Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova Lectures 13-15.

Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova

Lectures 13-15

Newton’s Laws

1st Law: A body acted on by no net force moves with constant velocity (which may be zero) and zero acceleration2nd 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

Reading quizzes (Chs 5,6)

Hockey Puck

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

a)

b)

c)

Newton’s 1st Law

A body acted on by no net force moves with constant velocity (which may be zero) and zero acceleration

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

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

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

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?

H

Coefficient of friction:

What is the normal force?

What is the velocity of the block when it reaches the bottom?

Newton’s 3rd Law

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

Skater• Skater pushes on a wall • The wall pushes back

– Equal and opposite force

• The push from the wall is a force– Force provides an

acceleration – She flies off with some

non-zero speed

P m1 m2

No friction

m1

Free body diagram

m1

m1g

P

N1

F21

m2g

F12

N2

m2

F12=F21

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

Massless, unstretchable string; frictionless pulley

Force of tension

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)

V0

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

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

Block 1, of mass m1, is placed at rest on an inclined plane. It is attached by a massless, unstretchable string to block 2, of mass m2. The pulley is massless and frictionless and just changes the direction of the tension in the string. The coefficient of friction between the plane and m1 is the constant .

2

1

Determine what range of values for mass m2 will keep the system at rest.

Find acceleration if mass 2 goes down.

F

Find F necessary to drag the box 1 at constant speed.

1

2

Friction everywhere.

The advantage of a pulley

What minimum force F is needed to lift the piano of mass M?

Quiza) A crate of mass m is on the flat bed of a pick up truck. The coefficient of friction between the crate and the truck is . The truck is traveling at the constant velocity of magnitude V1. Draw the free body diagram for the crate.

b) The truck starts to accelerate with an acceleration ac. Draw the free body diagram for the crate, if the crate does not slip.

The Elevator Problem

Have a great day!

Reading: Chapter 7Hw: Chapter 6 problems and exercises