Worksheet: Mechanical Advantage of Machines

In this worksheet, we will practice calculating the mechanical advantage produced by machines that apply forces over distances, such as pulleys and gears.

Q1:

A system of pulleys is used to lift a load of 45 N a distance of 1.5 m by applying a force of 15 N. What is the mechanical advantage of the pulley system?

Q2:

Which of the following is a correct definition of the mechanical advantage provided by a machine to which an input force 𝐹IN is supplied and which produces an output force 𝐹OUT?

  • A(𝐹−𝐹)2INOUT
  • B𝐹−𝐹INOUT
  • C(𝐹+𝐹)2INOUT
  • D𝐹𝐹INOUT
  • E𝐹𝐹OUTIN

Q3:

Two gear wheels have lever arm lengths of 𝑑 and 𝑑, as shown in the diagram. The larger wheel is used to turn the smaller wheel. The input force used to turn the larger wheel is 35 N and the output force from the smaller wheel is 70 N.

What is the mechanical advantage of using the larger wheel to turn the smaller wheel?

What is the ratio of 𝑑 to 𝑑?

Q4:

A block with weight 𝑊 is lifted a distance 𝑑 by a rope that slides over a pulley, as shown in the diagram. The rope is pulled a distance 𝑑 when a force 𝐹=𝑊 is applied.

Which of the following is the correct relation between the magnitudes of 𝑑 and 𝑑?

  • A𝑑>𝑑
  • B𝑑<𝑑
  • C𝑑=𝑑

Which of the following is a correct possible value for the mechanical advantage of the pulley?

  • A1
  • B𝑑𝑑
  • C𝑑𝑑

Q5:

A uniform cubic block is attached to two ropes, each rope the same horizontal distance from the block’s center of mass, as shown from above in the diagram. The ropes are sliding around some fixed pulleys and are pulled simultaneously to move the block so that it does not rotate. The masses of the pulleys and ropes are negligible and produce negligible friction. Which of the following statements correctly describes the relationship between the rate at which the free ends of the ropes move perpendicularly to the line P?

  • AThe ends of both ropes move at the same rate.
  • BThe end of rope I moves faster.
  • CThe end of rope II moves faster.

Q6:

A block with weight 𝑊 is suspended at rest from a rope that slides over a frictionless and weightless pulley, as shown in the diagram. The force on the end of the rope that does not suspend the weight prevents the weight from falling. The force on the same end of the rope is increased by F, and the weight is lifted a distance 𝑑 when the rope is pulled a distance 𝑑.

What is the ratio of 𝑑 to 𝑑?

What is the ratio of F to 𝑊?

What is the mechanical advantage of the pulley?

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