Physical ScienceCh 5 (Part II): Simple Machines

• A pulley is a grooved wheel with a rope or chain in the groove, which rotates around a fixed point.

• A single fixed pulley is attached to an immovable surface.

It changes the direction of the force, but not the size. So the M.A. is 1.

• A single movable pulley is not attached to a stationary surface, and is free to move.

• A single movable pulley has a mechanical advantage of 2.

• Does the mechanical advantage of 2 for a single movable pulley mean that you’ll increase the amount of work you get out of the pulley?

• No, it doesn’t.

If you get twice as much

force out then you have to

pull out twice as much rope,

but the amount of work (f x d)

would not be effected.

So how could you change the amount of work produced by the machine?

• A block and tackle is a combination of fixed and movable pulleys.

• The M.A. is equal to the number of rope segments supporting the weight.

What is the mechanical advantage of this block & tackle?

• A wheel and axle consists of 2 different sized wheels which rotate together around the same axis.

• The mechanical advantage of a wheel and axle is determined by dividing the radius of the wheel by the radius of the axle.

M.A. = Rw / RA

• A gear is a wheel with interlocking teeth which prevent slippage.

• An inclined plane (ramp) is a slanted surface used to raise or lower objects.

Inclined planes are usually stationary.

• A wedge is a movable inclined plane.

• What does sharpening a knife do to it’s mechanical advantage?

• Is a sharper object always going to perform better than a dull one?

• A screw is an inclined plane wound around a cylinder.

• The closer the threads, the greater the mechanical advantage.

• Which screw would have the greater M.A.?

• Which would be hardest to drive into a block of wood?

• Which would require more turns?

A B

The front sprocket on a bike has 2 gears which act as axles, while the circle created by the pedal acts as the wheel. The outer gear has a radius of 6 inches and the smaller inner one has a radius of 4 inches. If the pedal goes in a circle with a radius of 12 inches, calculate the mechanical advantage provided by each of the different gears.

• In the previous example, which gear would you want to be in if you were pedaling up a steep hill? Why?

The lugnut on a large dump truck has a radius of 5 cm, and requires a force of 1,800 N to loosen. Lenny, however, can only produce 150 N of force. He knows that if he gets a long enough wrench then he can produce that much force. How long would the wrench need to be?

• Carl is applying 200 N of force to push a wheelbarrow up a ramp. If the ramp is 6 m long and allows him to roll the wheelbarrow to a height of 1.5 m, what is the mechanical advantage of the ramp?

• How much force would Carl need to apply if he were not using the ramp?

• How much force would Waylon need to apply in order to lift a 375 N weight, using the pulley shown?

• How much rope would he need to pull out in order to raise the weight 4 m?

• Using the 3 pulleys shown below, how much force would Ned need to apply to each to lift a 400 N weight?

• Why wouldn’t he just always use the one which requires the least force?

• In the diagram below, the inclined plane is 5 m long and 2 m high. The wheel and axle have radii of 25 inches and 10 inches respectively. How much force would be required to move the weight up the inclined plane? (assume no friction)

• How much work is being done by the machine?

• Paul used the setup on the right (called a Bosun’s Chair) to lift himself up to a higher position at his construction site.

• What is wrong with the way Paul has the chair set up?

• What would need to be done in order for the setup to work properly?

• Compare and contrast the operation of the 2 pulleys shown above (1 similarity and 1 difference).

• If they performed the same operation, would they be doing the same amount of work?

• Large water wheels were often used in the past to accomplish such tasks as grinding grain and cutting lumber in lumber mills. Pick one of these tasks, and draw a simple diagram showing how the motion of the water used simple machines to accomplish the task.

• Steamboats required huge wheels to produce the mechanical advantage necessary to turn the rudder. If the wheel in the picture has a diameter of 3 m, and is attached to an axle with a diameter of .5 m, what mechanical advantage would be produced?

• If the pilot applies 500 N of force to produce one complete revolution of the wheel (10 m), how much force was produced and how much work was done?

• What is the total mechanical advantage for the block and tackle setup at the right?

• If 1,000 N was being lifted 20 m, how much force would you need to apply, how much rope would you need to pull out, and how much work would you be doing?

• In the picture, gears A and B are the small gears, C is the large one.

• If C is turned clockwise, what direction(s) will the other gears turn?

• If A is turned counter-clockwise, what direction would B and C turn?

• If C is twice as large as A and B, what M.A. is gained?

• If 100 J of work is used to

turn C, how much work will

A and B do?

• In the diagram below, the inclined plane is 6 m long and 2 m high. The wheel and axle have radii of 20 inches and 10 inches respectively. How much force would be required to move the weight up the inclined plane? (assume no friction)

• How much work is being done by the machine?

• Bob has an old house with very inefficient windows, so he had them all replaced with new insulated windows. When the workers had finished the installation, he noticed a pile of metal weights which were left behind from the old windows. What were they, what purpose did they serve, and how did they work?

• Hint:

• If the elevator shown is in a tall building, would the motor probably be used to turn the wheel or the axle of the pulley?

• What is the device shown above, and how does it work?

• Hint:

• In the huge trebuchet shown below, what purpose do you think the wheel at the bottom serves? Think!

• Using the car jack shown, Dwight was able to raise a 3,000 pound car by only applying 15 pounds of turning force to the handle.

• What mechanical advantage did he gain?

• If the car was raised 1 foot, how many feet did he have to turn the handle?

• What effect did the jack have on the amount of work done?

• Andy is trying to lift a 1,000 pound weight. Tell how much force he would need to apply using each of the pulley systems shown.

A. B.

C. D.