Equilibrium Examples: 45 Problems with Answers

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

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

Concept Recap

A state in which all forces acting on an object balance so that the net force equals zero and there is no acceleration.

All forces cancel out — the object doesn't accelerate, though it may still be moving at constant velocity.

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: Equilibrium 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 equilibrium 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

25 \text{ N}

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

Answer

T = 25 N

First step

The lamp is in static equilibrium, meaning the net force on it is zero:

\sum F = 0

Full solution

2
Identify the forces: tension $T$ acts upward, weight $W = 25 \text{ N}$ acts downward.
3
Set net force to zero and solve: $T - W = 0 ⟹ T = 25 N$

An object in equilibrium has zero net force. For a hanging object, the tension in the supporting cord equals the object's weight.

Example 2

hard

50 \text{ N}

sign hangs from two cables, each making a

30°

angle with the horizontal. What is the tension in each cable?

Example 3

medium

For

\text{H}_2 + \text{I}_2 \rightleftharpoons 2\text{HI}

, at equilibrium

[\text{H}_2] = 0.20\,\text{M}

[\text{I}_2] = 0.20\,\text{M}

[\text{HI}] = 1.00\,\text{M}

. Find

K

Example 4

medium

Given

\text{A} \rightleftharpoons \text{B}

with

K = 3.0

. At equilibrium

[\text{A}] = 0.20\,\text{M}

. Find

[\text{B}]

Example 5

medium

For

\text{N}_2\text{O}_4 \rightleftharpoons 2\text{NO}_2

K = 0.211

at equilibrium

[\text{N}_2\text{O}_4] = 0.500\,\text{M}

. Find

[\text{NO}_2]

Example 6

hard

For

\text{A} \rightleftharpoons 2\text{B}

, start with

[\text{A}]_0 = 1.00\,\text{M}

, no B. At equilibrium

[\text{A}] = 0.40\,\text{M}

. Find

K

Example 7

hard

Reaction

\text{X} \rightleftharpoons \text{Y}

has

K = 16

25^\circ\text{C}

and

K = 4

80^\circ\text{C}

. Is the forward reaction exothermic or endothermic?

Example 8

challenge

For

\text{H}_2 + \text{I}_2 \rightleftharpoons 2\text{HI}

K = 50

. If

[\text{H}_2]_0 = [\text{I}_2]_0 = 1.00\,\text{M}

, no HI initially, find

[\text{HI}]

at equilibrium.

Practice Problems

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

Example 1

medium

An object is in equilibrium under three forces:

F_1 = 10 \text{ N}

east,

F_2 = 10 \text{ N}

north. What is the magnitude and direction of the third force

F_3

F₁

Example 2

easy

40 \text{ N}

sign is held at rest by two vertical supports. One support pulls upward with

25 \text{ N}

. What upward force must the second support provide for equilibrium?

One support gives 25 N up — find F₂ so the 40 N sign stays at rest.

Example 3

easy

A book rests motionless on a table. What is the net force on it?

Example 4

easy

5

kg lamp hangs at rest from a cord (

g=10

m/s

^2

). What is the cord's tension?

Find the cord tension for a 5 kg lamp hanging at rest (g

Example 5

easy

An object in equilibrium experiences

8

N up. What downward force must act?

8 N acts upward — what downward force keeps the object in equilibrium?

Example 6

easy

A crate slides at a constant

3

m/s across a floor. Is it in equilibrium?

Example 7

easy

A sign hangs from two vertical wires, each pulling up

20

N. What is the sign's weight in equilibrium?

Two vertical wires each pull 20 N upward — find the sign's weight.

Example 8

easy

2

kg block sits on a table (

g=10

m/s

^2

). What is the normal force?

Find the normal force on a 2 kg block at rest on a table (g

Example 9

easy

Three horizontal forces give equilibrium. Two are

5

N left and

3

N left. What is the third?

Two leftward forces (5 N and 3 N) act on an object — find F₃ for equilibrium.

Example 10

easy

A picture hangs in equilibrium. The wire tension is

30

N up. What is the picture's weight?

Wire tension is 30 N up — find the picture's weight in equilibrium.

Example 11

medium

4

kg mass hangs from two ropes making

30^\circ

each from vertical, sharing the load equally (

g=10

m/s

^2

). Find each tension.

Two ropes each make 30° with the vertical — find tension T in each (g

Example 12

medium

6

kg block on a

30^\circ

incline is held at rest by a rope along the slope (

g=10

m/s

^2

, frictionless). Find the tension.

