Laws of NewtonPhysics 11

So, no more elevator death problems?

Sir Isaac Newton

• The understanding of force and motion progressed slowly from the time of Aristotle through to Galileo and then to Newton.• In 1686, Sir Isaac Newton summarized 3

laws of motion that are currently used to predict force and motion interactions for macroscopic objects.• Albert Einstein later on added significant

concepts to the field of mechanics.

Newton’s 1st Law – The Law of Inertia• An object at rest or in uniform motion will remain at rest or in

uniform motion unless acted on by an external force.

Using Appropriate Frames of Reference• In order to apply Newton’s laws to

predict motion of an object, you must assign a reference frame and a coordinate system.• In some reference frames, the law of

inertia seems to be invalid.• There is no right or wrong reference

frame, but some make calculations and predictions much easier than others do.

Think about this…

• Imagine that you are riding along a straight, smooth road at a constant velocity. Then the driver suddenly slams on the brakes and your upper body falls forward until the seat belt stops you.• In the frame of reference of the car, you were initially at rest and then

suddenly began to accelerate.• According to the 1st law, a force is needed to cause your body to

accelerate. However, in this situation you cannot attribute your acceleration to any observable force.• It would appear that your motion relative to the car did not conform

to Newton’s 1st law.

Inertial Frame of Reference

• An inertial frame of reference is one in which Newton’s laws of motion are valid. Inertial frames of reference are at rest or in uniform motion, but they are not accelerating.

Non-Inertial Frame of Reference

• A non-inertial frame of reference is one in which Newton’s laws of motion are not valid. Accelerating frames of reference are always non-inertial.

Example 1

• Passengers in a high-speed elevator feel as though they are being pressed heavily against the floor when the elevator starts moving up. After the elevator reaches its maximum speed, the feeling disappears.

a) When do the elevator and passengers form an inertial frame of reference? A non-inertial frame of reference?

b) Passengers feel a certain pressure when the elevator starts to move upward. Is the pressure a fictitious force?

Newton’s 2nd Law

• The net force, or the vector sum of all the forces acting on an object, is the product of its mass and its acceleration.

Where is the net force (N)m is the mass (kg)a is the acceleration (m/s2)

Systems in Equilibrium

• In accordance with Newton’s 2nd Law, objects or systems have two possible states:• Equilibrium: Net force is equal to zero

• May be resting or moving at a constant velocity• Non-Equilibrium: Net force is equal to any non-zero value

• Velocity is either increasing or decreasing

Example 2

•What net force is needed to accelerate a 1200 kg car along a horizontal surface from rest to 130 km/h in 8.0 seconds?

Example 3

•What mass would a sled on ice have if it requires a horizontal force of 100 N to change its velocity from 30 km/h to 120 km/h in 5.0 s?

Example 4

•What would be the tension in a cable lifting an elevator and a person having a combined mass of 575 kg moving:

a) upward at a rate of 5.0 m/s2 ?b) downward at a rate of 5.0 m/s2 ?

Example 5

• A big building block with a mass of 0.5 kg is resting at the center of a room. Two children in a daycare immediately see it, grab hold of it and pick it up. Not wanting to share, obviously, they begin to pull the block in opposite directions. Sean is pulling with a force of 0.3 N to the left, and Diane is pulling to the right with 0.5 N. Their cute little dispute lasts 4 seconds.• If the room has a dimension of 4 m x 4 m, will they hit a wall?

Homework Practice

p.163 # 1, 2, 3p.168 # 4, 5, 6, 7, 8

Determining the Net Force

• Analyzing the FBD leads to 2 component net forces: X and Y.• For all force vectors, find their X and Y components.• Convention: find the sum of all the forces in one dimension.

Example 6: Fill in the Blanks

Homework Practice

p.170 # 10, 11, 12, 13p.174 # 17

Newton’s 3rd Law

• For every action force on object B due to object A, there is a reaction force, equal in magnitude but opposite in direction, due to object B acting back on object A.

Action-Reaction Examples

Can you think of any examples demonstrating Newton’s 3rd law?

Gun Recoil

• Guns demonstrates Newton’s 3rd law with recoil.• Recoil is the reaction

of a gun’s shot.

Walking..?

Other Examples…

Example 7• A train at rest begins to accelerate. • Consider the following:

• The engine train has a mass of 7,500 kg.• The animals’ wagon has a combined mass of

4,850 kg.• The coefficient of kinetic friction of the

railroad is 0.62.• The engine is pulling the train with a force of

76,500 N.

a) What is the train’s acceleration?b) If the train accelerates for 3 minutes,

what will be its speed? Its distance travelled?

c) What is the tension on the hitch pulling the animals’ wagon?

Homework Practice

p.182 # 18, 19, 20

A Quick Review of Newtons’ Laws…

Newton’s 1st Law

Newton’s 2nd Law