Newton’s Laws 2nd

Newton’s Laws 2nd

• acceleration of an object

is directly proportional

to the net force on it and

inversely proportional to

its mass

• (defines the newton)

Newton’s second law of Motion

• F=ma

• Force = mass x acceleration

• Mass = kilogram

• Acceleration = m/s2

• Force = 1 N (Newton)

• Force = 1 kg-m/s2


• A larger force acting on an object causes a greater acceleration

• A larger mass requires a greater force than a smaller mass would require to achieve the same acceleration.

• Hitting a ball harder causes a greater acceleration

• If you hit a ping pong ball and a tennis ball with the same force, would they have the same acceleration?

The greater the mass, the greater the force must be for a given

acceleration.• the amount of

acceleration depends not only on the force but on the mass being pushed.

•For a given force, the acceleration produced is inversely proportional to the mass.

Apr 20, 2023 Physics 1 (Garcia) SJSU

More Mass, Less Acceleration

The greater the mass of an object, the less it accelerates when acted on by a force.


• A net force acting on an object causes the object to accelerate in the direction of the force.

• Acceleration is determined by the size of the force and the mass of the object.

• F= ma


Mass & Acceleration

For a given force, greater mass, smaller the acceleration

Double the Mass

Triple the Mass

Half the Mass

impliesHalf the Acceleration

Third of the Acceleration

Double the Acceleration

implies

implies

Acceleration goes as

the inverse of mass. Mathematically, we write,

Acceleration ~ 1/(Mass).


Demo: Hammer Head

Hammer a nail into a piece of wood placed on top of massive object (gold brick or huge book).

Inertia of massive object keeps it from moving; can place on top of head and not feel it.

Force is a scalar property

depends on 2 things;

Size or strength of the

force

and the

Direction of the force.

• Vector.

• A quantity with size

and direction

• Scalars

• are described by

size only

Force• You can measure force with

a Spring scale.

Mass and Weight should not be confused with...

• Volume• the quantity of space an

object occupies

• Density • the quantity mass per

unit volume

• Mass• the quantity of matter

in an object

• the measurement of the inertia

• measured in kilograms (kg)


Mass: Quantity of matter in an objectWeight: Force of gravity on an object

Mass is a universal property.Weight depends on gravity

(different on Moon).

Mass is the measure of inertia.Metric unit for mass is the kilogram.Metric unit for weight is Newton (since it’s a force)

Mass & Weight

Earth Moon

Weight

Mass Vs. Weightmass vs. force

Mass Weight

• is a measure

of the force of

the Earth’s

gravity on the

mass of the

object.

is a measure of

the total amount

of matter

contained within

an object.

In metric units, the unit of force is the newton,

• . A 1-kilogram brick weighs about 10 newtons (more precisely, 9.8 N).

• The books offer the same resistance to speeding up or slowing down regardless of whether it’s on Earth, on the Moon, or on any other body attracting it.

• You’d have to provide the same amount of force to accelerate a huge truck to a given speed on a level surface on the Moon as on Earth.

An anvil in outer may be weightless, but it is not

massless.• The astronaut in space finds

that it is just as difficult to shake the “weightless” anvil as it would be on Earth.

• If the anvil were more massive than the astronaut, which would shake more—the anvil or the astronaut?

Newton’s 2nd Law of Motion

• F=ma

• N = Kg*m/s2

• Newton was the first to discover the

relationship between—acceleration,

force, and mass.

• It states; an object is directly proportional

to the net force acting on the object, is in

the direction of the net force, and is

inversely proportional to the mass of the

object.

NEWTON'S 2nd LAW OF MOTION

Fa

or amF

F am

F am

m

F a

m

m

m

F a

F a

F aM

m

a1

M

M

Acceleration is directly

proportional to force.


