Work and Energy Problems
1) WORK DONE VERTICALLY: A 70 kg hiker increases his altitude by 950 m while
hiking to a peak in the flatirons. He then stops to have lunch. Answer the following
questions about this situation.
a. What is the Hiker’s weight?
b. How much work did the hiker do to overcome gravity?
c. How much more gravitational potential energy (GPE) does the hiker now have
compared to what he had at the bottom of the mountain? (explain)
d. Where did this potential energy (GPE) come from? (Try to map this energy
all the way back to the sun!!)
e. (bonus) If this same hiker went hiking again the next day and gained
450,000 J of GPE, to what height did he hike this time? He started at an
altitude of 5600 feet. Watch units here! 1 m = 3.28 ft.
2)
WORK DONE HORIZONTALLY: A sprinter is running full speed at a constant
9.5 m/s. She is pushing of with a force of 200 N to maintain this constant
speed, and sprints at this speed for 75 m. Answer the following questions.
a. What kind of force is she working against? (name it)
b. How much work does she do against this force?
1
c. How much more potential energy does she have at the end of the 75 m
compared to the beginning? Why?
d. (bonus) If a different sprinter does 12,500 J of work during the same sprint
and also maintains a constant speed, how much force does this other
sprinter exert against the ground?
3)
A 52 kg cheetah can go from 0 to a maximum speed of 30 m/s.
a. How much kinetic energy (KE) does the cheetah have at top speed?
b. How much work does the cheetah do to get from rest to top speed?
c. Bonus: If the cheetah exerts a force of 1170 N to get from rest to top
speed, over what distance does the cheetah accelerate to get to top speed?
d. Bonus: If this cheetah’s 33 kg cub can only give herself 6600 J of kinetic
energy (KE) when accelerating from rest to top seed, what is the cub’s top
speed?
e. Bonus: If the cheetah’s other cub can only reach a top speed of 15 m/s, and
does this by giving herself a kinetic energy of 2000 J, what is this other
cub’s mass?
2