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GCSE Physics · GCSEChapter 13 · Forces, vectors and Newton's laws
GCSE · Chapter 13

Forces, vectors and Newton's laws

By the end of this chapter you will be able to

  • Classify forces as contact or non-contact, and quantities as scalar or vector
  • Calculate weight, and the resultant force in one line
  • Use F = m a to find force, mass or acceleration, including with a net force
  • Identify action-reaction pairs and explain why a falling object reaches terminal velocity

You should already know

  • Speed, distance and time (KS3 Maths and Science)
  • Energy stores and transfers (Chapter 1)

Where this leads

  • Momentum, moments and pressure (Chapter 14)
  • Motion graphs and acceleration (Chapter 16)

GCSE Physics. Content follows the GCSE (9-1) subject content for England (Edexcel and AQA). Content references: Distinguish scalar and vector quantities, and contact and non-contact forces, Calculate weight from mass using W = mg, with g = 9.8 N/kg near the Earth, Find the resultant of forces acting in the same and opposite directions, by calculation and by scale drawing; draw free-body diagrams, State and use Newton's first law (balanced forces, equilibrium), second law (F = m a) and third law (action-reaction pairs), Explain friction and drag, and terminal velocity, using the balance of forces.

Exercise P  Do you remember?

1
FWhat is 6 x 2.5? Write the number.
2
FWhat is 10 minus 4? Write the number.
3
FWhat is the unit of force? Write the unit.
4
FWhat is 1000 divided by 4? Write the number.
5
FWhat is the speed of a car that travels 60 m in 10 s? Write the number of metres per second.
13.1

Scalars, vectors and types of force

GCSE
Distinguish scalar and vector quantities, and contact and non-contact forces, Calculate weight from mass using W = mg
Video lesson: Scalars, vectors and types of forceComing soon
Context. Leo pushes a trolley across a car park. A friend asks, “How far did it go and in which direction?” Speed alone is not enough: the direction matters for a force. Forces are vectors, so they have both a size and a direction.

A scalar has only a size (for example mass, speed, distance, time). A vector has a size and a direction (for example force, velocity, displacement). A force is a push or a pull. A contact force needs the objects to touch (friction, normal contact force, drag). A non-contact force acts at a distance (gravity, magnetic and electrostatic forces).

The weight of an object is the force of gravity on it. It depends on the mass and the gravitational field strength:

W = m x g, with g = 9.8 N/kg near the Earth

ForceContact or non-contactExample
weightnon-contactgravity pulling a book down
magneticnon-contacta magnet pulling an iron nail
electrostaticnon-contacta charged balloon attracting paper
frictioncontacta block sliding on a table
normal contact forcecontactthe table pushing up on a book
drag (air resistance)contactair slowing a falling parachute
Some forces, and whether they are contact or non-contact

Key ideas

  • Scalar: size only. Vector: size and direction.
  • Force is measured in newtons (N).
  • Weight W = m x g, with g = 9.8 N/kg. Mass is in kg; weight is in N.
  • Mass does not change with place; weight does.
Worked example 13.1.1
A 5 kg book sits on a table. Calculate its weight. Write the number of newtons.

Method. Use W = m x g.

  1. Take the numbers. m = 5 kg and g = 9.8 N/kg.
    m = 5, g = 9.8
  2. Multiply. W = 5 x 9.8 = 49 N.
    5 x 9.8 = 49
  3. Write the answer.
    49 N

Check. 49 / 9.8 = 5 kg. ✓

Worked example 13.1.2
A 60 kg person stands on a bathroom scale. Calculate the weight. Write the number of newtons.

Method. Use W = m x g.

  1. Take the numbers. m = 60 kg.
    m = 60
  2. Multiply. W = 60 x 9.8 = 588 N.
    60 x 9.8 = 588
  3. Write the answer.
    588 N

Check. 588 / 60 = 9.8 N/kg. ✓

Worked example 13.1.3
Is a magnet pulling a nail a contact or a non-contact force? Write contact or non-contact.

