SPH3U · Unit 2 test review

Forces: Test Review

Everything for the Unit 2 test on one page: the key facts from all 5 lessons, the mistakes that cost the most marks, and a practice test that points you back to the lessons you need.

Key facts

Forces, Weight and Free-Body Diagrams

A force is a push or pull measured in newtons, $1 N = 1 kg \cdot m/s^{2}$ , and it is always a vector.
$F_{g} = m g$ with $g = 9.81 m/s^{2} = 9.81 N/kg$ . Mass must be in kilograms.
Mass is matter in kilograms and does not change with location; weight is a force in newtons and does.
Normal means perpendicular to the surface — and $F_{N}$ is not automatically equal to the weight.
Tension is always a pull along the rope, away from the object.
A free-body diagram shows one isolated object and only the forces acting on it.

Newton's Three Laws of Motion

First law: with zero net force, an object keeps its velocity — at rest or moving in a straight line at constant speed.
Inertia is resistance to a change in velocity, and mass is its measure.
Second law: $F_{n e t} = m a$ . The acceleration points along the net force, not along any single force.
Zero net force means zero acceleration, which is the first law restated.
Third law: if A pushes B, B pushes A equally and oppositely. The two forces act on different objects.
Action-reaction pairs never cancel, because they never act on the same object.
Weight and normal force are not a third-law pair — same object, different force types.

Net Force in One Dimension

$Σ F = F_{n e t} = F_{+} + F_{-}$ — add the forces with their signs, after declaring a positive direction.
Balanced forces (net zero) mean equilibrium: at rest or moving at constant velocity.
Unbalanced forces produce acceleration in the direction of the net force, with $F_{n e t} = m a$ .
A scale reads the normal force, not the weight. They differ whenever there is vertical acceleration.
Accelerating upward makes you feel heavier; accelerating downward makes you feel lighter; free fall gives $F_{N} = 0$ .
Connected objects share one acceleration. Find it with the system approach, then get tension from one object alone.
In an ideal rope the tension is the same throughout, and an ideal pulley only redirects it.

Friction and the Coefficient of Friction

Friction opposes relative sliding between surfaces and always acts along the surface.
$μ = \frac{F _{f r i c t i o n}}{F _{n or ma l}}$ , so $F_{f r i c t i o n} = μ F_{n or ma l}$ . It is a ratio, so it has no units.
Static friction adjusts to match the applied force up to a maximum; kinetic friction is constant and lower.
$μ_{s t a t i c} > μ_{kin e t i c}$ , which is why an object lurches as it breaks free.
Friction depends on the surface pair and the normal force — not on the apparent contact area.
On level ground with no extra vertical force, $F_{N} = m g$ .
The coefficient describes two surfaces together, never one material alone.

Forces in Action: Air Resistance, Terminal Velocity and Safety

Air resistance opposes motion through the air and grows as the object speeds up; it also grows with frontal area and with a less streamlined shape.
As a falling object speeds up, drag grows, the net force shrinks and the acceleration shrinks — the object is still speeding up, just more slowly.
Terminal velocity is reached when drag exactly balances weight: net force zero, acceleration zero, velocity constant and large.
Opening a parachute multiplies the drag, so the net force points upward while the motion is still downward — rapid slowing to a new, far lower terminal velocity.
A feather and a hammer fall together only in a vacuum; in air the feather's huge area-to-mass ratio gives it a tiny terminal velocity.
In a collision the change in velocity is fixed. Extending the stopping time reduces the acceleration, and $F_{n e t} = m a$ then reduces the force by the same factor.
Crumple zones, airbags, helmets and padded surfaces all work the same way: they make the stop take longer.

