Tension Examples in Physics

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

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

Concept Recap

The pulling force transmitted through a rope, string, or cable when it is pulled taut at both ends.

The 'tightness' you feel in a rope when both ends are being pulled in opposite directions.

Read the full concept explanation →

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: Tension 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 tension 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

3 \text{ kg}

lamp hangs from a single vertical rope. What is the tension in the rope? Use

g = 9.8 \text{ m/s}^2

Lamp hanging from a single vertical rope

Answer

T = 29.4 \text{ N}

First step

The lamp is in static equilibrium, so the net force is zero.

Full solution

2
The tension must balance the weight: $T = mg = 3 \times 9.8 = 29.4 \text{ N}$
3
The tension acts along the rope, pulling the lamp upward.

Tension is the pulling force transmitted through a rope, string, or cable. For a single vertical rope supporting a stationary object, the tension equals the object's weight.

Example 2

medium

5 \text{ kg}

block is pulled upward by a rope with an acceleration of

3 \text{ m/s}^2

. What is the tension in the rope? Use

g = 9.8 \text{ m/s}^2

Block accelerating upward at 3 m/s²

Example 3

medium

A 5 kg mass hangs from a rope. Find the tension in the rope. (Use

g = 9.8

m/s\u00b2)

Mass hanging from rope at rest

Example 4

medium

6 \text{ kg}

block hangs in an elevator that accelerates upward at

2 \text{ m/s}^2

. Find the tension in the supporting rope. Use

g = 9.8 \text{ m/s}^2

Elevator accelerating upward at 2 m/s²

Example 5

medium

Two blocks (

2 \text{ kg}

and

3 \text{ kg}

) on a frictionless surface are connected by a rope. A

20 \text{ N}

force pulls the

3 \text{ kg}

block. Find the tension in the connecting rope.

Example 6

medium

Three blocks

1, 2, 3 \text{ kg}

are tied in a row by light ropes on a frictionless surface. A

24 \text{ N}

force pulls the

3 \text{ kg}

block. Find the tension in the rope between the

1

and

2 \text{ kg}

blocks.

Example 7

hard

An Atwood machine has masses

3 \text{ kg}

and

5 \text{ kg}

on a frictionless ideal pulley. Find the rope tension. Use

g = 9.8 \text{ m/s}^2

Atwood machine: 3 kg and 5 kg, heavier side shown

Example 8

hard

Block A (

4 \text{ kg}

) on a frictionless table is connected over a pulley to block B (

1 \text{ kg}

) hanging vertically. Find the rope tension. Use

g = 9.8 \text{ m/s}^2

Hanging 1 kg block — table-pulley system

Example 9

challenge

50 \text{ kg}

tightrope walker is at the center of a

20 \text{ m}

rope that sags

0.5 \text{ m}

in the middle. Find the tension in the rope. Use

g = 9.8 \text{ m/s}^2

Practice Problems

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

Example 1

medium

Two blocks (

3 \text{ kg}

and

5 \text{ kg}

) are connected by a rope on a frictionless table. A

24 \text{ N}

force pulls the

5 \text{ kg}

block. What is the tension in the connecting rope?

Example 2

hard

4 \text{ kg}

mass hangs from a rope over a frictionless pulley, connected to a

6 \text{ kg}

mass on the other side. What is the tension in the rope and the acceleration of the system? Use

g = 9.8 \text{ m/s}^2

Example 3

easy

4

kg mass hangs at rest from a single rope (

g=10

m/s

^2

). What is the tension?

4 kg mass hanging at rest, g = 10 m/s²

Example 4

easy

A rope pulls a

3

kg box horizontally on a frictionless floor, accelerating it at

2

m/s

^2

. Find the tension.

3 kg box accelerating at 2 m/s² on frictionless floor

Example 5

easy

Two people pull a rope in opposite directions, each with

50

N, and it stays still. What is the tension in the rope?

Example 6

easy

2

kg lamp hangs from a rope in an elevator at rest (

g=10

m/s

^2

). Find the tension.

Example 7

easy

A massless rope connects two blocks. The tension at one end is

12

N. What is the tension at the other end?

Example 8

easy

5

kg bucket hangs from a rope being lowered at constant velocity (

g=10

m/s

^2

). Find the tension.

Example 9

easy

A horizontal rope holds a

20

N box against a wall by pulling it sideways; the box is in equilibrium horizontally with a

20

N wall push. What is the rope tension?

Example 10

easy

Two blocks (

3

kg and

2

kg) connected by a rope are pulled so they accelerate at

4

m/s

^2

on a frictionless floor. Find the tension pulling the

2

kg block.

2 kg block (trailing) pulled via rope, system acceleration 4 m/s²

Example 11

medium

2

kg mass hangs from a rope in an elevator accelerating upward at

3

m/s

^2

(

g=10

m/s

^2

). Find the tension.

Elevator accelerating upward at 3 m/s²

Example 12

medium

2

kg mass hangs from a rope in an elevator accelerating downward at

4

m/s

^2

(

g=10

m/s

^2

). Find the tension.

Elevator accelerating downward at 4 m/s²

Example 13

medium

Blocks of

4

kg and

6

kg are connected by a rope on a frictionless floor; a

20

N force pulls the

6

kg block. Find the rope tension.

