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Homework Problems

 

HW#19   Ch 7: Kinetic Energy and Work

Instructions: Show your work by writing formulas and showing substitutions to earn full credit.

1.    A 40 kg statue is raised a distance of 3 meters by a vertical force of 480 N. Find (a) the work done by the force, (b) the work done by gravity, and (c) the final kinetic energy of the statue if it is released from rest.

2.    Victor the Huge (aka Victor Hugo) runs a race against his friend. Initially they both have the same kinetic energy, but Victor finds that his friend is beating him. When he increases his speed by 25%, he runs at the same speed as his friend. If his mass is 100 kg, what is his friend’s mass?

3.    A 4 kg sack of onions is moving with a speed of 3 m/s when it is at x = 0. It is subjected to a single force Fx that varies with position as shown in the figure below. (a) What is the kinetic energy of the sack when it is at x = 0? (b) How much work is done by the force as the sack moves from x = 0 to x = 4 m? (c) What is the speed of the sack when it is at x = 4 m?

Force versus distance

4.    Valia’s latest invention, designed to appeal to all the dog lovers in the MA community, is a leash made out of a special material that exerts a force Fx = −kx2 − ax3 when it is stretched a distance x, where k and a are constants. Valia is out for a nice walk with her dog when all of a sudden the dog starts chasing after Michael’s cat. Find the work done on the dog by the leash if Valia doesn’t move while her dog runs from x = 0 to x = x0.