Method. Think about whether they touch.

  1. Look. The magnet can pull the nail from a short distance without touching it.
    at a distance
  2. Decide. So it is a non-contact force.
    non-contact
  3. Write the answer.
    non-contact

Check. ✓

Watch out

Watch out: weight is a force in newtons. Mass is in kilograms and does not change with place. Do not say “my weight is 60 kg”.

Exam tip

Exam tip. When asked to give the weight, write it in newtons (N). When asked to give the mass, write kilograms (kg).

Exercise 13A  Vectors, forces and weight

1
FWhich of these is a vector: speed or velocity? Write the word.
2
FWhich of these is a scalar: force or mass? Write the word.
3
FWhat is the unit of weight? Write the unit.
4
FName a contact force. Write the word.
5
FName a non-contact force. Write the word.
6
FCalculate the weight of a 2 kg object, using g = 9.8 N/kg. Write the number of newtons.
7
FCalculate the weight of a 0.5 kg apple. Write the number of newtons.
8
FCalculate the weight of a 10 kg object, using g = 9.8 N/kg. Write the number of newtons.
9
PSAn object has a weight of 294 N on Earth, with g = 9.8 N/kg. What is its mass? Write the number of kilograms.
10
PSA spring balance reads 98 N for an object. What is the mass of the object? Write the number of kilograms.
11
RExplain why a force is a vector, in one sentence. Accept any sentence that says it has both a size and a direction.
12
RA pupil says “the mass of an astronaut is smaller on the Moon, because the astronaut weighs less.” Explain why this is wrong. Accept any answer that says the mass is the same; only the weight changes.
13
PSWhich is a force of the same type as the weight: magnetic or friction? Write the word.
14
PSCalculate the weight of 3.5 kg of sugar. Write the number of newtons.
15
PSA person of weight 735 N stands on the floor. What is the mass? Write the number of kilograms.
13.2

Resultant forces and free-body diagrams

GCSE
Find the resultant of forces acting in the same and opposite directions, by calculation and by scale drawing; draw free-body diagrams
Video lesson: Resultant forces and free-body diagramsComing soon
Context. A tug of war team pulls on a rope. The team on the left pulls with 300 N, and the team on the right pulls with 280 N. Which way does the rope move, and by how much is the net pull? The answer comes from the resultant force.

The resultant force is the single force that has the same effect as all the forces acting on an object together. Forces in the same direction add together. Forces in opposite directions subtract, and the resultant is in the direction of the larger force.

A free-body diagram shows the object as a box or a dot, with arrows for each force acting on it. The length of each arrow shows the size of the force, and it points in the direction it acts.

resultant of 10 N right and 4 N left10 N right4 N leftresultant 6 N right
Forces in opposite directions: the resultant is the difference
scale drawing: 1 cm = 2 N6 N = 3 cm4 N = 2 cm
A scale drawing: 1 cm = 2 N, so 6 N is 3 cm long

Key ideas

  • Same direction: add the forces.
  • Opposite directions: subtract; the resultant is in the direction of the larger force.
  • Scale drawing: choose a scale, draw the arrows, and measure the resultant.
  • Free-body diagram: show only the forces acting on the object.
Worked example 13.2.1
A 10 N force pulls to the right and a 4 N force pulls to the left on the same object. Find the resultant. Write the number of newtons and the direction, as a number then a word.

Method. The forces are in opposite directions, so subtract.

  1. Subtract. Resultant = 10 - 4 = 6 N.
    10 - 4 = 6
  2. Direction. The larger force is to the right, so the resultant is 6 N to the right.
    right
  3. Write the answer.
    6 N right

Check. ✓

Worked example 13.2.2
Two people push a box in the same direction with forces of 30 N and 45 N. Find the resultant force. Write the number of newtons.

Method. The forces are in the same direction, so add.

