Physics 1D03 - Lecture 61 Newton’s Laws of Motion Newton’s Laws Forces Mass and Weight.

Physics 1D03 - Lecture 6 1

Newton’s Laws of MotionNewton’s Laws of Motion

• Newton’s Laws• Forces• Mass and Weight


Newton’s First Law (Law of Inertia)

An isolated object, free from external forces, will continue moving at constant velocity, or remain at rest.

Earlier, Aristotle said objects were “naturally” at rest, and needed a continuing push to keep moving.

Galileo realized that motion at constant velocity is “natural”, and only changes in velocity require external causes.

Objects in equilibrium (no net external force) also move at constant velocity.


Forces

• A force is a push or pull that tends to cause motion (more exactly, changes in motion)

• From the Second Law, force should have units of

• Force is a vector

• In Newton’s dynamics, all influences on a particle from its surroundings are expressed as forces exerted on that particle

(N) newton 1 m/skg 1 2


Newton’s Second Law

Fnet (or Ftotal) is the vector sum of all forces acting on the particle of mass m:

The acceleration a is parallel to the total force, and proportional to it. The proportionality constant is the particle’s mass. Newton defines mass as a measure of an object’s inertia.

amFnet

i i

iinet amFF


Contact Forces : direct contact is required

examples - normal forces, friction, air resistance, buoyancy, ...

Non-Contact Forces :

gravity, electromagnetic, weak and strong forces

The gravitational force is also called weight and is measured in Newtons.

Weight is proportional to mass : Fw = mg, where g is the gravitational field (and is also the acceleration of an object in free fall).


Weight and Mass

Weight is a force; it can be measured using a spring scale

On Earth, a baseball weighs 2.40 N

On the moon, a baseball weighs 0.40 N


• Mass is a measure of inertia : on the earth or on the moon, a 24.5 N force applied to the baseball will give it an acceleration of 100 m/s2 (its mass is m = F/a = 0.245 kg)

• We can compare masses with a balance, because of the remarkable property :

mass weight

1,gF

2,gF

Weights are equal when masses are equal


Newton’s Third Law (action and reaction)

If object A exerts a force on object B, object B exerts an equal, opposite force back on A.

gF

Block pushes down on table


Newton’s Third Law : examples

What is the “reaction” to the following forces?

gF

Gravity (of block) pulls earth up

Balloon pushes on air outside

You push on a block


Contact Forces

Examples : A heavy block on a table

• The table must push up on the block to prevent it from falling

• The type of contact force is called a normal force if it is perpendicular (normal) to the surfaces in contact.

• The normal force will be as large as necessary to hold the block (until the table breaks)

gF

Forces on Block

tableF


This is really an elastic force; the table behaves like a spring.

At the atomic level, all contact forces are due to electromagnetic forces.

If we look closely, the normal force arises from the table being bent : as the table tries to straighten, it pushes back.


A 140-kg wrestler and a 90-kg wrestler try to push each other backwards out of the ring. At first they are motionless as they push; then the large wrestler moves the other one backwards. Compare the forces they exert on each other. Which statement is correct?

a) The forces are always equal.

b) The larger wrestler always exerts a larger force.

c) When they are motionless, the forces are equal; they start to move when the large wrestler exerts a larger force on his opponent than his opponent exerts back on him.

Quiz


You wash your hands, and as you don’t have a towel handy, you shake them to get rid of the water. You are able to shake water off of your hands mainly due to:

a) Newton’s First Law

b) Newton’s Second Law

c) Newton’s Third Law

Quiz


10 min rest


Free-Body Diagrams

• Pick one object (the “body”).

• Draw all external forces which act directly on that body (gravity, contact, electromagnetic). Imagine cutting around the body to separate it from its surroundings. Replace each external object with a force applied at the point of contact.

• Indicate the direction of the acceleration of the object beside the diagram; but remember, ma is not a forceon the diagram.


