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- How much gravitational potential energy (in J) (relative to the ground on which it is built) is stored in an Egyptian pyramid, given its mass is about 6 ✕ 109 kg and its center of mass is 26.0 m above the surrounding ground? What is the ratio of this energy to the daily food intake of a person (1.2 ✕ 107 J)?A person on an icy expedition is trying to lower a crate of mass m1 = 5.65 kg crate to the bottom of a steep ravine of height h2 21.8 m using a rope over a simple pulley. The person, who m2 frictionless %| weighs m2 = 60.9 kg, is being careful to lower the crate at a constant speed of 1.50 m/s. Unfortunately, when the crate reaches a point h = 12.1 meters above the ground, the person slips and the crate immediately accelerates toward the ground, dragging the hapless person across the ice and toward the edge of the cliff. h If we assume the ice is perfectly slick (that is, no friction between the person and the ice once he slips and falls down), at what speed will the crate hit the ground? Assume also that the rope is long enough to allow the crate to hit the ground before the crewman slides over the side of the cliff. speed: m/s At what speed will the person hit the bottom of the ravine? (Assume no air friction.) speed: m/sThe Top Thrill Dragster at Cedar Point amusement park in Sandusky, Ohio, is one of the world’s most impressive roller coasters. Wearing only a lap harness in the open air, riders on a 10.5-ton train are accelerated by hydraulic motors on a level track to 120 mph in just 3.8 s. After this, no more power is supplied to the train, and it moves on its own. The train shoots straight up (twisting along the way) along the track to a height of 420 ft, before a straight-down descent. Calculate the kinetic energy of the train after the 3.8-s launch. Round the final answer to two decimal places.
- 15. The following plot shows the speed v(r) at which stars orbit about the center of a galaxy, as a function of their distance r from the center. v(r) Assuming the galaxy has a spherically symmetric mass distribution, which plot best shows the mass of the galaxy M(r) enclosed within radius r?Match the graph shown below with the correct set of m, b and r. 2.5 2 2 1.5 0.5 0.05 0.1 0.15 0.2 mass (kg) m 0.80 s/kg b = 1.2 s r= 0.852 m = 8.0 s/kg b 1.2 s r= 0.995 3. 1.