  1. Read. The forces are 30 N and 45 N, both pushing the same way.
    30 and 45
  2. Add. Resultant = 30 + 45 = 75 N in the same direction.
    30 + 45 = 75
  3. Write the answer.
    75 N

Check. 75 - 30 = 45 N. ✓

Worked example 13.2.3
A block has a 20 N push to the right, a 12 N friction force to the left, and a 5 N force to the left. Find the resultant. Write the number of newtons and the direction, as a number then a word.

Method. Add the forces in each direction, then subtract.

  1. Right. Total to the right = 20 N.
    20 N right
  2. Left. Total to the left = 12 + 5 = 17 N.
    17 N left
  3. Resultant. Resultant = 20 - 17 = 3 N to the right.
    20 - 17 = 3
  4. Write the answer.
    3 N right

Check. ✓

Watch out

Watch out: a resultant force is a single arrow. When forces act in opposite directions, subtract them; do not add them.

Exam tip

Exam tip. Write the direction of the resultant with its size. A resultant of 6 N with no direction loses marks.

Exercise 13B  Resultant forces and diagrams

1
FTwo forces of 5 N act in the same direction on an object. What is the resultant? Write the number of newtons.
2
FTwo forces of 8 N and 3 N act in opposite directions. What is the resultant? Write the number of newtons.
3
FTwo forces of 12 N and 12 N act in opposite directions on the same object. What is the resultant? Write the number of newtons.
4
FA 7 N force to the right and a 2 N force to the left act on a crate. Find the resultant, and give its direction. Write the number and direction.
5
FForces of 4 N, 6 N and 3 N act to the right on an object. Find the resultant. Write the number of newtons.
6
FA 9 N force acts to the right and a 9 N force acts to the left. Find the resultant. Write the number.
7
PSOn a scale drawing, 1 cm represents 2 N. A force of 10 N is drawn. How long is the arrow in cm? Write the number of cm.
8
PSOn a scale drawing with 1 cm = 5 N, a resultant arrow is 3 cm long. What is the resultant force? Write the number of newtons.
9
PSTwo forces act on a box: 25 N to the right and 10 N to the left. Find the resultant and draw its arrow in a scale drawing using 1 cm = 5 N. Write the length of the arrow in cm.
10
RA free-body diagram of a book on a table shows its weight downwards and a normal contact force upwards. What is the resultant if they are equal? Write the number of newtons, if the weight is 5 N.
11
RExplain why a free-body diagram shows only the forces on the object, in one sentence. Accept any sentence that says it shows the forces acting on the object, not the forces the object exerts on other things.
12
PSA box is pushed with 40 N to the right. Friction is 15 N to the left. Find the resultant. Write the number and direction.
13
PSThree forces act on a boat: 100 N forward, 60 N backward and 15 N backward. Find the resultant. Write the number and direction.
14
RA pupil claims the resultant of 8 N and 8 N in the same direction is zero. Is this right? Write yes or no.
15
RExplain in one sentence why the resultant of two forces in opposite directions is smaller than their sum. Accept any sentence that says the forces partly cancel each other.
13.3

Newton's first law: balanced forces

GCSE
State and use Newton's first law (balanced forces, equilibrium)
Video lesson: Newton's first law: balanced forcesComing soon
Context. A book rests on a table. It does not move. A football is kicked and rolls across a field, slowing down only slowly. Why do they behave differently? Newton’s first law explains both.

Newton’s first law says: an object remains at rest, or continues to move at a constant velocity, unless a resultant force acts on it. When the forces on an object are balanced (the resultant is zero), the object is in equilibrium. A book on a table is in equilibrium: its weight is balanced by the normal contact force.

A moving object does not need a force to keep moving. It only needs a force to speed up, slow down or change direction.

LawWhat it saysExample
firstan object stays at rest or moves at constant velocity unless a resultant force actsa book on a table
secondresultant force = mass x acceleration (F = m a)a car speeding up
thirdtwo forces in a pair are equal and opposite, on two different objectsa rocket pushing gas back
Newton's three laws in brief

Key ideas

  • Balanced forces: resultant = 0; the object stays at rest or moves at constant velocity.
  • Equilibrium: the forces are balanced.
  • A resultant force changes the velocity (speeds up, slows down, or turns).
  • No force is needed to keep a moving object going at a steady speed in a vacuum.
Worked example 13.3.1
A book on a table has a weight of 5 N downwards and a normal contact force of 5 N upwards. Is the book in equilibrium? Write yes or no.

