AP Physics Particle Mechanics Problem with Solution

Today I would like to provide a solution to yesterday’s AP Physics Particle Mechanics question. Here is the question one more time, followed by an explanation:

Particle Mechanics Free Response Question with Explanation

Superman is able to leap over tall buildings in a single bound. The tallest building in the world is currently the Burj Khalifa in Dubai, which is about 800 m tall and will soon be overtaken by the Jeddah Tower in Saudia Arabia, which will be 1 km tall. Assuming that Superman’s legs act like springs and that he can bend them 0.5 m, estimate the strength of Krypton’s gravitational acceleration relative to the Earth’s.

Solution: If Superman is able to leap over a building of height h, he must give himself an energy mg_eh, where m is his mass and g_e  is the Earth’s gravitational acceleration. If this energy is to be supplied by the springs in his legs, by energy conservation we must have mg_eh = 1/2 kx², where x is the amount he can bend them and k is his legs’ effective spring constant. On Krypton he must be able to support his own weight by his legs, and so we require by Hooke’s law mg_k = kx, where g_k is the gravitational acceleration on Krypton. Thus, g_k/g_e = 2h/x. If h = 1000 m and x = 0 .5 m, then g_k/g_e = 4000. Krypton is a truly exceptional planet.

More Test Prep Books from Get 800

Check out my product page to see all of the other books from the Get 800 collection: Get 800 Product Page

If you think your friends might be interested in this article, please share it with them on Facebook:

Thank you all for your continued support!

Comments

comments