Unit 2 · Topic 2.2 Beta

Forces and Free-Body Diagrams

A force is an interaction between two objects.

Practice 1: Creating RepresentationsPractice 3: Scientific Questioning and Argumentation

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Question set for this topic

Part 1 · Hook

Why this matters

Kick a soccer ball and it flies off; let go of a phone and it drops; lean on a wall and the wall holds you up. Each of these is an interaction between two objects. Learning to see every interaction acting on one object, and to draw them as a free-body diagram, is the single most tested skill in this course.

Part 2 · Before you start

What this builds on

Part 3 · Prerequisite check

Quick check before you start

1. Which quantity is a vector?

  1. Force
  2. Mass
  3. Distance
  4. Time
Show the answer

A force has a size and a direction, so it is a vector. Mass, distance and time are sizes only.

  • Correct: Force:
  • Mass:
  • Distance:
  • Time:

2. On a line, a 30 m/s velocity to the right and a 10 m/s velocity to the left are written as

  1. +30 m/s and −10 m/s
  2. +30 m/s and +10 m/s
  3. −30 m/s and +10 m/s
  4. 30 m/s and 10 m/s, with no sign
Show the answer

Pick right as positive; then left is negative.

  • Correct: +30 m/s and −10 m/s:
  • +30 m/s and +10 m/s:
  • −30 m/s and +10 m/s:
  • 30 m/s and 10 m/s, with no sign:

3. The center of mass of a system is

  1. its mass-weighted average position
  2. its geometric middle in every case
  3. the heaviest part of it
  4. the point where it touches the ground
Show the answer

x_cm = Σm·x ÷ Σm weights each position by its mass.

  • Correct: its mass-weighted average position:
  • its geometric middle in every case:
  • the heaviest part of it:
  • the point where it touches the ground:

Part 4 · See it

See it first

Left: a 40 kg crate on a floor pulled to the right by a horizontal rope, moving at constant velocity. Right: its free-body diagram, a dot with four arrows starting on it: F_N, floor on crate, up; F_g, Earth on crate, down, the same length; F_T, rope on crate, right; F_f, floor on crate, left, the same length as F_T. Velocity is not drawn on the diagram.
Each force on the crate, drawn from a dot and labeled with its type and agent. Velocity stays in the scene. LevlPrep original diagram.

Part 5 · Step by step

How it works, step by step

  1. Two objects interact (they touch, or one is Earth)each exerts a force on the other: a push or pull with a size and a direction
  2. You choose one object and list everything that touches it, plus Earthyou have every force on it, each with an agent
  3. You draw each force as an arrow starting on a dot at the center of massyou get a free-body diagram: whole forces, labeled with type and agent, lengths in proportion
  4. You add the forces as vectors, with signs on each axisyou get the net force, which is a result of the diagram, not one of its arrows

Part 6 · Key ideas

Key ideas

  • A force is a push or pull between two objects, measured in newtons (1 N = 1 kg·m/s²). It is a vector.
  • Contact forces (normal force, tension, friction) need touching. Weight, F_g = mg, is Earth's pull at a distance; near Earth g = 9.8 m/s² (10 m/s² is accepted).
  • A free-body diagram: a dot for the object, one arrow per force starting on the dot, labeled type and agent ("F_N, floor on box"), no components, no velocity, no net force arrow.
  • The net force is the vector sum of all the forces. Find it from the diagram; never draw it on the diagram.

Part 7 · Misconception

A common mistake

The wrong idea: A moving object has a "force of motion" pushing it along, and the free-body diagram should show it.

What actually happens: Every force needs an agent touching the object (or Earth). Once a thrown ball leaves the hand, only Earth (and air) act on it. Motion does not need a forward force.

Part 8 · Check yourself

Check yourself

Exam-style questions. Anything you miss goes into your review queue.

Diagram

A loaded sled slowing down

A sled loaded with firewood moves to the right across level snow. A person ahead of it pulls a horizontal rope, but the sled is slowing down. The snow rubs on the sled's runners. Air resistance is negligible.

v (decreasing)rope

1. How many forces act on the loaded sled?

  1. Four
  2. Three
  3. Five
  4. Two
Show the answer

Four objects interact with the sled: the rope pulls it right, the snow rubs on it to the left (friction), the snow pushes up on it (the normal force), and Earth pulls it down (the weight).

