Pulley Systems Examples: 45 Problems with Answers

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Pulley Systems.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Physics.

Concept Recap

Pulley systems are arrangements of ropes and wheels used to change the direction of a force or to gain mechanical advantage.

A pulley can make lifting easier by sharing the load between several rope segments.

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How to Use These Examples

Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Pulley Systems asks students to choose the object, list external interactions, and reason from the resulting force or torque pattern.

Common stuck point: Students often know a formula related to pulley systems but skip the recognition step: Have I isolated one system and listed the external forces or torques acting on it before applying a law? That leads to a correct-looking substitution attached to the wrong physical model.

Sense of Study hint: Ask: Have I isolated one system and listed the external forces or torques acting on it before applying a law?

Worked Examples

Example 1

easy

Show that a fixed pulley does no useful multiplication of force. Pull

90\,\text{N}

on the rope; what weight is lifted at constant speed?

Answer

W = 90\,\text{N}

First step

Isolate the load: tension up, weight down,

a = 0

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Example 2

medium

A pulley system has ideal

MA = 4

but only

75\%

efficient. To lift a

600\,\text{N}

load, what force is actually needed?

Example 3

hard

An Atwood machine (

5\,\text{kg}

and

3\,\text{kg}

g = 10\,\text{m/s}^2

) is released from rest. After

2.0\,\text{s}

, what speed does each block have?

Example 4

hard

An Atwood machine with

m_1 = 5\,\text{kg}

and

m_2 = 3\,\text{kg}

is released from rest with

m_1

starting

1.6\,\text{m}

above the floor (

g = 10\,\text{m/s}^2

). With what speed does

m_1

hit?

Atwood: 5 kg starts 1.6 m high; find speed at floor ≈ 2.83 m/s

Example 5

challenge

In an Atwood machine the pulley has moment of inertia

I = 0.02\,\text{kg}\cdot\text{m}^2

and radius

r = 0.10\,\text{m}

. Masses are

m_1 = 4\,\text{kg}

and

m_2 = 2\,\text{kg}

(

g = 10\,\text{m/s}^2

). Find the acceleration.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy

A single fixed pulley redirects a rope to lift a

50\,\text{N}

load at constant speed. Ignoring friction, what force must you pull with?

Forces on the 50 N load at constant speed (single fixed pulley)

Example 2

easy

In an ideal massless rope over a frictionless pulley, how does the tension compare on the two sides?

Example 3

easy

A movable pulley supports a load with two rope segments. To lift a

60\,\text{N}

load, what is the ideal pull force?

Movable pulley: two rope segments share the 60 N load

Example 4

easy

A pulley system has 4 rope segments supporting the load. What is its ideal mechanical advantage?

Example 5

easy

To lift a load using a system with mechanical advantage 3, you pull

20\,\text{N}

. What load can you lift (ideal)?

Example 6

easy

With a single movable pulley you pull the rope

2\,\text{m}

. How far does the load rise (ideal)?

Example 7

easy

A 100 N load hangs from a movable pulley supported by two rope segments. What is the tension in the rope (ideal)?

Movable pulley supporting 100 N; find the rope tension

Example 8

easy

Does an ideal pulley system let you do less total work to lift a load to a given height?

Example 9

medium

An Atwood machine has masses

3\,\text{kg}

and

1\,\text{kg}

over a frictionless pulley (

g = 10\,\text{m/s}^2

). Find the acceleration.

Atwood machine: 3 kg mass (net downward force gives a

Example 10

medium

For the same Atwood machine (

3\,\text{kg}

1\,\text{kg}

a = 5\,\text{m/s}^2

g = 10\,\text{m/s}^2

), find the rope tension.

Atwood machine: 1 kg mass accelerates upward, T

Example 11

medium

A 2 kg block on a frictionless table is connected over a pulley to a

3\,\text{kg}

hanging block (

g = 10\,\text{m/s}^2

). Find the acceleration.

Example 12

medium

In the table-pulley system (

2\,\text{kg}

on table,

3\,\text{kg}

hanging,

a = 6\,\text{m/s}^2

g = 10

), find the rope tension.

2 kg table block: T

Example 13

medium

A block-and-tackle with 5 supporting segments lifts a

500\,\text{N}

load at constant speed. Find the ideal pull force.

Example 14

medium

A pulley system with MA 4 lifts a load

0.5\,\text{m}

. How much rope must be pulled?

Example 15

medium

An Atwood machine with

5\,\text{kg}

and

5\,\text{kg}

over a frictionless pulley. Find the acceleration and tension (

g = 10\,\text{m/s}^2

Example 16

medium

A 200 N load is lifted by a system. You pull

80\,\text{N}

to lift it at constant speed (with friction). Find the actual mechanical advantage.

Example 17

medium

An Atwood machine has masses

7\,\text{kg}

and

3\,\text{kg}

over a frictionless pulley (

g = 10\,\text{m/s}^2

). Find the acceleration.