Example of a free-body diagram

A block is pulled up a frictionless ramp:

m

Note :

• title, to indicate the chosen object (use m or mA etc)

• contact forces, to replace the rope and the ramp

• gravity doesn’t require contact

• a may be indicated for reference, but is not a forcegm

TF

n

a

Forces on Block


Ropes

• Tension is uniform in a rope of negligible mass• The tension is not changed if the rope passes over

an ideal pulley (assume frictionless and massless)• Tension has units of force (newtons)

• A rope attached to something exerts a force parallel to the rope

• The magnitude of the force is called the tension in the rope

rope

Force


- normal force : is perpendicular to the surfaces in contact

- friction : is parallel to the surface

n

f

friction has a more complex behaviour than the normal force (next lecture)

Moving a Block

n

AF

gF

f

!@%&*#$

Divide the contact force from the table into two components:


Friction

Friction is the force which resists sliding of two surfaces across each other.

We distinguish between static and kinetic friction:

Static Friction :

- there is NO relative motion

- fs prevents sliding

Kinetic Friction :

- the block is sliding

- fk is opposite to v

sfFA

kf

0F

v


Friction is complicated. A useful empirical model was presented by Charles Coulomb in 1781:

1. The force of static friction has a maximum value; if you push too hard, the block moves. This maximum value is proportional to the normal force the surfaces exert on each other.

2. Once the object is sliding, kinetic friction is approximately independent of velocity, and usually smaller than the maximum static friction force. The force of kinetic friction is also proportional to the normal force.


Define two pure numbers (no units):

s (“coefficient of static friction”)

k (“coefficient of kinetic friction”)

(“” is a Greek letter, pronounced “mu”)

Then Coulomb’s rules are:

Question : would it be correct to write these as vector equations, ?

nf

nf

kk

ss

nf

AF

n

f

gm


Copper on steel 0.53 0.36

Aluminum on aluminum 1.5 1.1

Teflon on Teflon 0.04 0.04

• Values depend on smoothness, temperature, etc. and are approximate

• Usually < 1, but not always

• Usually, k is less than s , and never larger

• The coefficients depend on the materials, but not on the surface areas, contact pressure, etc.

s k


A block of mass 10kg is resting on a surface with a coefficient of static friction μs=0.50. What minimum force F is needed to move the block?

Quiz

a) 10 N

b) 49 N

c) 98 N10 kgF


A block of mass 10kg is resting on a surface with a coefficient of static friction μs=0.50. Once the block is moving, what force is needed to accelerate it?

Quiz

a) less than 49 N

b) 49 N

c) more than 49 N10 kgF


Each block weighs 100 N, and the coefficient of static friction between each pair of surfaces is 0.50. What minimum force F is needed to pull the lower block out?

100 N

100 N

Quiz

a) 50 N

b) 100 N

c) 150 NF


10 min rest


Newton’s Laws (III)Newton’s Laws (III)

• Blocks, ramps, pulleys and other problems


Equilibrium

• A special case : (object doesn’t move, or moves at constant velocity)

• Newton’s second law gives

• This is equivalent to three independent component equations:

• We can solve for 3 unknowns (or 2, in 2-D problems)

0a

0 amF

The vector sum of forces acting on a body in equilibrium is zero

0,0,0 zyx FFF


Remember, when doing problems with “F=ma”

• Draw the free-body diagram carefully.

• You may need to know the direction of a from kinematics, before considering forces (for friction).

• Any axes will do, but some choices make the algebra simpler – set up equations for each direction.

• You need one (scalar) equation for each (scalar) unknown, in general (the mass will often cancel out).


Block on a rampDetermine all the forces acting on this block.

Given m, θ and μk, what would the acceleration be:

a) without friction

b) with friction

θ

m


a)

b)


Example

A block is in equilibrium on a frictionless ramp. What is the tension in the rope?

m

T


Quiz

The block has weight mg and is in equilibrium on the ramp. If s = 0.9, what is the frictional force?

m

37o

A) 0.90 mg

B) 0.72 mg

C) 0.60 mg

D) 0.54 mg


Example

Obtain an expression for the stopping distance for a skier moving down a slope with friction with an initial speed of v0.

Find the distance given that μk=0.18, v=20m/s and θ=5.0º.

θ

d


Accelerated motion

Example: A block is pushed with a force FA at an angle to the horizontal, find the acceleration. Friction is given by μk.

m

θ

FA


Increasing so that , the block slips, from which we get:

f

n

mg

sThis is an easy method of measuring

max

maxtan s

Question : Can we calculate μs ?

Physics 1D03 - Lecture 61 Newton’s Laws of Motion Newton’s Laws Forces Mass and Weight.

Documents

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