Method. Find the resultant.

  1. Resultant. 5 - 5 = 0 N.
    5 - 5 = 0
  2. Decide. The resultant is zero, so the book is in equilibrium.
    yes
  3. Write the answer.
    yes

Check. ✓

Worked example 13.3.2
A car travels at a constant 20 m/s on a straight road with no resultant force. What happens to its speed? Write the word: increases, decreases or stays the same.

Method. Use Newton’s first law.

  1. Law. With no resultant force, the velocity stays constant.
    constant
  2. Decide. So the speed stays the same.
    stays the same
  3. Write the answer.
    stays the same

Check. ✓

Worked example 13.3.3
A block at rest on a table has a 7 N push to the right and 7 N of friction to the left. What is the resultant force? Write the number of newtons.

Method. The forces are equal and opposite.

  1. Subtract. Resultant = 7 - 7 = 0 N.
    7 - 7 = 0
  2. Decide. The block stays at rest, so the forces are balanced.
    balanced
  3. Write the answer.
    0 N

Check. ✓

Watch out

Watch out: a moving object does not need a force to keep moving. A force is needed to change its velocity, not to maintain it (friction and drag are forces that slow it).

Exam tip

Exam tip. When asked about constant velocity, say “the resultant force is zero”, and name the balanced forces.

Exercise 13C  Newton's first law

1
FWhat is the resultant force on an object at rest on a table? Write the number of newtons.
2
FWhat is the name of the state when the forces on an object are balanced? Write the word.
3
FA car moves at a steady 15 m/s. What is the resultant force on it? Write the number of newtons.
4
PSA cyclist is coasting at a steady speed on a flat road. The air resistance is 20 N backwards. What must the forward force be for steady speed? Write the number of newtons.
5
PSA trolley is pushed with 10 N forward and 10 N friction backward. Does it accelerate? Write yes or no.
6
RExplain why a book stays on a table, using Newton’s first law, in one sentence. Accept any sentence that says the weight is balanced by the normal contact force, so the resultant is zero.
7
RA pupil says “a moving object always needs a force to keep it moving.” Explain why this is wrong. Accept any answer that says no force is needed for constant velocity, only for a change of velocity.
8
PSA parachutist falls at a steady speed. The weight is 700 N and the drag is 700 N upwards. What is the resultant force? Write the number of newtons.
9
PSA cart is at rest, and a 6 N force is applied to it, with 2 N of friction opposing it. What is the resultant force? Write the number of newtons.
10
RExplain why a satellite in space keeps moving at a steady speed with no engine on, in one sentence. Accept any sentence that says there is almost no friction or drag in space, so the resultant force is nearly zero.
11
PSA block is in equilibrium on a slope. Name two forces that must be balanced in this case, and say whether they are equal. Write yes or no.
13.4

Newton's second law: F = m a

GCSE
State and use Newton's second law (F = m a)
Video lesson: Newton's second law: F = m aComing soon
Context. A parent pushes a pram. The harder the push, the faster the pram speeds up. A heavier pram speeds up more slowly for the same push. Newton’s second law gives the exact relationship.

Newton’s second law says that the resultant force on an object equals its mass times its acceleration:

F = m x a

where F is the resultant force in newtons (N), m is the mass in kilograms (kg), and a is the acceleration in metres per second squared (m/s2). Rearranging gives a = F / m and m = F / a. A larger resultant force gives a larger acceleration; a larger mass gives a smaller acceleration for the same force.

Key ideas

  • F = m x a, with F in newtons, m in kilograms, a in m/s squared.
  • a = F / m; m = F / a.
  • F = resultant force. Use the net force, not the individual forces.
  • For a given mass, the acceleration is proportional to the resultant force.
Worked example 13.4.1
A 2 kg trolley is pushed with a resultant force of 6 N. Calculate its acceleration. Write the number of m/s squared.

