.

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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)?
 
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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.
 


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).
 


"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?
 


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).
 
dance_sg said:
"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?
 

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