Find rope tension T to hold a 6 kg block on a frictionless 30° incline (g

Example 13

medium

50

N weight hangs from a horizontal rod, held by a wire at

37^\circ

above horizontal. Find the wire tension (

\sin37^\circ=0.6

Example 14

medium

A box is pushed right at

12

N and stays still due to friction. What is the friction force?

A 12 N push cannot move the box — find the friction force keeping it still.

Example 15

medium

10

kg traffic light hangs from two cables at

45^\circ

each from the horizontal (

g=10

m/s

^2

). Find each tension.

Two cables each at 45° from horizontal support a 10 kg traffic light — find each tension (g

Example 16

medium

3

kg object hangs from a spring and a rope that pulls up with

10

N (

g=10

m/s

^2

). What is the spring force?

A rope (10 N up) and a spring hold a 3 kg mass at rest — find the spring force (g

Example 17

medium

2

kg block rests on a

30^\circ

frictionless incline against a horizontal wall at its base. Is it in equilibrium without friction? Explain with the slope-direction net force.

Is this 2 kg block on a frictionless 30° incline in equilibrium? Identify the net slope-direction force.

Example 18

medium

5

kg sign hangs from a single rope. A side wind pushes it horizontally with

30

N, holding the rope at an angle. Find the rope tension (

g=10

m/s

^2

Wind pushes 30 N right; rope holds sign at angle — find rope tension T (g

Example 19

medium

8

N force points east and a

6

N force points west on a

2

kg block held still by a wall. What wall force keeps it in equilibrium?

8 N east, 6 N west, and a wall reaction keep the block still — find the wall force.

Example 20

challenge

4

kg mass hangs from ropes A (horizontal) and B (at

30^\circ

above horizontal from a wall). Find tension in rope B (

g=10

m/s

^2

Rope A is horizontal, rope B at 30° above horizontal — find tension in rope B (g

Example 21

challenge

A uniform

6

20

N beam is supported at both ends. A

60

N weight sits

2

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

Example 22

challenge

10

kg block is held on a

37^\circ

frictionless incline by a horizontal force

F

(

g=10

m/s

^2

\tan37^\circ=0.75

). Find

F

Find the horizontal force F to hold a 10 kg block on a frictionless 37° incline (g

Example 23

easy

At chemical equilibrium, what is true about the forward and reverse reaction rates?

Example 24

easy

Which arrow symbol indicates a reversible reaction at equilibrium?

Example 25

easy

K \gg 1

for

\text{A} \rightleftharpoons \text{B}

, which side dominates at equilibrium?

Example 26

easy

K \ll 1

for a reversible reaction, which side dominates?

Example 27

easy

For

\text{A}+\text{B} \rightleftharpoons \text{C}

, write the equilibrium expression

K

Example 28

medium

For

\text{N}_2 + 3\text{H}_2 \rightleftharpoons 2\text{NH}_3

, if you add more

\text{N}_2

, which way does the equilibrium shift?

Example 29

medium

For an exothermic equilibrium, increasing temperature shifts it which way?

Example 30

medium

For

2\text{SO}_2 + \text{O}_2 \rightleftharpoons 2\text{SO}_3

, if pressure is increased (constant T), which way does the equilibrium shift?

Example 31

medium

For

\text{A} \rightleftharpoons \text{B}

, at some instant

Q = 5

and

K = 2

. In which direction does the reaction proceed?

Example 32

medium

For a reversible reaction at equilibrium, if you remove a product, what happens?

Example 33

hard

For an endothermic reaction at equilibrium, what happens to

K

when temperature is increased?

Example 34

hard

If the equation

\text{A} \rightleftharpoons \text{B}

has

K_1 = 4

, what is

K_2

for the reverse reaction

\text{B} \rightleftharpoons \text{A}

Example 35

hard

For

2\text{A} \rightleftharpoons \text{B}

with

K_1

, what is K for

4\text{A} \rightleftharpoons 2\text{B}

Example 36

hard

For

\text{CaCO}_3(s) \rightleftharpoons \text{CaO}(s) + \text{CO}_2(g)

, write the equilibrium expression

K

Example 37

challenge

Explain why two simultaneous equilibria sharing a common species (e.g., a common ion) interact through Le Chatelier's principle.

← Back to Equilibrium Practice Mode

Related Concepts

Net Force Acceleration Statics Tension

Background Knowledge

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

net forceacceleration