Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova

Lecture 11

Hockey Puck

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

a)

b)

c)

Newton’s Laws (cont.)

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

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

Newton’s 3rd Law

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

Quiz

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

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

Units of Force

2/111 smkgNNewton

British system:

kgslug 59.141 units of mass:

units of force: Nsftsluglbpound 448.4/111 2

One pound is 0.4536 kg

One pound is the weight of 0.4536 kg on the Earth

Units are important!The Mars Climate Orbiter was part of missions conducted by NASA.

US$327.6 million mission

The craft ended up with a trajectory 170 km closer to Mars than planned

Reason of the failure: CONFUSION IN UNITS!

Thrust information was sent in pounds instead of Newtons!

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.

1. What is the magnitude of the acceleration?

2. What angle maximizes the acceleration?

What is the normal force?

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

H

No friction: =0

H

Coefficient of friction:

What is the normal force?

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

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?

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

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

A block of mass 20 kg is pushed against a vertical surface as shown. The coefficient of friction between the surface and the block is 0.2. If θ=300, what is the minimum magnitude of P to hold the block still?

θ

P

Have a great day!

Reading: Chapters 5,6Hw: Problems 1, 2, 3, 4, 6 and exercises 1, 4, 5, 6, 9