Statics Examples in Physics

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

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

Concept Recap

Statics is the study of objects in equilibrium, where the net force and net torque are both zero.

If something is not speeding up, slowing down, or rotating more, the pushes and twists must balance.

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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: Statics 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 statics 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

medium

A uniform

5

m beam weighing

200

N rests on supports at its ends. A

400

N point load sits

1

m from the left support. Find each support force.

Answer

N_L = 420 \text{ N},\ N_R = 180 \text{ N}

First step

Torque about left:

N_R(5) = 200(2.5) + 400(1) = 500 + 400 = 900

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Example 2

medium

A horizontal

6

m massless beam is pinned at the wall and held at the far end by a cable at

40^\circ

above the beam. A

90

N weight hangs at

4

m from the wall. Find the cable tension.

Example 3

hard

A uniform

300

5

m ladder leans against a frictionless wall; the floor coefficient is

\mu_s = 0.4

. Base

3

m from wall, top

4

m up. Will it slip?

Example 4

hard

60

kg person walks out on a uniform

4

20

kg diving board cantilevered from the left end. How far from the support can the person walk if the board tip can hold

500

N downward before snapping? (

g = 10

m/s

^2

Example 5

hard

A uniform

4

100

N sign is suspended from two cables at its two top corners. The left cable goes vertically up; the right cable goes diagonally at

30^\circ

from vertical. Find the left cable tension.

Example 6

challenge

4

m uniform beam (

150

N) is supported by a pivot at the left end and a cable at the right end at

50^\circ

above the beam. A

100

N load hangs

1

m from the pivot and a

200

N load hangs

3

m from the pivot. Find the cable tension.

Practice Problems

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

Example 1

easy

An object is in static equilibrium. What must be true of the net force and net torque on it?

Example 2

easy

A box hangs from a single vertical rope. If the box weighs

50\,\text{N}

and is in equilibrium, find the rope tension.

Example 3

easy

Two upward support forces of

30\,\text{N}

and

20\,\text{N}

hold a beam in equilibrium. Find the beam's weight.

Example 4

easy

A sign hangs in equilibrium pulled left by

12\,\text{N}

and right by an unknown horizontal force. Find that force.

Example 5

easy

A torque of

10\,\text{N·m}

clockwise acts on a balanced beam. What counterclockwise torque is needed for rotational equilibrium?

Example 6

easy

A 100 N weight rests symmetrically on two identical supports. By symmetry, find each support's force.

Example 7

easy

A picture hangs from two equal wires, each making the same angle, sharing a

40\,\text{N}

weight. Find the vertical component each wire supports.

Example 8

easy

A book rests motionless on a table. Name the two vertical forces that balance.

Example 9

medium

A uniform 2 m beam weighing

40\,\text{N}

rests on a support at its left end and one at its right end. Find the force on the right support (weight acts at center).

Example 10

medium

Same beam (uniform,

40\,\text{N}

, two end supports). Find the left support force.

Example 11

medium

A 60 N weight hangs from a horizontal beam. A support at the left end and a cable at the right end (2 m away) hold it; the weight hangs at

1.5\,\text{m}

from the left. Find the cable tension (beam massless).

Example 12

medium

A 10 kg sign hangs from a wire at

30^\circ

above horizontal and a horizontal strut. Find the wire tension's required vertical component (

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

Example 13

medium

From the previous sign, the wire is at

30^\circ

and its vertical component is

100\,\text{N}

. Find the full wire tension.

Example 14

medium

A 30 N weight hangs from the middle of a rope whose two halves each make

30^\circ

below horizontal. Find the tension in each half (symmetric).

Example 15

medium

A uniform beam (weight

80\,\text{N}

, length

4\,\text{m}

) is supported at

1\,\text{m}

from the left end and at the right end. Find the right support force (take torques about the left support point).

Example 16

medium

A 50 N weight sits

0.5\,\text{m}

from the pivot of a seesaw. Where must a 25 N weight sit on the other side for balance?

