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C. Forces · Forces

Forces: Unit Review

C1.1 C1.2 C2.1 C2.2 C2.3 C2.4 C2.5 C2.6 C3.1 C3.2 C3.3 C3.4 A1.12 A2.1 A2.2About 40 minutes
Learning goals
  • I can draw free-body diagrams and use Newton's three laws to explain and predict motion.
  • I can solve one-dimensional problems involving gravity, normal force, friction, tension and air resistance.
  • I can plan and analyse an investigation into forces.
  • I can assess technologies that apply forces and explain how Galileo and Newton changed our understanding of motion.

Words to know

net force (Fnet)
The vector sum of all forces on an object.
Newton's laws
First: Fnet = 0 gives constant velocity. Second: Fnet = ma. Third: forces come in equal and opposite pairs on different objects.
Fg = mg
Gravitational force (weight) equals mass times gravitational field strength (9.8 N/kg on Earth).
friction
Static: Ff,s ≤ μs FN. Kinetic: Ff,k = μk FN.
terminal velocity
The constant velocity reached when air resistance equals weight.

Let's review!

In this unit you learned to name forces and draw free-body diagrams, and you followed the story of how Galileo and Newton replaced Aristotle's ideas with the idea of inertia. You used Newton's three laws to explain and calculate motion: balanced forces and constant velocity, Fnet = ma, and action-reaction pairs. You related mass, g and weight, measured and used coefficients of friction, analysed free fall and terminal velocity, solved connected-object problems, designed your own inquiry, and assessed technologies from ABS to winter tires.

This review has a few questions from every lesson. Try each one, then press Show answer to check.

How to use this review

Do one or two sections at a time. For every calculation, draw the free-body diagram first and write your + direction. Use g = 9.8 N/kg, convert km/h to m/s (÷ 3.6), and round only final answers (usually 2 or 3 significant digits). For each question you get wrong, write down why (wrong FBD? used a single force instead of the net force? mass instead of weight? forgot static friction can be less than μs FN?) and go back to that lesson's worked examples. Finish with the 10-question quiz.

First lawFnet = 0 ⟹constant velocitySecond lawFnet = maa in direction of FnetThird lawF(A on B) = −F(B on A)pairs act on different objects
Newton's three laws on one line. The first is the special case of the second with Fnet = 0; the third tells you where every force comes from.

Types of Forces and What They Do

1

Classify as contact or action-at-a-distance: tension, magnetic force, air resistance.

2

A sled slides east and slows down. Which way does friction point?

3

In which direction does the normal force act on a box resting on a ramp?

Free-Body Diagrams and Net Force

1

Forces of 35 N right, 12 N left and 8 N left act on a cart. Find the net force.

2

A 6.0 kg box rests on the floor while you pull up on it with 20 N. Find the normal force.

3

A wagon is pulled with 70 N and the net force is 25 N forward. Find friction.

From Aristotle to Galileo and Newton: The Idea of Inertia

1

What did Aristotle believe about forced motion?

2

What did Galileo conclude from his double-ramp thought experiment?

3

In what year was Newton's Principia published, and what did it contain?

Newton's First Law: Inertia and Balanced Forces

1

A 900 kg car drives at a constant 80 km/h; resistive forces total 600 N. What forward force does the road provide?

2

Why does a passenger without a seatbelt keep moving forward when a car stops suddenly?

3

A 40 kg crate is lowered at constant speed by a rope. Find the tension.

Newton's Second Law: Fnet = ma

1

A net force of 45 N acts on a 15 kg object. Find a.

2

A 1200 kg car goes from 0 to 24 m/s in 8.0 s. Find the net force.

3

A 20 kg box is pushed with 100 N and accelerates at 3.0 m/s². Find friction.

4

If Fnet is tripled and m is doubled, how does a change?

Investigating Acceleration, Net Force and Mass

1

On a graph of a against Fnet for a cart, the slope is 0.40 /kg. Find the cart's mass.

2

What should you plot against a to get a straight line when the force is constant and the mass changes?

3

Expected 2.0 m/s², measured 1.8 m/s². Find the percent error and suggest one cause.

Mass, Weight and Gravitational Field Strength

1

Find the weight of a 72 kg astronaut on Earth and on the Moon (g = 1.6 N/kg).

2

A 50 kg student stands on a scale in an elevator accelerating down at 1.8 m/s². Find the reading.

3

Why do astronauts on the ISS float, even though g there is about 8.7 N/kg?

Newton's Third Law: Action-Reaction Pairs

1

Give the reaction to: "The road pushes forward on a car's tires."

2

A 55 kg skater and an 80 kg skater push apart with 110 N. Find each acceleration.