  • Correct: Four: Right: rope, friction from the snow, normal force from the snow, and weight.
  • Three: Three leaves one out, usually the normal force: the snow both rubs on the runners and pushes up on them, and those are two separate forces.
  • Five: A fifth "force of motion" has no agent. Moving does not need its own force; every force on the sled comes from an object touching it or from Earth.
  • Two: Two forces would leave out the vertical pair: Earth pulls the sled down and the snow pushes it up.

2. Which label correctly describes the friction arrow on the sled's free-body diagram?

  1. F_f, snow on sled
  2. F_f, sled on snow
  3. F_f, rope on sled
  4. F_f, Earth on sled
Show the answer

A free-body diagram shows forces exerted ON the sled, each labeled with its type and the object that exerts it (the agent). The snow exerts the friction on the sled.

  • Correct: F_f, snow on sled: Right: type (friction), agent (snow), object (sled).
  • F_f, sled on snow: The sled does push on the snow, but that force acts on the snow, so it belongs on the snow's diagram, not the sled's.
  • F_f, rope on sled: The rope exerts a tension force on the sled, not friction.
  • F_f, Earth on sled: Earth exerts the weight on the sled; friction comes from the surface the sled slides on.

3. A student's free-body diagram of the sled shows five arrows: F_T (rope on sled), F_f (snow on sled), F_N (snow on sled), F_g (Earth on sled) and an arrow to the right labeled v. What should she change?

  1. Remove the arrow labeled v
  2. Remove the friction arrow, since the sled moves
  3. Add an arrow for the force of motion
  4. Remove F_N, since F_g already covers the snow
Show the answer

Velocity is not a force: no object exerts it. It describes the motion, so it can go beside the scene, but never on the free-body diagram.

  • Correct: Remove the arrow labeled v: Right: only forces, each with an agent, go on the diagram.
  • Remove the friction arrow, since the sled moves: Friction acts precisely because the runners slide on the snow; it stays.
  • Add an arrow for the force of motion: There is no force of motion. A moving object needs no force to keep moving (this unit explains why).
  • Remove F_N, since F_g already covers the snow: F_N and F_g come from different agents (the snow and Earth) and are different forces; both belong.

4. The rope pulls the sled with a force of 55 N, and the net force on the sled is 30 N to the left. The vertical forces cancel. How large is the friction on the sled, in newtons?

Type a number in N.

Show the answer

Take right as positive. The net force is the sum of the horizontal forces: +55 N + F = −30 N, so F = −85 N. Friction is 85 N to the left.

  • Answer: 85 N

5. A block rests on a ramp tilted 30° above the horizontal. In which direction does the normal force on the block point?

  1. Perpendicular to the ramp's surface, away from it
  2. Straight up, opposite the weight
  3. Up the ramp, along its surface
  4. Straight down, into the ramp
Show the answer

A surface pushes perpendicular to itself and away from itself. On a tilted ramp, perpendicular to the surface is tilted 30° from vertical.

  • Correct: Perpendicular to the ramp's surface, away from it: Right: "normal" means perpendicular to the surface.
  • Straight up, opposite the weight: The normal force is straight up only when the surface is level.
  • Up the ramp, along its surface: A push along the surface would be friction, not the normal force.
  • Straight down, into the ramp: A surface can only push an object away from itself; it does not pull it in.

6. A hockey puck slides across level ice after leaving the stick. Friction and air resistance are negligible. Which arrows belong on its free-body diagram? Select all that apply.

  1. F_g, Earth on puck, down
  2. F_N, ice on puck, up
  3. The force of the stick, forward
  4. The force of motion, forward
Show the answer

Only objects touching the puck now, plus Earth, exert forces on it. The stick stopped touching it when it was hit.

  • Correct: F_g, Earth on puck, down: Right: Earth pulls the puck down.
  • Correct: F_N, ice on puck, up: Right: the ice pushes up on the puck.
  • The force of the stick, forward: The stick no longer touches the puck, so it exerts no force on it now.
  • The force of motion, forward: There is no force of motion: the puck keeps sliding with no forward force at all.

Part 9 · Summary

Summary

A force is an interaction between two objects. To draw a free-body diagram, list every object touching your object plus Earth, and draw each force as a whole arrow from a dot, labeled with type and agent; the net force is their vector sum and is never drawn as an extra arrow.

Part 10 · Up next

What comes next

Part 11 · Connections

Connections