Forces, Rotation & Equilibrium — Chapter quiz · Physics & Environmental Science, Grade 12

Use force diagrams, friction, circular motion, springs, and torque to explain motion and balance.

Problem 1

A net force of 18 N acts on a 3 kg cart. Find its acceleration.
Answer and explanation

6 m/s²

a = ΣF ÷ m = 18 ÷ 3 = 6 m/s².

Problem 2

Passengers lurch forward when a bus stops suddenly. This is best explained by…
  1. the force of gravity
  2. air resistance
  3. Newton's third law
  4. their inertia (Newton's first law)
Answer and explanation

their inertia (Newton's first law)

The passengers were moving with the bus, and their inertia keeps them moving forward when the bus stops — Newton's first law.

Problem 3

You stand still on the ground. Which pair are a Newton's third-law action–reaction pair?
  1. Earth pulling you down and you pulling Earth up
  2. Your mass and your weight
  3. Your weight and the normal force from the ground
  4. The ground pushing up on you and gravity pulling you down
Answer and explanation

Earth pulling you down and you pulling Earth up

A third-law pair acts on two different objects: Earth pulls you down, and you pull Earth up. Weight and normal force act on the same object, so they are not a pair.

Problem 4

Two horizontal forces act on a box: 70 N right and 25 N left. Find the net force.
Answer and explanation

45 N

Net force = 70 − 25 = 45 N to the right.

Problem 5

A 1,000 kg car accelerates from 15 m/s to 25 m/s in 4 seconds. Find the net force acting on it.
Answer and explanation

2500 N

First find acceleration: a = (25 − 15) ÷ 4 = 2.5 m/s². Then ΣF = ma = 1,000 × 2.5 = 2,500 N.

Problem 6

A block is pressed to a surface with a normal force of 40 N and slides with μₖ = 0.35. Find the kinetic friction force.
Answer and explanation

14 N

f = μₖN = 0.35 × 40 = 14 N.

Problem 7

A 12 kg block rests on a frictionless 30° incline. Find its acceleration down the slope. (g = 9.8 m/s²)
Answer and explanation

4.9 m/s²

On a frictionless ramp, a = g sinθ = 9.8 × sin 30° = 9.8 × 0.5 = 4.9 m/s². (Mass does not matter.)

Problem 8

A car rounds a curve of radius 25 m at 15 m/s. Find its centripetal acceleration.
Answer and explanation

9 m/s²

a = v²/r = 15² ÷ 25 = 225 ÷ 25 = 9 m/s².

Problem 9

For an object in uniform circular motion, the acceleration points…
  1. backward, opposing the motion
  2. toward the center of the circle
  3. along the direction of motion
  4. away from the center, outward
Answer and explanation

toward the center of the circle

Centripetal acceleration always points toward the center of the circular path.

Problem 10

A 0.2 kg ball moves in a circle of radius 0.5 m at 3 m/s. Find the centripetal force.
Answer and explanation

3.6 N

F = mv²/r = 0.2 × 3² ÷ 0.5 = 0.2 × 9 ÷ 0.5 = 1.8 ÷ 0.5 = 3.6 N.

Problem 11

If the distance between two masses is tripled, the gravitational force between them becomes…
  1. 3 times as strong
  2. 9 times as strong
  3. 1/9 as strong
  4. 1/3 as strong
Answer and explanation

1/9 as strong

Gravitation is inverse-square (F ∝ 1/r²). Tripling r gives a force 1/3² = 1/9 as strong.

Problem 12

Explain why an astronaut inside an orbiting space station appears weightless, even though Earth's gravity still acts strongly on them.
Answer and explanation

The astronaut and the station are both in continuous free-fall around Earth — gravity is pulling on both equally, so they fall together at the same rate. With nothing pushing up on the astronaut (no normal force), they feel weightless, even though gravity is still supplying the centripetal force that keeps them in orbit.

Problem 13

Explain the following claim and supply a valid example or counterexample: Action/reaction forces act on different objects, so they do not cancel in one object’s diagram.
Answer and explanation

a=Fnet/m=2 m/s² along the net force. Action/reaction forces act on different objects, so they do not cancel in one object’s diagram.

Response criteria

  • State a scientifically accurate conclusion.
  • Show the calculation or mechanism that supports it.
  • Include units, conditions, or limits where relevant.

Problem 14

Independent chapter check: A 4 kg cart has forces 18 N east and 6 N west. Find acceleration and the partner of the 18 N force.
Answer and explanation

Net=12 N east; a=3 m/s² east. Its third-law partner is the cart’s 18 N force on the pulling agent, not the 6 N resistance on the cart.

Net=12 N east; a=3 m/s² east.

Its third-law partner is the cart’s 18 N force on the pulling agent, not the 6 N resistance on the cart.

