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Forces and Newton's Laws

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Why this chapter
Why this chapter exists

Kinematics told you how a body moves: where it is, how fast, how its velocity changes. It never asked why. This chapter answers that question with three laws that Newton wrote on a single page in 1687. A body keeps its velocity unless a force acts. A net force changes the velocity at a rate fixed by the mass. Every force has a partner on another body. With these laws and one careful drawing, the free-body diagram, you can work out the motion of anything from a Metro train to a cricket ball.

You will learn
By the end of this chapter you will
  1. Name every force on a body, with its agent and its direction: weight, normal force, tension, spring force and an applied force.
  2. State the first law, explain inertia with Galileo's argument, and say when the net force on a body is zero.
  3. Use \(\sum \vec F = m\vec a\) as a vector law, along each axis, and tell mass from weight.
  4. Draw a complete free-body diagram, one force at a time, with no missing force and no invented one.
  5. Identify third-law pairs correctly and solve a single-body problem with the four-step plan.
Before you begin
Before you begin

You should know the kinematics of Unit 2: velocity and acceleration as vectors, the equations of motion for constant acceleration, and how to split a vector into two perpendicular components. You should be able to use sine and cosine for a given angle.

Already know this?

Lessons

1
What a Force Is
A force is a push or a pull that one body exerts on another. The forces you meet in every problem: weight, the normal force, tension, the spring force and an applied push or pull.
What a force isWeight normal force and tensionThe spring force
15 min0%
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2
Inertia and the First Law
A body left alone keeps its velocity. Galileo's argument from ramps, the puck on ice, Newton's first law, and the frames of reference in which the law holds.
Inertia and galileos argumentNewtons first law
14 min0%
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3
The Second Law
How much a body accelerates. The net force equals mass times acceleration, as a vector and along each axis. The newton, and the difference between mass and weight.
Force mass and accelerationSecond law as a vectorMass and weight
16 min0%
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4
Free-Body Diagrams
The drawing that every dynamics problem starts from. Cut one body free, then draw the forces on it one at a time, gravity first and then one force for every contact.
Isolating the bodyDrawing a free body diagram
13 min0%
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5
The Third Law and the Plan
Forces come in pairs that act on two different bodies. The pairs students confuse, weight and normal force above all, and the four-step plan that solves every dynamics problem.
Newtons third lawThird law pairs students confuseThe plan for a dynamics problem
16 min0%
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Read in order. The small labels are the topics of each lesson. They take your colour as you answer the checks.

Glossary

The key words of this chapter, with the meaning this chapter gives them.

action-reaction pair
The two forces of one interaction: the force of A on B and the force of B on A. They are equal, opposite, of the same kind, and act on different bodies.
contact force
A force that acts only while two bodies touch, such as a push, the normal force, tension or friction.
extension
The change in length of a spring from its natural length. A compression is a negative extension.
force
A push or a pull exerted by one body on another. It is a vector, measured in newtons.
free-body diagram
A drawing of one body alone with an arrow for every force acting on it, and for nothing else.
friction
The force a rough surface exerts parallel to itself, opposing the sliding of a body along it. It has its own chapters later in this unit.
inertia
The tendency of a body to keep its velocity, at rest or in uniform motion. It is a property of the body, not a force.
inertial frame
A frame of reference in which Newton's first law holds; a frame that is not accelerating. The ground is one, to a very good approximation.
mass
The measure of a body's inertia, in kilograms. It is a scalar and does not depend on where the body is.
net force
The vector sum of all the forces acting on a body, \(\sum \vec F\).
newton
The SI unit of force. One newton gives a mass of one kilogram an acceleration of one metre per second squared: \(1\,\text{N} = 1\,\text{kg·m/s}^2\).
non-contact force
A force that acts across space without contact. In mechanics the only one is gravity.
normal force
The push of a surface on a body in contact with it, perpendicular to the surface. A surface can push but never pull.
spring constant
The force needed per unit extension of a spring, \(k = F/x\), in N/m. A stiff spring has a large \(k\).
spring force
The force a stretched or compressed spring exerts on whatever holds its end, directed towards its natural length.
tension
The pull of a string or rope on a body tied to it, along the string and away from the body.
weight
The gravitational pull of the Earth on a body, \(W = mg\), directed vertically downward.