2211_Sp21_MT2

PHYS 2211 - Mini-Test 2 - Spring 2021 “In accordance with the Georgia Tech Honor Code, I have completed this test while adhering to these instructions.” Sign your name on the line above

Apollo 13 [50pts] Apollo 13, launched on April 11, 1970, was the seventh crewed mission in the Apollo space program and the third meant to land on the Moon. However, an oxygen tank explosion three days into the mission (at 55hr, 54min) forced cancelling the landing and a change in trajectory was set (at 61hr 29min into the mission) to save the crew. The change led Apollo 13 into what is called a free return trajectory where the Moon’s gravitational force produces a slingshot back to the Earth instead of using the spaceship’s energy which was very limited after the explosion. The image shows Apollo 13 and the point when the explosion and then the change of trajectory from the original (dashed) to the new free return trajectory (solid). Consider the Earth as the origin. Then the position of Apollo 13 with respect to Earth at the moment the change in trajectory is initiated is given by ~ r Earth , and the position of the Moon relative to the Earth is ~ r Moon . The masses of the Earth, Moon, and Apollo 13 are M E , M m , and m a , respectively. All numerical values necessary for this problem can be found in the table below. ~ r Earth < 3 ⇥ 10 8 , 6 . 5 ⇥ 10 7 , 0 > m ~ r Moon < 4 ⇥ 10 8 , 3 . 5 ⇥ 10 7 , 0 > m M E 5 . 97 ⇥ 10 24 kg M m 7 . 35 ⇥ 10 22 kg m a 2 . 89 ⇥ 10 4 kg 1. [10 pts] What is the (vector) gravitational force of the Earth on Apollo 13?

Golfing on the Moon [50pts] Commander Alan Shepard smuggled a couple of golf balls and a golf club when he went to the Moon in the Apollo 14 mission in 1971. He then proceeded to play an out-of-this-world (literally) round of golf – though it was also a most di ffi cult round of golf, given the bulky spacesuit and the lunar surface being too sandy. 1. [5 pts] The acceleration due to gravity at the surface of the Earth is approximately g = 9 . 8 m/s 2 . You can determine this by equating the magnitude of the weight force that an object feels near the surface of the Earth ( mg ) to the magnitude of the gravitational force between the object and the Earth ( GmM e /R 2 e ). If the Moon’s radius is R m = 1 . 73 ⇥ 10 6 m and its mass is M m = 7 . 35 ⇥ 10 22 kg, what is the gravitational acceleration g m on the surface of the moon? 2. [20 pts] A golf ball has mass m = 46 g. When Commander Shepard finally hit the ball, he imparted it an initial velocity ~ v i = < 10 , 5 , 0 > m/s (not his best game). What was the maximum height of the ball’s trajectory above the surface of the Moon? You can assume that there is no air resistance on the Moon. Make sure to start from a fundamental principle and work the problem symbolically first, only plugging in numbers in the final step.

3. [20 pts] How far away did the golf ball get when it fell back to the ground? In other words, what was the horizontal range of this projectile motion? You can again assume there is no air resistance on the Moon. Make sure to start from a fundamental principle and work the problem symbolically first, only plugging in numbers in the final step. 4. [5 pts] Imagine that Commander Shepard did this same play back on Earth – same golf ball ( m = 46 g), same initial velocity ( ~ v i = < 10 , 5 , 0 > m/s), wearing a spacesuit for some strange reason, playing in a sand trap, and pretending air resistance doesn’t exist. Would the ball end up farther away from him (larger horizontal range) or closer to him (smaller horizontal range) than when he did it on the Moon? Explain your reasoning. · y max L · X , 0 , 87 Tex - Nix + Vix t - 8 + 10) 5) . 2 * Double the time bl it is 2x the time to got to ymax - 10 = 61m closer bl gravity is inversely poportiona , 5. a larger gravity 19 . 8) 1 . 6) will make The distances less