(A) What Should the Spring Constant Be If We Assume the Spring Has Negligible Mass?

Problem Set 14 Leader: Noah Session 3, week 5 Course: Phys 221 Supplemental Instruction Instructor: Canfield Iowa State University Date: 10/04/14

Note that we will probably not cover everything from this sheet in each session. If you have any issues with remaining questions, bring them to the next session.

1. You are asked to design spring bumpers for the walls of a parking garage. A freely rolling car of mass 1200 kg moving at 0.65 m/s is to compress the spring no more than a distance of 9 cm before stopping. Friction is negligible for parts a and b.

(a) What should the spring constant be if we assume the spring has negligible mass?

(b) If no spring is available from the store with this spring constant, should you buy the spring with the next value up or the next value down?

(c) If the coefficient of kinetic friction between the tires of the car and the pavement is 0.094, what should the new spring constant be?

(d) What should the coefficient of static friction between the tires and the pavement be so that the car does not bounce off the spring back into the driving lane?

(e) If the car comes to a stop in 5 seconds, what is the power output of the spring? (use the coefficient from part a)

(f) Engineers considered the spring design too expensive. If inclines were used instead, how far would the car have to travel up the ramp to stop? The angle of the incline is 1.23 degrees. (treat the car as a point mass)

2. A 50.0 kg marathon runner runs up the stairs to the top of Chicago’s 443-m tall Sears Tower. To lift herself to the top in 15.0 minutes, what must be her average power output in watts?

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