Example 18

challenge

An Atwood machine:

4\,\text{kg}

and

2\,\text{kg}

g = 10\,\text{m/s}^2

. The

4\,\text{kg}

mass starts

1.8\,\text{m}

above the floor and is released. Find the time to reach the floor.

Example 19

challenge

A 6 kg block on a frictionless incline at

30^\circ

is connected over a pulley to a hanging

4\,\text{kg}

block (

g = 10\,\text{m/s}^2

\sin 30^\circ = 0.5

). Find the acceleration (positive if the hanging block descends).

6 kg block on 30° incline connected to hanging 4 kg; find a

Example 20

challenge

A block-and-tackle with MA 3 is used to lift a

300\,\text{N}

load, but the system is only 80% efficient. Find the actual force you must pull.

Example 21

easy

A single fixed pulley redirects the rope used to lift a

75\,\text{N}

bucket at constant speed. What pull force is required (ideal)?

Example 22

easy

A movable pulley supports a

120\,\text{N}

load with two rope segments. Find the ideal pull force.

Movable pulley: two rope segments split the 120 N load

Example 23

easy

You pull

15\,\text{N}

on a system with ideal

MA = 5

. What load can you lift at constant speed?

Example 24

easy

80\,\text{N}

weight hangs from a movable pulley supported by two rope segments. What is the rope tension (ideal)?

Movable pulley supporting 80 N load; rope tension T

Example 25

medium

An Atwood machine has masses

4\,\text{kg}

and

2\,\text{kg}

over a frictionless pulley (

g = 10\,\text{m/s}^2

). Find the acceleration.

Example 26

medium

For the Atwood machine in the previous question (

4\,\text{kg}

and

2\,\text{kg}

a \approx 3.33\,\text{m/s}^2

g = 10\,\text{m/s}^2

), find the tension.

Atwood 2 kg side: T ≈ 26.7 N, accelerates upward at 3.33 m/s²

Example 27

medium

4\,\text{kg}

block on a frictionless table is connected over a pulley to a

6\,\text{kg}

hanging block (

g = 10\,\text{m/s}^2

). Find the acceleration.

4 kg table block pulled by rope over pulley toward 6 kg hanging mass

Example 28

medium

Using the previous setup (

4\,\text{kg}

on table,

6\,\text{kg}

hanging,

a = 6\,\text{m/s}^2

g = 10\,\text{m/s}^2

), find the rope tension.

Example 29

medium

A block-and-tackle with 6 supporting segments lifts an

840\,\text{N}

load at constant speed. Find the ideal pull force.

Example 30

medium

An ideal pulley system with

MA = 5

lifts a load

0.4\,\text{m}

. How much rope must be pulled?

Example 31

medium

An Atwood machine has masses

8\,\text{kg}

and

8\,\text{kg}

(

g = 10\,\text{m/s}^2

). Find the acceleration and tension.

Example 32

medium

400\,\text{N}

load is lifted at constant speed when you pull

200\,\text{N}

(with friction). Find the actual mechanical advantage.

Example 33

medium

An Atwood machine has masses

9\,\text{kg}

and

6\,\text{kg}

(

g = 10\,\text{m/s}^2

). Find the acceleration.

Example 34

medium

For the Atwood (

9\,\text{kg}

6\,\text{kg}

a = 2\,\text{m/s}^2

g = 10\,\text{m/s}^2

), find the tension.

Example 35

medium

A worker pulls

3.6\,\text{m}

of rope through a system with

MA = 3

to raise a load. How high did the load rise (ideal)?

Example 36

hard

Two masses

m_1 = 10\,\text{kg}

and

m_2 = 6\,\text{kg}

are connected over a pulley. The pulley itself has friction giving a constant retarding torque equivalent to

4\,\text{N}

of opposing tension difference. Find the acceleration (

g = 10\,\text{m/s}^2

Example 37

hard

4\,\text{kg}

block on a frictional table (

\mu_k = 0.2

) is pulled by a rope over a pulley to a

3\,\text{kg}

hanging block (

g = 10\,\text{m/s}^2

). Find the acceleration.

4 kg block on table with μ_k=0.2; friction opposes tension from 3 kg hanging mass

Example 38

hard

A block-and-tackle with

MA = 4

lifts a

500\,\text{N}

crate

2.0\,\text{m}

. The system is

80\%

efficient. How much work does the user do?

Example 39

hard

5\,\text{kg}

block on a frictionless

37^\circ

incline is connected over a pulley to a hanging

2\,\text{kg}

block (

g = 10\,\text{m/s}^2

\sin 37^\circ = 0.6

). Find the acceleration with the incline block sliding down.

5 kg block on 37° incline connected to 2 kg hanging mass; incline block slides down at a ≈ 1.43 m/s²

Example 40

challenge

A compound pulley uses two movable pulleys in series, each adding a factor of 2 to the MA, plus a fixed direction-change pulley. What is the ideal MA, and what pull lifts a

400\,\text{N}

load?

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Related Concepts

Tension Equilibrium

Background Knowledge

These ideas may be useful before you work through the harder examples.

tensionequilibrium