Principles of Engineering
Name: ________________________
Simple Machines Problems
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Inclined Planes
What are the formulas for calculating the ideal mechanical advantage and the actual
mechanical advantage of the inclined plane?
A wheelchair ramp is 10 m long and 2 m high. A 450 N person in a wheel chair roles
up the incline.
a. Sketch and annotate the incline system described above.
b. What is the ideal mechanical advantage of the ramp? (5 m)
c. If the ramp has 100% efficiency, how much force does the person have to
apply to roll up the ramp?
A flight of stairs was originally 5 meters high. A switch-back ramp was put in to
make it handicap accessible. The new ramp is now 50 meters long. What is the
ideal mechanical advantage? (10)
A box weighing 100 N is pushed up an inclined plane that is 5 meters long. A force
of 75 N is required to push it up the incline. If the box is lifted 2 meters, calculate
the:
a. Ideal mechanical advantage (2.5)
b. Actual mechanical advantage (1.3)
c. Efficiency (52%)
What could you do to increase the mechanical advantage of the inclined plane?
Levers
What are the formulas for calculating the ideal and actual mechanical advantages of
a lever?
A car jack has an effort arm of 45 centimeters. The resistance arm is 6 centimeters.
What is the ideal mechanical advantage of the jack? (7.5)
A seesaw 4 meters long has a fulcrum at the center. What is the ideal mechanical
advantage of the seesaw? (1)
A crowbar, 1 meter long, is used to pryopen a box. The fulcrum of the crow bar is
0.2 meters from the resistance end. What is the ideal mechanical advantage of the
crow bar? (4)
A first class lever in static equilibrium has 50 lb resistance hanging from one end.
15 lb of effort is applied 4 ft from the fulcrum.
a. Sketch and annotate the lever system above.
b. What is the actual mechanical advantage of the system?
c. Assuming a 100% efficient machine, calculate the length from the fulcrum to
the resistance force?
A wheel barrow is used to lift a 200 lb load. The length from the center of the wheel
to the center of the load is 2 ft. The length from the wheel to the effort is 5 ft.
a. Illustrate and annotate mechanical advantage of the system.
b. What is the ideal mechanical advantage of the system?
c. Calculate the ideal effort force needed to overcome the resistance force in the
system if it is 100% efficient.
Pulleys
1. How do you calculate the ideal and actual mechanical advantage of a pulley(you
should have three methods listed in your answer)?
2. Explain the difference between a fixed pulley and moveable pulley.
3. A window blind is pulled down 3 feet to raise the blind 2 feet. What is the
mechanical advantage of the blind?
4. Study the following pulley systems and determine their ideal and actual mechanical
advantages.
For the following pulley systems assume that they have 100% efficiency.
a. IMA = _______________________
Effort Force = _____________________
Effort Distance= _____________________
b. IMA = _______________________
Effort Force = _____________________
Effort Distance= _____________________
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Wheel and Axle
What is the formulas for calculating the ideal mechanical advantage and actual
mechanical advantage of a wheel and axle system?
A wheel and axle can have a mechanical advantage less than 1. Give an example of
occurring and describe why it would be an advantage.
A wheel and axle can also have a mechanical advantage greater than 1. Give an
example of this occurring and describe what the advantage of this is.
What is the formula for calculating the linear distance traveled by a wheel?
What is the linear distance traveled in one revolution of a 36 in diameter wheel?
An industrial water shutoff valve is designed to operate with 30 lb of effort force.
The valve will encounter 200 lb of resistance force applied to a 1.5 in diameter axle.
a. What is the required actual mechanical advantage of the system?
b. What is the required minimum diameter required for the wheel to overcome
the resistance force?
A car has wheels with a diameter of 27 in. The axle of the care is 5 in.
a. What is the IMA of this system?
b. How far does the car travel with one rotation of the axle?