Chapter 4 Newton’s Laws of Motion

Sir Isaac Newton Philosophiae Naturalis Principia Mathematica (1687) Opticks (1704) "Nature and nature's laws lay hid in night; God said 'Let Newton be' and all was light."

Newton’s Three Laws Inertia: “Every body continues in its state of rest, or of uniform motion in a straight line, unless it is compelled to change that state by a force impressed on it.” Force, Mass, Acceleration ( F=ma ): “The change in motion is proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed.” “Action = Reaction”: “To every action there is always opposed an equal reaction; or, the mutual actions of two bodies are always equal, and directed to contrary parts.”

Newton’s Law Summary 1.Velocity is zero or constant when net force is zero. 2. F=ma 3.Action = Reaction (in opposite direction)

Net Force Net force (or total force) is the sum of all the forces applied to an object. For example, if there are three people, A, B and C pushing the crazy kid. The net force on him is:

First Law and Net Force no net force The First Law deals with cases when there is no net force. state of rest uniform motion “Every body continues in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by a force impressed on it.”

Puck on ice Ice has very little friction (so no net force), so the inertia keeps the puck moving once it is set in motion.

Mass or Inertia  Inertia is the tendency of an object to remain at rest or in motion with constant speed along a straight line.  Mass ( m ) is the quantitative measure of inertia. Mass is the property of an object that measures how hard it is to change its motion.  Units: kg

Mass vs. Weight intrinsic property  Mass is an intrinsic property of an object.  A rock has same mass whether it is on the moon or on Earth.  Mass does not change force W=mg  Weight is the force exerted on an object by gravity: W=mg  This is different depending upon the strength of the gravitational force.  You weigh less on the Moon than on Earth.

Example What is the weight of a man of mass 70kg on Earth? N Weight is measured in N. (Pound : 1lb = 4.448N )

Same mass, different weight

Newton’s 1st Law total 1. is pointing upward 2. is pointing downward 3. is pointing forward 4. is pointing backward 5. is zero There are many forces act on the plane, including weight (gravity), drag (air resistance), the thrust of the engine, and the lift of the wings. At some point the velocity of the plane is constant. At this time, the total (or net) force on the plane: 1. is pointing upward 2. is pointing downward 3. is pointing forward 4. is pointing backward 5. is zero lift weight drag thrust correct

Newton’s 1st Law no net force constant Newton's first law states that if no net force acts on an object, then the velocity of the object remains constant. Since the velocity is constant, the total force on the plane must be zero, according to Newton's first law. lift weight drag thrust

Newton’s Second Law F = ma non-zero net force Deals with the effect of a non-zero net force. acceleration Non-zero net force causes acceleration. Unit: N (Newton)

Some Math What does the vector symbol mean? independently F = ma applies to each component independently.

NET FORCE F means NET FORCE!!! net force The F in F = ma is the net force on the object. If you are careful, you may write instead: F net = ma Always remember to find the net force first!

Simple Examples: Find a m = 10kg F = 200N F = 150N

Find the magnitude of a

When the net force is zero

Zero Net Force on a Lamp

When F net is non-zero F net ≠ 0a≠0 When F net ≠ 0, since F=ma, we have a≠0. No net force, no acceleration. Net force leads to acceleration. accelerating non-zero net force If an object is accelerating, there must be a non-zero net force.

Example The mass of m = 2kg is accelerating upward at 4m/s 2. Find the tension.

Example The mass of m = 2kg is accelerating downward at 4m/s 2. Find the tension.

T-mg or mg-T ? a magnitude positive In non-vector notation, we usually assume the variable a represents the magnitude of the acceleration, and is therefore positive whether it is up or down. In other words, unless stated otherwise, we will not use the up/positive, down/negative convention. a a With this new convention, whenever you have opposing forces, the forces pointing in the same direction as a comes first, minus the forces in the opposite direction as a.

T-mg or mg-T ? Another way to remember, if a > 0, you want: (big number) - (small number) = ma or (same direction) - (opposite direction) = ma

Two forces m = 10kg F 1 = 200N F 2 = 350N a

Newton’s Third Law  For every force, there is an equal and opposite force  every “action” has a “back-reaction”  these are precisely equal and precisely opposite

Newton’s Third Law You cannot push without being pushed back just as hard In tug-of-war, each side experiences the same force (opposite direction) When you push on a brick wall, it pushes back on you!

Force Pairs Illustrated Force on person by box Force on floor by box Force on box by floor Force on box by person Force on person by floor Force on floor by person Not shown are the forces of gravity and the associated floor forces

Don’t all forces then cancel? Force on box by floor Force on box by person Net Force on box How does anything ever move (accelerate) if every force has an opposing pair? Action and reaction force act on different objects.

Exercise: Action/Reaction  Suppose a tennis ball (m= 0.1 kg) moving at a velocity v = 40 m/sec collides head-on with a truck (M = 500 kg) which is moving with velocity V = 10 m/sec.  During the collision, the tennis ball exerts a force on the truck which is smaller than the force which the truck exerts on the tennis ball. TRUE or FALSE ?  The tennis ball will suffer a larger acceleration during the collision than will the truck. TRUE or FALSE ?  Suppose the tennis ball bounces away from the truck after the collision. How fast is the truck moving after the collision? 10 m/sec ? 10 m/sec ?

Exercise: Action/Reaction solution  During the collision, the tennis ball exerts a force on the truck which is smaller than the force which the truck exerts on the tennis ball. TRUE or FALSE ? Equal and opposite forces! The tennis ball will suffer a larger acceleration during the collision than will the truck. TRUE or FALSE ? Acceleration = Force / mass  Suppose the tennis ball bounces away from the truck after the collision. How fast is the truck moving after the collision? 10 m/sec ? 10 m/sec ? Force from the ball causes deceleration.

Normal Force Force from a solid surface (e.g. wall, ground) providing support for an object. “Normal” means “perpendicular”, Normal Force is always perpendicular to the solid surface. Notations: F N, F n, N or n

Example of Normal Force Suppose the elevator is not accelerating. m=70kg, what does the scale read?

Example of Normal Force 2 Suppose the elevator is accelerating up. m=70kg, a=5m/s 2

Example of Normal Force 3 Suppose the elevator is accelerating down. m=70kg, a=5m/s 2

Be careful with the normal force

What is F n now?

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Think First Law no net forcehorizontally In the next two examples, there are no net force acting on the objects horizontally. However, vertically they are subjected to gravitational force, which causes vertical acceleration.

Questions (First Law) Suppose you are on an airplane travelling at constant velocity with a speed of 500 miles per hour (roughly 200 m/s) If you throw a ball straight up, does it return to you? How does it appear to you? How does the path of the ball look to an observer on the ground? inside the airplane Can you think of any experiment done inside the airplane that would detect the motion of the airplane at constant velocity?

Solution To person on airplane Time = 1 sec 200 m 1.25 m To person on ground - Time = 1s

What about pouring coffee? To person on airplane Time = 1/2 sec 1.25 m To person on ground Time =1/2 sec 1.25 m 100 m