Newton’s Laws

Newton-1: Law of Inertia• Newton’s First Law• An object subject to no external forces

is at rest or moves with a constant velocity if viewed from an inertial inertial reference framereference frame.– If no net forces act, there is no

acceleration.

0 0netF a $$$$$$$$$$$$$$$$$$$$$$$$$$$$

Minimizing Friction

• One way to minimize friction is to float objects on a cushion of air. You will use an air track in lab this week.

• Any horizontal force exerted on the cart is the net force acting on the cart.

1 1F a

1 12 2F a

Acceleration vs Force• Experiments show thatAcceleration is proportional to force

1M a

112

2M a

Acceleration vs Mass• Acceleration is inversely proportional to

mass

Or, more familiarly,

Fa

m

Units: Mass has SI units of kg, and acceleration has SI units of m/s2. The SI unit of force is:1 newton = 1 N = 1kg m/s2.

Newton-2 • Combining these two observations gives

Fa

m and by an appropriate choice of

units

Example: Accelerated Mass

A net force of 3.0 N produces an acceleration of 2.0 m/s2 on an object of unknown mass.

What is the mass of the object?

1 21

(3.0 N)= 1.5 kg

(2.0 m/s )

Fm

a

m1

Newton-2 (Second Law of Motion)

Newton-2 (Second Law of Motion)

netFam

Combining Forces

1 21

n

net ii

F F F F

Forces add as vectors.

Force Addition ACTForce Addition ACT

(a) (b)

(c)(d)

Two forces are exerted on an object. Which third force would make the net force point to the left?

Free-body diagrams:

A free-body diagram shows every force acting on an object.

Isolate the object of interest

Choose a convenient coordinate system

Sketch the forces

Resolve the forces into components

Apply Newton’s second law in each coordinate direction

Free Body Reprise

Free-body Diagram Example

Kinematics & Dynamics ComboYou are stranded in space, away from your

spaceship. Fortunately, you have a propulsion unit that provides a constant net force F for 3.0 s. You turn it on, and after 3.0 s you have moved 2.25 m.

If your mass is 68 kg, find F.1 12 2

0 0 2 2x x v t at at

22 2

2 2(2.25 m)0.50 m/s

(3.0 s)

xa

t

20.50 m/sa

2(68 kg)(0.50 m/s ) 34 NnetF ma

Since there is only one force, we call that direction positive x and only worry about magnitudes.

Kinematics

Dynamics

Free-body ACTFree-body ACT

Example: Three Forces

Moe, Larry, and Curley push on a 752 kg boat, each exerting a 80.5 N force parallel to the dock.(a) What is the acceleration of the boat if they all push in the same direction?(b) What is the acceleration if Moe pushes in the opposite direction from Larry and Curley as shown?

1 3(80.5 N) 241.5 Nnet M L CF F F F

2 80.5 Nnet M L CF F F F

21 1 / (241.5 N) / (752 kg) 0.321 N/kg 0.321 m/sneta F m

22 2 / ( 80.5 N) / (752 kg) 0.107 m/sneta F m

Newton’s Third Law of MotionNewton’s Third Law of Motion

Forces always come in pairs, acting on different objects:

If Object 1 exerts a force F on Object 2, then object 2 exerts a force –F on Object 1.

These forces are called action-reaction pairs.

Newton’s Third Law of MotionNewton’s Third Law of MotionSome action-reaction pairs:

Contact forces:The force exerted by one box on the other is different depending on which one you push.Boxes 1 and 2 rest on a frictionless surface. What is the acceleration in each case? What is the force between the boxes in each of the cases?

3 kg 12 N

1 kg

1 kg3 kg12 N