4 kg + 6 kg system on frictionless floor, 20 N applied to 6 kg block

Example 14

medium

3

kg block on a frictionless table connects over a pulley to a hanging

2

kg block (

g=10

m/s

^2

). Find the system acceleration.

Example 15

medium

In the previous pulley setup (

3

kg on table,

2

kg hanging,

a=4

m/s

^2

g=10

m/s

^2

), find the rope tension.

Example 16

medium

10

kg sign hangs from two ropes at

30^\circ

from horizontal on each side, sharing the load equally (

g=10

m/s

^2

). Find each tension.

Example 17

medium

A rope can hold at most

80

N. A

6

kg mass hangs from it in an elevator (

g=10

m/s

^2

). What maximum upward acceleration is allowed?

Example 18

medium

1

kg ball on a string is whirled in a horizontal circle; the string is nearly horizontal and provides

25

N. Treating tension as the centripetal force, find the speed if

r=1

Example 19

medium

A rope holds a

4

kg bucket being raised at constant velocity (

g=10

m/s

^2

). Find the tension.

Example 20

challenge

5

kg and

3

kg mass hang over a frictionless pulley (Atwood machine,

g=10

m/s

^2

). Find the acceleration.

Example 21

challenge

For the Atwood machine above (

5

kg,

3

kg,

a=2.5

m/s

^2

g=10

m/s

^2

), find the rope tension.

Example 22

challenge

2

kg ball on a string swings as a pendulum; at the lowest point its speed is

4

m/s and

r=1

m (

g=10

m/s

^2

). Find the string tension there.

Pendulum at lowest point, v = 4 m/s, r = 1 m

Example 23

easy

7 \text{ kg}

chandelier hangs from a single vertical rope and is at rest. Find the tension. Use

g = 9.8 \text{ m/s}^2

Chandelier hanging from a single vertical rope

Example 24

easy

2 \text{ kg}

mass is pulled vertically up by a rope with constant velocity (

g = 9.8 \text{ m/s}^2

). Find the tension.

Constant velocity upward — net force is zero

Example 25

easy

4 \text{ kg}

block is pulled horizontally by a rope with

30 \text{ N}

across a frictionless surface. Find the tension in the rope and the block's acceleration.

4 kg block pulled horizontally on frictionless surface

Example 26

medium

6 \text{ kg}

block hangs in an elevator descending at

3 \text{ m/s}^2

. Find the tension. Use

g = 9.8 \text{ m/s}^2

Elevator descending with acceleration 3 m/s²

Example 27

medium

10 \text{ kg}

mass hangs from two ropes, each making

30°

with the ceiling. Find the tension in each rope (assume symmetric and

g = 9.8 \text{ m/s}^2

Example 28

medium

1.5 \text{ kg}

mass swings in a horizontal circle on a string

0.5 \text{ m}

long at

4 \text{ m/s}

. Find the string tension (ignore gravity for the horizontal whirl).

Example 29

medium

2 \text{ kg}

block hangs from a rope. The rope is attached to a

5 \text{ kg}

block on a frictionless table, connected by an ideal pulley. Find the tension. Use

g = 9.8 \text{ m/s}^2

Hanging mass on Atwood-style pulley (2 kg vs 5 kg on table)

Example 30

medium

Climbing rope can hold

5000 \text{ N}

. A

90 \text{ kg}

climber falls freely until the rope snaps taut, decelerating him at

5g

. Will the rope hold? Use

g = 9.8 \text{ m/s}^2

Example 31

medium

10 \text{ kg}

mass is supported by two ropes attached to a horizontal ceiling: one vertical, one at

45°

. In static equilibrium, find the tension in the angled rope. Use

g = 9.8 \text{ m/s}^2

Vertical rope + 45° rope — only one rope carries the load

Example 32

medium

3 \text{ kg}

block is pulled up an inclined plane (frictionless) at

30°

by a rope parallel to the surface with constant velocity. Find the rope tension. Use

g = 9.8 \text{ m/s}^2

Example 33

hard

Two ropes hold a

5 \text{ kg}

mass: one at

30°

from the ceiling and one at

60°

from the ceiling (so the ropes are perpendicular to each other). Find the tension in the

30°

rope. Use

g = 9.8 \text{ m/s}^2

Example 34

hard

0.4 \text{ kg}

ball whirls in a vertical circle on a string of

0.6 \text{ m}

5 \text{ m/s}

. Find the tension at the lowest point. Use

g = 9.8 \text{ m/s}^2

Example 35

hard

0.4 \text{ kg}

ball whirls in a vertical circle on a string of

0.6 \text{ m}

5 \text{ m/s}

. Find the tension at the top. Use

g = 9.8 \text{ m/s}^2

Example 36

hard

5 \text{ kg}

mass hangs from a string at rest. A horizontal wind pushes it sideways with

30 \text{ N}

, deflecting the string from vertical. Find the rope tension. Use

g = 9.8 \text{ m/s}^2

Example 37

hard

An Atwood machine has masses

4 \text{ kg}

and

6 \text{ kg}

. Find the system acceleration. Use

g = 9.8 \text{ m/s}^2

Atwood machine 4 kg vs 6 kg — find acceleration

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Related Concepts

Force Pulley Systems Equilibrium

Background Knowledge

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

force