Gravitational Force Between Triton and Neptune
1 (5 points): When it exploded, the Death Star was traveling through space at about 460 kilometers per second while moving along a parabolic path towards the Rebel base on Yavin 4. How did its center of mass move after it exploded? Assume that any gravitational effects from Yavin and its moons and any changes in momentum from collisions were negligible.
2 (10 points): A catapult launches a 25-kilogram rock at 30 m/s.
A: If the rock lands 86 meters away from the catapult, at what angle was it launched?
B: What is its maximum potential energy?
3 (15 points): The Nardò Ring is a test track in northern Italy owned by Porsche. The track is circular, has a radius of 2 kilometers, and is one of the fastest tracks in the world.
A: The current speed record on the Nardò Ring was set by a Volkswagen W12 in 2002. It circled the Nardò Ring for 24 hours at an average speed of 89.69 m/s. What was its average centripetal acceleration?
B: In 2003, Loris Bicocchi was test driving a prototype of the Bugatti Veyron along the Nardò Ring when two of his tires exploded. He was traveling at about 110 meters per second at the time and managed to stop the car by sliding the side of the car along the guard rail. He managed to bring the car to a stop after driving for about 1.8 kilometers – and escaped with only minor injuries. What was the coefficient of friction between the car and the guard rail? (Assume that friction was the only thing affecting how the car moved.)
C: How much time did it take Bicocchi to stop the car?
4 (20 points): The Moon has a mass of kg and an average radius of 1,737.4 km.
A: What is the acceleration due to gravity on the surface of the Moon?
B: The lunar excursion modules (LEMs) used during the Apollo program had a mass of roughly 15,200 kg. During the Apollo 11 mission, the LEM accelerated from about 7 m/s to about 0.762 m/s over the course of roughly one minute. What was the net force acting on the LEM?
C: How much force was the LEM’s engine exerting?
D: How much work was done on the LEM?
5 (10 points): The Voyager 1 space probe is moving away from Earth at approximately 17 km/s, relative to the Sun. It communicates with Earth using radio signals traveling at the speed of light ( m/s) transmitted at either 2.3 GHz or 8.4 GHz.
A: What are the wavelengths of these two signals?
B: The Earth orbits the Sun at approximately 30 km/s. If Voyager 1 transmits a signal at 8.4 GHz, what frequency will an observer on Earth receive if the Earth is moving directly towards the spacecraft? What frequency will an observer on Earth receive if the Earth is moving directly away from the spacecraft?
6 (25 points): Captain Marvel intercepts a Kree warhead traveling towards Earth. Captain Marvel has a mass of 60 kilograms and is flying away from the Earth at 15 kilometers per second. The warhead has a mass of 2000 kilograms and is traveling towards the Earth at 7 kilometers per second. She was far enough away from Earth that its gravity was negligible.
A: Captain Marvel catches the warhead, which essentially means she collides with the warhead in a head-on, inelastic collision. What is their velocity after the collision?
B: After thirty seconds, Captain Marvel brings the warhead to a stop, relative to the Earth. How much force did she exert on the warhead?
C: Once she’s stationary, Captain Marvel takes the warhead by its tip and flings it towards the Kree spacecraft that launched it, causing the warhead to tumble end over end. Assume the warhead is a solid right cone rotating through its center of mass () with a diameter of 2 meters and a height of 2.5 meters. If it took her 1.65 seconds to get the warhead spinning at 3.5 revolutions per second, how much torque did she exert on the warhead?
D: After Captain Marvel throws the warhead, it moves away from her at 3.3 meters per second while spinning. What is the warhead’s total kinetic energy?
E: Describe how Captain Marvel moves after she throws the warhead. Assume she doesn’t exert any forces or torques to try to stop herself.
7 (15 points): Triton has a mass of kilograms and orbits Neptune at an average distance of 354,759 kilometers. It takes Triton about 5.88 days to complete one orbit.
A: Use Triton’s orbit to calculate the mass of Neptune.
B: What is the gravitational force between Triton and Neptune?
C: How much work does Neptune do on Triton over the course of one complete orbit? Explain your reasoning.