3

Are the weight of a book on a table and the normal force on it an action-reaction pair? Explain.

objectFN = mg (level, no other vertical forces)Fg = mgFaFf = μ FNThe FBD that solves most problems in this unit
Start every problem here: gravity, normal force, the applied force or tension, and friction (static up to μs FN, or kinetic μk FN). Then add the forces along a line and use Fnet = ma.

Static and Kinetic Friction: Coefficients of Friction

1

A 25 kg box needs 98 N to start sliding. Find μs.

2

The same box slides at constant speed with a 61 N pull. Find μk.

3

The box above (μs = 0.40) is pushed with 50 N. What is the friction force?

Solving Problems with Friction and Newton's Laws

1

A 15 kg crate is pulled with 80 N; μk = 0.40. Find a.

2

A puck slides with μk = 0.040 starting at 6.0 m/s. How far does it go?

3

A car skids 20 m from 60 km/h. How far would it skid from 120 km/h on the same road?

Free Fall, Air Resistance and Terminal Velocity

1

A rock falls freely from rest for 2.5 s. How fast is it moving and how far has it fallen?

2

A 70 kg skydiver feels 490 N of air resistance. Find her acceleration.

3

What is true about the net force at terminal velocity?

Just for fun

Unit summary in one sentence: things keep doing what they're doing, unless they're pushed, in which case they push back, and friction gets a vote.

Connected Objects, Tension and Pulleys

1

Carts of 2.0 kg and 4.0 kg are tied together and pulled by 18 N on a frictionless floor (force on the 4.0 kg cart). Find a and the tension between them.

2

A 3.0 kg cart on a frictionless table is pulled by a 1.0 kg hanging mass. Find a.

3

In an Atwood machine with 2.5 kg and 1.5 kg masses, find a.

Planning and Conducting a Forces Inquiry

1

Write a hypothesis for testing whether kinetic friction depends on contact area.

2

Convert a luggage-scale reading of 5.0 lb (force) to newtons.

3

A force sensor reads 0.2 N with nothing attached. What kind of error is this and how do you fix it?

Newton's Laws at Work: Analysing and Improving Technologies

1

Explain why ABS lets a driver steer while braking hard.

2

A launch coaster accelerates a 50 kg rider at 15 m/s². Find the seat-back force.

3

Propose one physics-based improvement to winter boots and one trade-off.

Forces, Safety Technology and Society

1

A 65 kg person moving at 14 m/s is stopped in 0.14 s. Find the average force.

2

How do crumple zones protect occupants?

3

Name one career that uses the physics of forces and its usual education.

Check your understanding

Quiz

1.

Which force is an action-at-a-distance force?

2.

A box moves at constant velocity across the floor. The net force on it is:

3.

A 5.0 kg object has a net force of 15 N on it. Its acceleration is:

4.

Who first used ramps and measurements to argue that objects keep moving unless a force like friction stops them?

5.

The weight of a 20 kg object on Mars (g = 3.7 N/kg) is:

6.

A hammer hits a nail with 300 N. The force of the nail on the hammer is:

7.

A 10 kg box on a floor (μs = 0.50) is pushed with 30 N. The friction force is:

8.

An object slides to a stop on a level floor with μk = 0.20. Its acceleration is about:

9.

A skydiver at terminal velocity has:

10.

Seat belts, airbags and crumple zones reduce injuries mainly by:

For parents and teachers

Use the review to find what to revisit:

  • Missing or extra forces in free-body diagrams, or sign errors when adding forces → Lessons 1 and 2 (Types of Forces; Free-Body Diagrams and Net Force).
  • Thinking a moving object needs a forward net force, or mixing up Aristotle's and Newton's ideas → Lessons 3 and 4 (Aristotle to Newton; Newton's First Law).
  • Using one force instead of the net force in F = ma, or errors linking F = ma to kinematics → Lesson 5 (Newton's Second Law).
  • Trouble with graphs, slopes or percent error → Lessons 6 and 13 (Investigating Acceleration; Planning a Forces Inquiry).
  • Confusing mass and weight, or elevator scale readings → Lesson 7 (Mass, Weight and g).
  • Pairing weight with normal force as a third-law pair → Lesson 8 (Newton's Third Law).
  • Using μs FN when the object is not about to slide, or forgetting that FN changes when someone pushes down or pulls up → Lessons 9 and 10 (Friction).
  • Believing heavy objects fall faster in a vacuum, or that a = 0 at the top of a throw → Lesson 11 (Free Fall and Air Resistance).
  • Using only one object's mass for a connected system → Lesson 12 (Connected Objects).
  • Vague technology proposals or one-sided assessments → Lessons 14 and 15 (Technologies; Safety Technology and Society).