Response criteria

  • Use the stated measurements or conditions, with correct units.
  • Connect the result to the physical or environmental mechanism or evidence relationship.
  • Identify the assumption, model limit or further evidence requested.

Problem 15

Explain the following claim and supply a valid example or counterexample: Draw only forces exerted on the selected object; motion arrows are not forces.
Answer and explanation

Net 12N right; a=12/4=3 m/s² right. Draw only forces exerted on the selected object; motion arrows are not forces.

Response criteria

  • State a scientifically accurate conclusion.
  • Show the calculation or mechanism that supports it.
  • Include units, conditions, or limits where relevant.

Problem 16

Independent chapter check: A 3 kg block is pulled by 15 N at 30° above horizontal. No vertical acceleration; resistance is 4 N. Find N and ax.
Answer and explanation

N=29.4−7.5=21.9 N. Horizontal net=15cos30°−4≈8.99 N; ax≈3.00 m/s². The tension is counted once through its components.

N=29.4−7.5=21.9 N.

Horizontal net=15cos30°−4≈8.99 N; ax≈3.00 m/s².

The tension is counted once through its components.

Response criteria

  • Use the stated measurements or conditions, with correct units.
  • Connect the result to the physical or environmental mechanism or evidence relationship.
  • Identify the assumption, model limit or further evidence requested.

Problem 17

Explain the following claim and supply a valid example or counterexample: Static friction adjusts up toμsN; it is not always equal to that maximum.
Answer and explanation

Static friction is 2N opposite the push, so net force is zero. It need not reach 5N. Static friction adjusts up toμsN; it is not always equal to that maximum.

Response criteria

  • State a scientifically accurate conclusion.
  • Show the calculation or mechanism that supports it.
  • Include units, conditions, or limits where relevant.

Problem 18

Independent chapter check: A 5 kg block has μs=0.40 and μk=0.30 on a level surface. For a 15 N push, find static friction; for a 25 N push during sliding, find acceleration.
Answer and explanation

N=49 N; static limit=19.6 N, so 15 N is balanced by 15 N friction. During sliding fk=14.7 N; a=(25−14.7)/5=2.06 m/s² along the push.

N=49 N; static limit=19.6 N, so 15 N is balanced by 15 N friction.

During sliding fk=14.7 N; a=(25−14.7)/5=2.06 m/s² along the push.

Response criteria

  • Use the stated measurements or conditions, with correct units.
  • Connect the result to the physical or environmental mechanism or evidence relationship.
  • Identify the assumption, model limit or further evidence requested.

Problem 19

Explain the following claim and supply a valid example or counterexample: Centripetal force is the net inward force, not an extra interaction added to gravity or tension.
Answer and explanation

ac=v²/r=8 m/s². Speed can be constant while velocity direction changes. Centripetal force is the net inward force, not an extra interaction added to gravity or tension.

Response criteria

  • State a scientifically accurate conclusion.
  • Show the calculation or mechanism that supports it.
  • Include units, conditions, or limits where relevant.

Problem 20

Independent chapter check: A 0.50 kg mass moves at 4.0 m/s in a 2.0 m horizontal circle. Find inward acceleration and required net force; name what else is needed to identify tension.
Answer and explanation

ac=16/2=8.0 m/s² and inward net force=0.50×8=4.0 N. Tension equals that net only if the specified geometry and other forces establish it as the sole inward contribution.

ac=16/2=8.0 m/s² and inward net force=0.50×8=4.0 N.

Tension equals that net only if the specified geometry and other forces establish it as the sole inward contribution.

Response criteria

  • Use the stated measurements or conditions, with correct units.
  • Connect the result to the physical or environmental mechanism or evidence relationship.
  • Identify the assumption, model limit or further evidence requested.

Problem 21

k=80N/m,x=.10 m. Find elastic energy.
Hints

Write the relationship first; substitute with consistent units.

Answer and explanation

0.4 J

.5×80×.01=.4.

Problem 22

What two conditions define static equilibrium?
Answer and explanation

Zero resultant force and zero resultant torque.

Response criteria

  • State a scientifically accurate conclusion.
  • Show the calculation or mechanism that supports it.
  • Include units, conditions, or limits where relevant.

Problem 23

Independent chapter check: A weightless 2 m beam is pivoted at its left end. A 60 N load acts 0.50 m from the pivot. An upward force acts at the right end. Find that force and vertical pivot reaction for equilibrium.
Answer and explanation

Torque balance: F×2=60×0.50, so F=15 N upward. Vertical balance gives pivot reaction=60−15=45 N upward. Both balances are necessary.

Torque balance: F×2=60×0.50, so F=15 N upward.

Vertical balance gives pivot reaction=60−15=45 N upward.

Both balances are necessary.

Response criteria

  • Use the stated measurements or conditions, with correct units.
  • Connect the result to the physical or environmental mechanism or evidence relationship.
  • Identify the assumption, model limit or further evidence requested.

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