1. Pieces of rock launched from an erupting volcano can reach speeds in excess of 340 m/s. If a piece of volcanic rock leaves the surface of the volcano at 340 m/s, how high above the surface of the volcano will it travel?
2. You are designing the launcher for a pin ball machine. The ball has a mass of 50.0g and will start from rest and must have a speed of 11.8 m/s when it leaves the launcher and can only travel 9cm. If there is no friction, what must be the spring constant of the spring for the launcher to work?
3. The science department has decided to allow Janet to do fall stunts. The department wants to develop a spring system to catch Janet and keep her from hitting the floor when she is dropped. Janet has a mass of about 6.0 kg and will fall from a height of no more than 1.5m above the spring. Determine the spring constant needed for the spring to be used if Janet is to stop in 15cm or less.
4. A large Trampoline can launch a person 5.0m upward into the air. Determine how fast the person is traveling at when they leave the trampoline and reach the maximum height.
5. A 0.100kg potato is tied to a string with a length of 2.50m, and the other end of the string is tied to a rigid support. The potato is held straight out horizontally from the point of the support, with the string pulled taut, and is then released. Determine the speed of the potato at the lowest point of the motion. Determine the tension in the string at the lowest point of the motion.
6. A marble, starting at rest, rolls down a linear ramp. The ramp starts at a height of 0.53m above the bottom and the slope is 1.03m long. The marble has a mass of 120g.
a. Determine the speed of the marble at the bottom of the ramp.
b. A spring with a spring constant of k=20N/m is placed 1m in front of the ramp so that the marble will hit the end of the spring. How far will the spring need to compress to bring the marble to a stop?
7. While traveling along at 96 km/h, a 14.6 kN auto runs out of gas 16 km from a service station. a. Neglecting friction, if the station is on a level 15.7 m above the elevation where the car stalled, how fast will the car be going when it rolls into the station, if in fact it gets there?