Real World Energy Problems

Groups A,E => Problem 1

Groups B,F => Problem 2

Groups C,G => Problem 3

Groups D,H => Problem 4

 

Problem 1.

The Navy wants a new airplane launcher for their aircraft carriers and you are on the design team. The launcher is effectively a large spring that pushes the plane for the first 5 meters of the 20 meter long runway. During that same time, the plane's jet engines supply a constant thrust of 5.4 x 104 N for the entire length of the runway. The 2000 kg planes need to have a velocity of 45 m/s by the end of the runway. What should be the spring constant for the launcher?

 

Problem 2.

You want to show your appreciation to the school by performing a stunt during the half-time show of the Homecoming football game. You are going to drive a car through the loop of radius R = 40 feet as shown below. You definitely want to stay on the track the whole time, and you want to jump off the end of the track when you are done.

  1. As a safety factor, you want the car to make it through the loop even if the engine fails. How high does ramp have to be if you assume 30% of the initial energy is transformed into heat due to friction and air resistance. You know that your car weighs about a ton with gas and your own weight included.

 

Problem 3.

A child's game consists of a block that attaches to a table with a suction cup, a spring connected to that block, a ball, and a launching ramp. By compressing the spring, the child can launch the ball up the ramp.

The spring has a spring constant k, the ball has a mass m, and the ramp rises a height h. The spring is compressed a distance s in order to launch the ball. When the ball leaves the launching ramp its velocity makes an angle q with respect to the horizontal.

  1. Assuming that friction and air resistance can be ignored for the purposes of this problem, describe the changes in the forms of energy in the system from the time the spring is compressed until the ball first hits the ground.
  2. Calculate the vector velocity of the ball when it leaves the launching ramp. Be sure to specify your coordinate system.
  3. The spring constant = 32 N/m, the spring's compression is 5 cm, the ball's mass is 20 grams, the height of the ramp is 10 cm, and the top of the table is 1 m above the floor. With what speed will the ball hit the floor? (Use g » 10 m/s2.)

 

 

Problem 4.

For next year's Physics Open House the Department is planning to set up a bungee jump from the top of the physics building. Assume that one end of an elastic band will be firmly attached to the top of the building and the other to the waist of a courageous participant. The participant will step off the edge of the building to be slowed and brought back up by the elastic band before hitting the ground (we hope). Estimate the length and spring constant of the elastic you would recommend using.