Example 17

medium

A 20 N weight hangs from the middle of a horizontal rope whose two halves each make

30^\circ

below horizontal. Find the tension in each half.

Example 18

challenge

A uniform ladder (weight

200\,\text{N}

, length

5\,\text{m}

) leans against a frictionless wall, base

3\,\text{m}

from the wall (height

4\,\text{m}

). Find the wall's horizontal reaction (take torques about the base).

Example 19

challenge

A 4 m uniform beam (weight

100\,\text{N}

) is hinged at the wall and held horizontal by a cable at the far end at

30^\circ

above the beam. Find the cable tension (take torques about the hinge).

Example 20

challenge

A 60 kg person stands

1\,\text{m}

from the left end of a uniform

4\,\text{m}

20\,\text{kg}

plank resting on two supports at its ends (

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

). Find the left support force.

Example 21

easy

20

kg sign hangs from a single vertical rope. Find the rope tension. (

g = 10

m/s

^2

Example 22

easy

A horizontal beam is held by two upward forces of

25

N and

35

N. Find the beam's weight.

Example 23

easy

A picture is held up by two identical wires, each pulling at

30^\circ

above horizontal, supporting a

20

N picture. Find the vertical force each wire supplies.

Example 24

easy

A book of mass

0.8

kg rests on a level table. Find the normal force from the table. (

g = 10

m/s

^2

Example 25

easy

100

N weight rests symmetrically across two identical supports. Find the force on each support.

Example 26

medium

60

N child sits

2

m from the pivot of a seesaw. Where must a

40

N child sit on the other side for balance?

Example 27

medium

A sign weighing

80

N hangs from a wire making

40^\circ

above the horizontal and a horizontal strut. Find the tension in the wire.

Example 28

medium

From the same setup as previous, find the compression in the horizontal strut.

Example 29

medium

A uniform horizontal

4

m beam of weight

120

N is supported by a pivot at its left end and a cable at the right end (vertical cable). Find the cable tension.

Example 30

medium

50

N weight hangs from the middle of a rope whose two halves each make

45^\circ

below horizontal. Find the tension in each half.

Example 31

medium

A uniform

3

m beam weighs

60

N and is supported by a pivot

1

m from the left and a vertical cable at the right end. Find the cable tension.

Example 32

medium

A uniform

2

30

N plank rests on two supports: one at its left end and one

0.5

m from the right end. Find the right support force (take torques about the left).

Example 33

medium

A 4 m uniform

200

N beam is supported at both ends. A

300

N load sits

1

m from the left support. Find the right support force.

Example 34

medium

Using the previous setup, find the left support force.

Example 35

medium

40

N picture hangs from two wires meeting overhead at an angle of

120^\circ

between them. Find the tension in each wire (symmetric).

Example 36

medium

50

N traffic light hangs from two cables: one horizontal and one at

30^\circ

above horizontal. Find the tension in the diagonal cable.

Example 37

hard

A uniform

4

m beam of mass

20

kg is hinged at a wall and held horizontal by a cable at

30^\circ

above the beam, attached at the far end. Find the cable tension. (

g = 10

m/s

^2

Example 38

hard

For the previous beam (4 m, 20 kg, hinge at wall, cable at far end at

30^\circ

T = 200

N), find the horizontal force from the hinge.

Example 39

hard

Three forces act on a body in equilibrium:

30

N east,

40

N north, and

F

in some direction. Find

|F|

and its direction.

Example 40

hard

5

kg lamp hangs from the ceiling on two ropes: one straight up to the ceiling at angle

60^\circ

from horizontal, and one diagonally to a wall at

30^\circ

above horizontal. Find the ceiling-rope tension. (

g = 10

m/s

^2

Example 41

challenge

1

m uniform rod of mass

2

kg is balanced on a knife-edge at

0.3

m from the left end. A

5

N force pushes vertically downward at the right end. Find the location of an additional

10

N downward force on the left side that keeps the rod balanced. (

g = 10

m/s

^2

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Related Concepts

Equilibrium Torque Rotational Equilibrium

Background Knowledge

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

equilibriumtorque