Method. Use a = F / m.

  1. Take the numbers. F = 6 N and m = 2 kg.
    F = 6, m = 2
  2. Divide. a = 6 / 2 = 3 m/s2.
    6 / 2 = 3
  3. Write the answer.
    3 m/s2

Check. 2 x 3 = 6 N. ✓

Worked example 13.4.2
A 1000 kg car accelerates at 2 m/s squared. Calculate the resultant force. Write the number of newtons.

Method. Use F = m x a.

  1. Take the numbers. m = 1000 kg and a = 2 m/s2.
    m = 1000, a = 2
  2. Multiply. F = 1000 x 2 = 2000 N.
    1000 x 2 = 2000
  3. Write the answer.
    2000 N

Check. 2000 / 1000 = 2 m/s2. ✓

Worked example 13.4.3
A resultant force of 30 N pushes a 5 kg object. Its push is opposed by 10 N friction, so the net force is 20 N. Find the acceleration. Write the number of m/s squared.

Method. First find the resultant (net) force, then use a = F / m.

  1. Net force. Net = 30 - 10 = 20 N.
    30 - 10 = 20
  2. Acceleration. a = 20 / 5 = 4 m/s2.
    20 / 5 = 4
  3. Write the answer.
    4 m/s2

Check. 5 x 4 = 20 N. ✓

Watch out

Watch out: use the resultant force in F = m a, not just one of the forces. Subtract opposing forces first.

Exam tip

Exam tip. Write F = m a, then the three numbers with their units, then rearrange. Check the unit of acceleration is m/s squared.

Exercise 13D  Newton's second law calculations

1
FA 4 kg object has a resultant force of 12 N. Calculate its acceleration. Write the number of m/s squared.
2
FA 2 kg object accelerates at 3 m/s squared. Calculate the resultant force. Write the number of newtons.
3
FA resultant force of 20 N acts on a 5 kg object. Calculate its acceleration. Write the number of m/s squared.
4
FA resultant force of 60 N gives an acceleration of 5 m/s squared. Find the mass. Write the number of kilograms.
5
FA 0.5 kg ball accelerates at 8 m/s squared. Calculate the resultant force. Write the number of newtons.
6
PSA 1500 kg car has a resultant force of 3000 N. Calculate its acceleration. Write the number of m/s squared.
7
PSA 60 kg runner has a resultant forward force of 90 N. Calculate the acceleration. Write the number of m/s squared to 2 decimal places.
8
PSA 3 kg object has a driving force of 15 N and a friction force of 6 N opposing it. Calculate its acceleration. Write the number of m/s squared.
9
PSA 0.2 kg object is accelerated at 15 m/s squared. Calculate the force. Write the number of newtons.
10
PSA net force of 36 N acts on a mass, which accelerates at 4 m/s squared. Find the mass. Write the number of kilograms.
11
PSA 1200 kg car travels at a steady speed. The engine force is 1800 N and the drag is 1800 N. What is the acceleration? Write the number of m/s squared.
12
RExplain in one sentence why a larger mass gives a smaller acceleration for the same resultant force. Accept any sentence that says a = F / m, so a bigger m gives a smaller a.
13
PSA car of mass 800 kg accelerates from rest to a constant acceleration of 2.5 m/s squared. Calculate the resultant force. Write the number of newtons.
14
RA pupil doubles the resultant force on a fixed mass. What happens to the acceleration: doubles, halves or stays the same? Write the word.
15
PSCalculate the resultant force on a 4 kg object accelerating at 2 m/s squared, if a friction force of 3 N acts against the motion. Write the driving force in newtons.
13.5

Newton's third law, friction, drag and terminal velocity

GCSE
State Newton's third law (action-reaction pairs), Explain friction and drag, and terminal velocity, using the balance of forces
Video lesson: Newton's third law, friction, drag and terminal velocityComing soon
Context. A rocket pushes gas downwards, and the gas pushes the rocket upwards. A parachutist falls faster and faster, until the drag balances the weight. Newton’s third law and the balance of forces explain both.