Where marks get lost

Using grams in $F_{g} = m g$ . The equation needs kilograms, or the answer is out by a factor of 1000. (Forces, Weight and Free-Body Diagrams)
Calling mass 'weight' and quoting it in newtons, or quoting a weight in kilograms. Kilograms are mass; newtons are force. (Forces, Weight and Free-Body Diagrams)
Drawing a 'force of motion' arrow in the direction something is travelling. Motion is not a force and nothing is applying it. (Forces, Weight and Free-Body Diagrams)
Assuming the normal force always equals the weight. It does on level ground with nothing else pushing vertically — and not otherwise. (Forces, Weight and Free-Body Diagrams)
Putting the object's push on the table onto the object's own free-body diagram. That force acts on the table. (Forces, Weight and Free-Body Diagrams)
Drawing the ramp, the rope and the floor in the diagram. A free-body diagram shows the object alone. (Forces, Weight and Free-Body Diagrams)
Forgetting that the normal force is perpendicular to the surface, which is not vertical on a slope. (Forces, Weight and Free-Body Diagrams)
Putting a single force into $F_{n e t} = m a$ when other forces are also acting. The equation takes the net force only. (Newton's Three Laws of Motion)
Thinking a moving object needs a continuous force to keep moving. Constant velocity requires zero net force. (Newton's Three Laws of Motion)
Claiming action-reaction pairs cancel, so nothing can accelerate. They act on different objects and never appear on the same diagram. (Newton's Three Laws of Motion)
Calling weight and normal force an action-reaction pair. Same object, different force types — they are balanced forces instead. (Newton's Three Laws of Motion)
Assuming the heavier object in a collision experiences the larger force. The forces are equal; only the accelerations differ. (Newton's Three Laws of Motion)
Using the mass of one part of a system when the whole system is being accelerated together. (Newton's Three Laws of Motion)
Adding force magnitudes without signs, so a $150 N$ push against $50 N$ of friction comes out as $200 N$ . (Net Force in One Dimension)
Including the weight and normal force in a horizontal net-force calculation. Handle each direction separately. (Net Force in One Dimension)
Treating 'moving upward' as 'accelerating upward'. A lift at constant speed has zero net force and reads your true weight. (Net Force in One Dimension)
Including the rope's tension as an external force when using the system approach. Internal forces cancel. (Net Force in One Dimension)
Using only one object's mass to find the acceleration of a connected pair. The whole system accelerates together. (Net Force in One Dimension)
Forgetting that the scale reads the normal force, and so quoting the weight whatever the lift is doing. (Net Force in One Dimension)
Declaring up as positive and then writing the weight as a positive number. (Net Force in One Dimension)
Giving $μ$ a unit. It is a ratio of two forces, so the units cancel completely. (Friction and the Coefficient of Friction)
Assuming $F_{N} = m g$ when something else also pushes vertically, or when the surface is not level. (Friction and the Coefficient of Friction)
Thinking a larger contact area means more friction. Only the normal force and the surface pair matter. (Friction and the Coefficient of Friction)
Using $μ_{s}$ when the object is already sliding, or $μ_{k}$ when deciding whether it will start to move. (Friction and the Coefficient of Friction)
Forgetting that 'constant velocity' means the applied force exactly equals friction, which is usually the information the question is handing you. (Friction and the Coefficient of Friction)
Treating friction as a property of one material. The coefficient always describes a pair of surfaces. (Friction and the Coefficient of Friction)
Adding friction to the applied force instead of subtracting it. Friction opposes the relative sliding. (Friction and the Coefficient of Friction)
Saying a skydiver at terminal velocity has no forces on her. Two very large forces act — weight and drag — and they cancel. It is the net force that is zero. (Forces in Action: Air Resistance, Terminal Velocity and Safety)
Reading terminal velocity as 'stops falling'. The acceleration becomes zero, so the velocity stops changing; she keeps falling at a steady, very high speed. (Forces in Action: Air Resistance, Terminal Velocity and Safety)
Claiming heavy objects always fall faster. In a vacuum every object accelerates at $9.81 m/s^{2}$ regardless of mass; in air the differences come from drag and area, not from weight alone. (Forces in Action: Air Resistance, Terminal Velocity and Safety)
Explaining a crumple zone by saying it 'absorbs the shock' or 'makes the impact softer'. State the chain: the change in velocity is fixed, a longer stopping time gives a smaller acceleration, and $F_{n e t} = m a$ then gives a smaller force. (Forces in Action: Air Resistance, Terminal Velocity and Safety)
Forgetting that when a parachute opens the velocity is still downward while the acceleration points upward. Opposite signs mean slowing down, not moving backwards. (Forces in Action: Air Resistance, Terminal Velocity and Safety)

Practice test

25 questions from across the unit. Each one shows the lesson it comes from.

