Reference no: EM131157489
The Energetic
1. Ski run: A 65 kg skier skis down an icy hillside, losing 50 m of altitude while moving 120 m horizontally. Assume that air drag and friction between the skis and the ice are negligible.
a) If she starts from rest, how fast will she be going at the bottom? Instead, she starts by pushing her ski poles strongly backwards, so that the ground exerts an approximately constant force on her of 200 N as she moves the first 1.2 meters forwards.
b) How fast will she be going at the end of the 1.2 meter push-off? c) How much faster will she be going at the bottom of the hill than if she'd started from rest? Now assume that she starts from rest as in part (a), but a strong headwind exerts a constant Horizontal force of 80 N on her all the way to the bottom.
d) How fast will she be going when she reaches the bottom? e) Why can you answer (d) without knowing the precise shape of the hillside? Justify your response carefully.
2. Railroad accident: You have been hired to investigate a railroad accident. One night, a 3300 kg railroad car was left parked on top of a hill, while a second 3300 kg car was standing down below. In the morning, both cars are found coupled together in a lake, as shown in the figure. (The tracks extend right to the shore, to facilitate loading boats with ore.) The company accuses the engineer of forgetting to set the brake on the upper car, so that during the night it rolled down, hit, and coupled to the lower car, and its momentum carried both into the lake. The engineer denies this, saying that someone must have released the brake and pushed the upper car. Can you use physics to determine whether the engineer is correct?
3. Moonshot: NASA has hired you to design an electromagnetic cannon that can launch containers from the surface of the moon fast enough to escape the moon's gravitational pull. The containers will have masses ranging from 150 kg to 3000 kg.
a) What initial speed must the cannon give the containers so that they will be moving at 500 m/s (relative to the moon) when they're very far from the moon? (You may ignore Earth's gravity for this part.)
b) What is the minimum initial speed necessary for the containers to make it to Earth, if fired directly towards Earth from the moon? (You may not ignore Earth's gravity for this part!)
4. Bond: Two molecules interact in a complicated way that can be described by the potential energy (V) vs. separation (r) graph shown. They are placed 16 nm apart and released from rest.
a) Describe their subsequent motion in detail.
b) What is the closest they will get?
c) At what separation distance(s) will they reach their maximum speed?
d) At what separation distance(s) could they be placed such that they would neither attract nor repel?