Simple Machine Problems

1. The Ramseys are moving to a new town, so they have called in the ACME moving company to take care of their furniture. Debbie, one of the movers, slides the Ramseys’ 2200-N china cabinet up a 6.0-m-long ramp to the moving van, which stands 1.0-m off the ground.
a) What is the ideal mechanical advantage of the incline?
b) If Debbie must exert a 500-N force to move the china cabinet up the ramp with a constant speed, what is the actual mechanical advantage of the ramp?
c) What is the efficiency of the ramp?

a) 6

b) 4.4

c) 73%

 

2. Jack and Jill went up the hill to fetch a pail of water. At the well, Jill used a force of 20.0N to turn a crank handle of radius 0.400m that rotated an axle of radius 0.100m, so she could raise a 60.0N bucket of water.
a) What is the ideal mechanical advantage of the wheel?
b) What is the actual mechanical advantage of the wheel?
c) What is the efficiency of the wheel?

a) 4

b) 3

c) 75%

 

3. When building the pyramids, the ancient Egyptians were able to raise large stones to very great heights by using inclines. If an incline has an ideal mechanical advantage of 4.00 and the pyramid is 15.0m tall, how much of an angle would the incline need in order for the Egyptian builder to reach the top?

14 degrees

 

4. Tom’s favorite pastime is fishing.

a) How much work is required for Tom to reel in a 10.0-kg bluefish from the water’s surface to the deck of a fishing boat, 5.20 m above the water, if the reel of his fishing pole is 85.0% efficient?

b) If Tom supplies a force of 15 N to the reel’s crank handle, what is the actual mechanical advantage of the fishing pole?

c) What is the ideal mechanical advantage of the fishing pole?

 

a) 600 J

b) 6.5

c) 7.6

 

5. A jackscrew with a handle 30.0 cm long is used to lift a car sitting on the jack. The car rises 2.0 cm for every full turn of the handle. What is the ideal mechanical advantage of the jack?

 

94

 

6. Clyde, a stubborn 3500-N mule, refuses to walk into the barn, so Farmer MacDonald must drag him up a 5.0-m ramp to his stall, which stands 0.50-m above ground level.

a) What is the ideal mechanical advantage of the ramp?

b) If Farmer MacDonald needs to exert a 450-N force on the mule to drag him up the ramp with a constant speed, what is the actual mechanical advantage of the ramp?

c) What is the efficiency of the ramp?

 

a) 10

b) 7.8

c) 78%