Forces, Weight and Free-Body Diagrams
1
What is the weight, in newtons, of a $25 kg$ crate on Earth?
N
Forces, Weight and Free-Body Diagrams
2
A $6.0 kg$ sign hangs at rest from one vertical cable. What is the tension in the cable, in newtons?
N
Forces, Weight and Free-Body Diagrams
3
A book rests on a table. Which pair of forces appears on the book's free-body diagram?
Forces, Weight and Free-Body Diagrams
4
Match each force to the direction it acts.
Gravity
Normal
Tension
Friction
Forces, Weight and Free-Body Diagrams
5
Why do astronauts on the International Space Station appear weightless?
Newton's Three Laws of Motion
6
A net force of $84 N$ acts on a $12 kg$ object. What is its acceleration in $m/s^{2}$ ?
m/s^2
Newton's Three Laws of Motion
7
A truck collides head-on with a small car. Which experiences the larger force?
Newton's Three Laws of Motion
8
A book rests on a table. Which force is the true Newton's-third-law partner of the book's weight?
Newton's Three Laws of Motion
9
Match each everyday situation to the law that explains it.
A passenger lurches forward as a bus brakes
The same push moves an empty cart more than a full one
A rocket accelerates by expelling exhaust gas
A puck glides at constant speed on frictionless ice
Newton's Three Laws of Motion
10
A crate is pushed across a floor. Order these situations from largest forward acceleration to smallest.
1. 1Push of $200 N$ , friction of $50 N$
2. 2Push of $100 N$ , friction of $100 N$
3. 3Push of $200 N$ , friction of $150 N$
4. 4Push of $300 N$ , friction of $50 N$
Net Force in One Dimension
11
Forces of $80 N$ right and $30 N$ left act on an object. What is the magnitude of the net force, in newtons?
N
Net Force in One Dimension
12
A lift moves upward at a constant $3.0 m/s$ . What does a scale inside read compared with the passenger's true weight?
Net Force in One Dimension
13
Two crates of $5.0 kg$ and $10.0 kg$ are joined by a rope on a frictionless floor and pulled with $45 N$ . What is their shared acceleration, in $m/s^{2}$ ?
m/s^2
Net Force in One Dimension
14
When using the system approach on two crates joined by a rope, why is the tension left out?
Net Force in One Dimension
15
Match each lift situation to what the scale reads.
At rest
Accelerating upward
Accelerating downward
Cable cut, in free fall
Friction and the Coefficient of Friction
16
A $30 kg$ crate sits on a level floor with $μ_{k} = 0.40$ . What is the kinetic friction force, in newtons, once it is sliding?
N
Friction and the Coefficient of Friction
17
A brick is turned from lying flat to standing on its narrow end. What happens to the friction force as it slides?
Friction and the Coefficient of Friction
18
A $50 kg$ crate is pushed with $250 N$ on a floor where $μ_{k} = 0.35$ . What is its acceleration, in $m/s^{2}$ ?
m/s^2
Friction and the Coefficient of Friction
19
Match each surface pair to its approximate coefficient of friction.
Rubber on dry concrete
Wood on wood
Oiled steel on steel
Steel on ice
Friction and the Coefficient of Friction
20
A box is pushed with $60 N$ and does not move. Maximum static friction is $75 N$ . What is the friction force acting?
Forces in Action: Air Resistance, Terminal Velocity and Safety
21
A skydiver has reached terminal velocity. Which statement is correct?
Forces in Action: Air Resistance, Terminal Velocity and Safety
22
A $65 kg$ skydiver is at terminal velocity. What is the air resistance acting on her, in newtons?
N
Forces in Action: Air Resistance, Terminal Velocity and Safety
23
Why does a crumple zone reduce the force on the occupants of a car?
Forces in Action: Air Resistance, Terminal Velocity and Safety
24
A feather and a hammer are released together inside a chamber from which all the air has been pumped out. What happens?
Forces in Action: Air Resistance, Terminal Velocity and Safety
25
Match each safety feature to what it physically does.
Crumple zone
Airbag
Helmet foam liner
Gym mat

Endless drill

Fresh numbers every time, for the calculation questions in this unit.

Endless drillnew numbers every time

Generating a problem…