Newton’s third law says that when object A exerts a force on object B, object B exerts an equal and opposite force on object A. These are an action-reaction pair. They act on different objects, so they do not cancel each other out.

Friction is a contact force that opposes motion between two surfaces. Drag (air resistance) is a force that opposes the motion of an object through a fluid. A falling object speeds up until the drag is equal to its weight. Then the resultant force is zero, and it falls at a constant speed called the terminal velocity.

Velocity of a falling object (example)0102030400246810terminal velocitytime (s)velocity (m/s)
Velocity against time for a falling object: it reaches terminal velocity when drag balances weight

Key ideas

  • Third law: action and reaction are equal, opposite, and act on different objects.
  • Friction and drag always oppose the motion.
  • Terminal velocity: when drag equals weight, the resultant is zero and the speed is constant.
  • A larger, heavier or more streamlined shape changes the terminal velocity.
Worked example 13.5.1
A book pushes down on a table with a force of 5 N. What is the reaction force, and on which object does it act? Write the size and the object, as a number and a word.

Method. The reaction is equal and opposite, and acts on the other object.

  1. Size. The reaction is equal in size: 5 N.
    5 N
  2. Object. It acts upwards on the book, from the table.
    the book
  3. Write the answer.
    5 N, the book

Check. ✓

Worked example 13.5.2
A parachutist has a weight of 700 N and drag of 700 N upwards. Describe the motion. Write the word: accelerating, constant velocity or stopped.

Method. Find the resultant force.

  1. Resultant. 700 - 700 = 0 N.
    0
  2. Decide. With zero resultant the parachutist moves at a constant velocity.
    constant velocity
  3. Write the answer.
    constant velocity

Check. ✓

Worked example 13.5.3
A ball moves upwards. Its weight of 4 N and the air resistance of 6 N both act downwards. Is the ball speeding up or slowing down? Write the word: speeding up or slowing down.

Method. Find the resultant, then compare its direction with the motion.

  1. Resultant. Both forces act downwards, so the resultant is 4 + 6 = 10 N downwards.
    10 N down
  2. Decide. The resultant opposes the upward motion, so the ball is slowing down.
    slowing down
  3. Write the answer.
    slowing down

Check. ✓

Watch out

Watch out: action and reaction forces never cancel each other out, because they act on different objects. Balanced forces act on the same object.

Exam tip

Exam tip. For terminal velocity, say “the drag increases until it equals the weight, so the resultant force is zero and the speed is constant.”

Exercise 13E  Newton's third law, friction and terminal velocity

1
FWhat is the name of a pair of equal and opposite forces that act on different objects? Write the two words.
2
FWhat force opposes motion between two surfaces that touch? Write the word.
3
FWhat force opposes the motion of an object through air? Write the word.
4
FWhat is the name of the constant speed a falling object reaches when drag equals its weight? Write the name.
5
FA rocket pushes gas backwards with a force of 500 N. What is the force on the rocket from the gas? Write the number of newtons.
6
FA falling object has a weight of 3 N and drag of 3 N. What is the resultant force? Write the number of newtons.
7
RExplain why a falling object speeds up at first and then reaches a steady speed, in one sentence. Accept any sentence that says the drag increases as it speeds up, until it balances the weight.
8
RExplain why a parachute with a larger surface area has a lower terminal velocity, in one sentence. Accept any sentence that says a larger area gives more drag, so the drag balances the weight at a lower speed.
9
RA pupil says “the action and reaction forces cancel each other out, so nothing moves.” Explain why this is wrong. Accept any answer that says they act on different objects, so they do not cancel.
10
PSA 2 kg box is pushed across a floor with a friction force of 4 N. If the push is 4 N, what is the acceleration? Write the number of m/s squared.
11
RDescribe the forces on a skydiver after she reaches terminal velocity, and say what the resultant force is. Accept any answer that says drag and weight are equal and opposite, so the resultant is zero.

