Physics graph question

[burnitup1]

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Which of the graphs below best represents gravitational potential energy versus the radius of the planet?

The picture is attached. Sometimes I am pretty bad at reading graphs. What is the best way to think about this problem? Thanks!

FYI the answer is d but I thought it was c. Please help!

 

[milski]

Gravitational potential increases as you go further away from the center of the planet. As such, the answer has to be either B or D. You also need to know that it increases towards some asymptotic value and not towards infinity - that value is set to be 0 by convention and that's what makes D the correct answer and not B.

C is certainly incorrect - it shows the potential energy decreasing when going further away form the planet - that would be equivalent to objects falling away from it, not towards it.

 

[circulus vitios]

U = -GMm/r

The relevant part is U ∝ -1/r. The radius between planets can't be negative so start at 0 and plug in increasingly large values for r.

For small r, the ratio 1/r is as large as it's going to be and the ratio -1/r will therefore be the most negative.

For large r, the ratio 1/r is as small as it's going to be and the ratio -1/r will therefore be the least negative.

A. Shows all values of U being greater than 0. This can't be correct.

B. Same reason for A: all values of U are shown being greater than 0.

C. For small r, this graph shows U being the most positive. Wrong.

 

[burnitup1]

Thanks so much guys. Your explainations really helped. I just get freaked out whenever I see graphs, but you made it pretty simple.

circulus vitios- thanks for the trick about just looking at the relevant part of the equation and plugging in values. I will use this trick next time 🙂