Gravitational potential energy of a car

[mike168]

Homework Statement

What is the gravitational potential energy of a car with centre of mass at a height h above the ground? On a level road the centre of mass is at a height of 0.1m above the ground.

Homework Equations

gravitational potential energy=mgh

The Attempt at a Solution

I would use the formula mgh to calculate the gravitational potential energy of the car. However, the book gives mg(h-0.1) as the answer. I am not convinced because I think the definition of gravitational potential energy is related to the position of the centre of mass above the ground, not its change of gravitational energy before and after. Am I correct?

 

[e^(i Pi)+1=0]

It depends on how you set up your coordinates. Either would give you correct answers when working problems.

 

[cepheid]

You can define the zero point to be wherever you want. Only changes in potential energy are relevant, not absolute values. So, if you define the GPE to be 0 when the car is on a level road, you're defining the GPE to be 0 at a height of 0.1 m above the road. So really the GPE in this case is given by mgy, where y = 0 at the position 0.1 m above the road. A height h above the road corresponds to a position of the centre of mass of y = h-0.1 m above the point where the GPE has been defined to be zero. Hence the GPE here is mgy = mg(h-0.1).

Instead, you could have defined GPE to be 0 at h = 0, in which case the car would have GPE mg(0.1 m) on a level road, and a GPE of mgh at the point specified in the problem. But this does not change the fact that the difference in GPE between the two points is mg(h-0.1)

An analogy is elevation. Really only differences in elevation matter. I could measure elevation from sea level, in which case, if I was at sea level, my elevation would be 0, and if I was 300 m above sea level, my elevation would be 300 m.

Alternatively I could measure elevation from the centre of the earth, in which case my elevation at seal level would be approx 6400 km, and my elevation at a point 300 m above sea level would be approx 6400.3 km. But the absolute elevation values don't really matter so much as the difference between them. Nothing has changed in the second case. The higher elevation point is still 300 m above the sea level point.

 

[mike168]

So the question in the book is inaccurate? We should always say gravitational potential energy "with respect to a reference point"?

 

[cepheid]

The question is indeed ambiguous. It should say something like, "what is the GPE of a car with its centre of mass at a height h above the ground given that we define its GPE to be 0 when it is on a level road with its centre of mass at 0.1 m above the ground?" This qualification makes it clear what the reference point is.

Without this qualification, a reasonable person would assume that the GPE was being measured using the ground as a reference point (i.e. GPE = 0 when h = 0).

 

[mike168]

cepheid,
Thanks for your clarification.