PhysicsInstructor: Dr. Tatiana Erukhimova

Lecture 6

Newton’s Laws

1st Law: A body acted on by no net force moves with constant velocity (which may be zero) and zero acceleration2st Law: The acceleration of an object is directly proportional to the net force acting on it and is inversely proportional to its mass. The direction of the acceleration is in the direction of the net force acting on the object.3rd Law: For every action there is an equal, but opposite reaction

Aristotle: a natural state of an object is at rest; a force is necessary to keep an object in motion. It follows from common sense.

Galileo: was able to identify a hidden force of friction behind common-sense experiments

1564-1642

384-322 B.C.

Galileo: If no force is applied to a moving object, it will continue to move with constant speed in a straight line

Galilean principle of relativity: Laws of physics (and everything in the Universe) look the same for all observers who move

with a constant velocity with respect to each other.

Inertial reference frames

Newton’s 3rd Law

For every action there is an equal, but opposite, reaction

2nd Law

From experiments we know:1.Force is a vector2.The direction of acceleration vector is the

same as the direction of the force vector3.The magnitude of the force and

acceleration are related by a constant which depends on number of blocks involved.

amF

Newton’s second law

The vector acceleration of an object is in the same direction as the vector force applied to the object and the magnitudes are related by a constant called the mass of the object.

A Recipe for Solving Problems1. Sketch Isolate the body (only external forces but not forces

that one part of the object exert on another part)

2. Write down 2nd Newton’s law

amF

Choose a coordinate system Write 2nd Newton’s law in component form:

yyxx

yxyx

maFmaF

jmaimajFiFF

,

3. Solve for acceleration

Newton’s 2nd Law

amF

xx maF yy maF

Newton’s 3rd Law

N

N

Gravitational force gmF

Normal force (perpendicular to the surface)

P m1 m2

No friction

m1

Free body diagram

m1

m1g

P

N1

F21

m2g

F12

N2

m2

F12=F21

What is the normal force?

H

No friction: =0

H

Coefficient of friction:

What is the normal force?

Friction

Two types of friction:1. Kinetic: The friction force

that slows things down2. Static: The force that

makes it hard to even get things moving

Kinetic Friction

• For kinetic friction, it turns out that the larger the Normal Force the larger the friction. We can write

FFriction = KineticN

Here is a constant• Warning:

– THIS IS NOT A VECTOR EQUATION!

Static Friction• This is more complicated• For static friction, the friction force can vary

FFriction StaticN

Example of the refrigerator: – If I don’t push, what is the static friction

force?– What if I push a little?

There is some maximum value the friction force can achieve, and once we apply a force greater than this maximum there is a net force on the object, so it accelerates.

The maximum of the force of friction varied linearly with the amount that the block pushes on the table.

NFfriction

- coefficient of friction, is the vertical force exerted by

the block on the table N

The friction force only exists when there is another force trying to move an object

H

Coefficient of friction:

What is the normal force?What is the acceleration of the block?

Mass m

Is it better to push or pull a sled?

You can pull or push a sled with the same force magnitude, FP, and angle , as shown in the figures.Assuming the sled doesn’t leave the ground and has a constant coefficient of friction, , which is better?

FP

FP

Pulling Against FrictionA box of mass m is on a surface with coefficient

of kinetic friction . You pull with constant force FP at angle The box does not leave the surface and moves to the right.

What is the magnitude of the acceleration?

Hockey Puck

• Which of these three best represents a hockey puck in the real world?

a)

b)

c)

A small block, mass 2kg, rests on top of a larger block, mass 20 kg. The coefficient of friction between the blocks is 0.25. If the larger block is on a frictionless table, what is the largest horizontal force that can be applied to it without the small block slipping?

F

gm1

1N

1NF

1N

gm2

2N

1N

V0

A block of mass m is given an initial velocity V0 up an inclined plane with angle of incline θ. There is non-zero coefficient of friction between the plane and the block, . Find acceleration of the block if a) = 0b) non-zero

A Problem With First Year Physics Strings and Pulleys

m1

m1, m2 are givenm2>m1

m2String is massless and unstretchable

Find accelerations of m1 and m2 (assume no friction)

A wedge with mass M rests on a frictionless horizontal tabletop. A block with mass m is placed on the wedge and a horizontal force F is applied to the wedge. What must the magnitude of F be if the block is to remain at a constant height above the tabletop?

F