1 Springs A 25.0 cm spring stands vertically on the ground, with its lower end secured in a base. A 1.5 Kg brick is held 40 cm directly above the spring and dropped onto the spring. The spring compresses to a length of 17.0 cm before starting to launch the brick back upward. Problem 1.1. Draw a pictorial diagram describing the brick and the spring system. Problem 1.2. What is the change in kinetic energy between the moment when the brick is dropped and the moment the spring stops compressing? Problem 1.3. What is the work done by the force of gravity?Problem 1.4. What is the work done by the spring? Problem 1.5. What is the spring’s spring constant?
1 Springs
A 25.0 cm spring stands vertically on the ground, with its lower end secured in a base. A 1.5 Kg brick is held 40 cm directly above the spring and dropped onto the spring. The spring compresses to a length of 17.0 cm before starting to launch the brick back upward.
Problem 1.1. Draw a pictorial diagram describing the brick and the spring system. Problem 1.2. What is the change in kinetic energy between the moment when the brick is
dropped and the moment the spring stops compressing? Problem 1.3. What is the work done by the force of gravity?Problem 1.4. What is the work done by the spring? Problem 1.5. What is the spring’s spring constant?
2 Center of Mass
You have just finished a space walk where you were fixing your space telescope using a tool with a mass that is one tenth of yours. You realize you have no way to get back to your spaceship which is 10 meters away from you, so you throw the tool as hard as you can in the opposite direction of the spaceship which causes you to move toward the spaceship.
Problem 2.1. When you finally reach the spaceship, how far away are you from the tool?
3 Momentum
In 1977 the planet Alderaan, with a mass of 3 × 1024 kg, exploded. Assume it was initially at rest and experienced no external interactions.
Problem 3.1. If the planet blew apart into two pieces with 40% of its mass flying away in one piece at 4,000 km/s, what speed did the rest of the planet have relative to its original frame?
Problem 3.2. Consider instead that the planet instead blew apart into three pieces, with 30% of its mass flying away at 3, 000 km/s, and 20% of its mass flying away at 5, 000 km/s at an angle of 120o relative to the velocity direction of the first fragment. Draw a diagram of this situation. What velocity did the rest of the planet have? Report the direction by specifying its angle relative to the velocity direction of the first fragment.
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