Chapter summary

SkillMethod
Vectors and scalarsVector: size and direction (force, velocity); scalar: size only (mass, speed)
WeightW = m x g, g = 9.8 N/kg
ResultantSame direction: add; opposite: subtract; balanced gives zero
Newton's 2nd lawF = m a; a = F / m; m = F / a
Newton's 3rd law and dragAction and reaction are equal, opposite, on different objects; terminal velocity when drag = weight

Can you…?

  • I can tell vectors from scalars and contact from non-contact forces
  • I can calculate weight with W = mg
  • I can find the resultant of forces in the same and opposite directions
  • I can use F = m a in all three forms
  • I can explain action-reaction pairs and terminal velocity

Key terms

vector
a quantity with both size and direction
scalar
a quantity with size only
resultant force
the single force that has the same effect as all the forces acting together
equilibrium
the state of an object when the forces on it are balanced
terminal velocity
the constant speed reached when drag equals weight
acceleration
the rate of change of velocity, in m/s squared

Exercise 13Z  Check-up

1
Calculate the weight of a 4 kg object, using g = 9.8 N/kg. Write the number of newtons.
2
Two forces of 7 N and 3 N act in opposite directions on an object. What is the resultant? Write the number of newtons.
3
Two forces of 3 N and 9 N act in the same direction. What is the resultant? Write the number of newtons.
4
A 5 kg object has a resultant force of 10 N. What is its acceleration? Write the number of m/s squared.
5
A 3 kg object accelerates at 4 m/s squared. What is the resultant force? Write the number of newtons.
6
What is the mass of an object that accelerates at 2 m/s squared under a resultant force of 14 N? Write the number of kilograms.
7
Name the force that acts between a tyre and the road to stop a car from sliding. Write the word.
8
Two equal and opposite forces act on an object. What is the resultant? Write the number of newtons.
9
A 1 kg object is pushed with 4 N, and friction is 1 N opposing it. Find the acceleration. Write the number of m/s squared.
10
Explain why a book on a table does not fall through the table, in one sentence. Accept any sentence that says the normal contact force from the table balances the weight.

Total 28 marks. Allow about 28 minutes.

Exercise 13X  Exam-style questions

1
FCalculate the weight of a 12 kg bag, using g = 9.8 N/kg. Write the number of newtons.[2 marks]
2
FA 1500 kg car has a resultant force of 4500 N. Calculate the acceleration. Write the number of m/s squared.[2 marks]
3
PSA 25 N push to the right and a 10 N friction force to the left act on a 3 kg crate. Calculate the resultant force and the acceleration. Write two values: the resultant in newtons, then the acceleration in m/s squared, separated by a comma.[3 marks]
4
RExplain, using Newton’s first law, why a trolley moving at a steady speed on a level track has no resultant force acting on it. Accept any answer that says the forces are balanced, so the velocity is constant.[3 marks]
5
PSA 0.8 kg ball is kicked and accelerates at 25 m/s squared. Calculate the resultant force on it. Write the number of newtons.[2 marks]
6
PSA parachutist of weight 800 N falls at a steady speed. Calculate the drag force and say what the resultant force is. Write two values: the drag in newtons, then the resultant in newtons, separated by a comma.[3 marks]
7
PSA 5 kg object has a driving force of 40 N and a drag force of 15 N opposing it. Calculate the acceleration. Write the number of m/s squared.[3 marks]
8
RExplain why a falling object reaches a terminal velocity, and describe the resultant force at this point. Accept any answer that says drag increases with speed until it equals the weight, so the resultant force is zero and the speed is constant.[4 marks]
9
RExplain why the forces in an action-reaction pair do not cancel each other out, using an example of a person walking. Accept any answer that says the forces act on different objects (the foot and the ground), so they cannot cancel.[3 marks]
10
PSA 0.4 kg object has a resultant force of 1.2 N. Calculate the acceleration, and state the direction of the acceleration if the resultant is to the left. Write the acceleration and direction, as a number then a word.[3 marks]
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