Demo: Elevator Cable

Tension in elevator cable depends on acceleration

10 N

1 kg

Zero acceleration

15 N

1 kg

5 m/s2 upward( ½ g upward)

5 N

1 kg

0 N

1 kg

5 m/s2 downward( ½ g downward)

10 m/s2 downward(Free fall)

WeightWeight• the force upon an object due to gravity

• Weight = Mass Acceleration of gravity

W = mg

• measured in Newtons (N) in the metric system or pounds (lb) in the British system

Mass and Weight

• On the Moon the gravitational force is only 1/6 as strong as on the Earth.

• In space you are “weightless” but not “massless”.

• Your mass does not depend on where your are.

• (e.g. Earth, Moon, or space).

WeightLocation Mass

Earth

Moon

Space

18.4 kg

18.4 kg

18.4 kg

180 N

30 N

0 N

http://observe.phy.sfasu.edu/images/KC135-Summer2001/

• The weight of a 10 kg brick is...• A) 98 N • B) 10 kg • C) 9.8 kg• D) 10 N • E) 98 kg

Newton’s Cradle

How much force is need to accelerate a 70 kg

rider and her 200 kg motorcycle at 4 m/s2?

• Mass of rider = 70 kg

• Mass of motorcycle =200 kg• Acceleration = 4 m/s2

• Force = unknown

• Equation F=ma

Example QuestionsExample Questions• How much acceleration does a 747

jumbo jet of mass 30,000kg experience in takeoff when the thrust of all of the engines is 120,000N?

• A) 747 N • B) 4 kg • C) 1/4 kg• D) 4 m/s2 • E) 30,000 kg times 9.8 m/s2

Example QuestionsExample Questions

• The same net force is applied to two blocks.

• If the blue one has a smaller mass than the yellow one, which one will have the larger acceleration?

• A) Blue• B) Yellow

F F

Example QuestionsExample Questions

• The same net force is applied to two blocks.

• If the blue one has a smaller mass than the yellow one, which one will have the larger acceleration?

F F

Inertia

• Friction increases with greater force

• Friction is in the opposite direction of the force applied

• Doesn’t want to change what it is doing

• Momentum

Frictionreduces net force & resulting

acceleration

Friction• Force that opposes the motion

between 2 surfaces that are in contact

Friction

• Depends on

• kinds of surfaces • Force pressing

surfaces together

• Life without Friction

• Couldn’t stand• Clothes wouldn’t stay

on

Friction

• is a result of irregularities in the surfaces of

objects.

• The force required to overcome friction is

called the static friction force.

• The force needed to keep a constant speed is

called the kinetic friction force.


FrictionOrigin of friction is molecular interaction between

solid surfaces.

Friction is complicated.

Friction depends on support force and on properties of the surface.

Basic properties of friction first established by Leonardo da Vinci.

Friction depends on 3 things:• The friction force depends on whether or not the

surfaces are moving.

• The friction force depends on the materials of which

the surfaces are made of.

• The friction force depends on how hard the

surfaces are pressed together. This is called the

Normal Force and depends on mass and gravity

also known as Weight

Imagine your car broke down and you have to push it.

Which takes more force, to get it started rolling or to keep it

rolling?

To get it started

Static friction is greater than kinetic friction.

How is a car affected by friction?

Types of Friction

Static

Sliding

Rolling

fluid

sliding friction is less than static friction

• Once tires start to

slide, the frictional

force is reduced and

off you go

• While the tire is

rolling, its surface

does not slide -it is

static friction—and

therefore greater

than sliding friction.

static friction and sliding friction

• It is very important that you not jam on the brakes in an emergency stop. (the tires lock in place), sliding, providing less friction than if they are made to roll to a stop.

Fluid Friction

•Occurs when moving through Air, water & oil

•includes falling through air

Fluid friction is called drag.

• Friction occurs also in liquids and gases, collectively called fluids (because they flow)

• drag in a fluid depends on the nature of the fluid

• drag does depend on speed and area of contact.

the amount of fluid pushed aside by a boat or airplane depends on the size and the shape of

the craft.

• A slow-moving boat or airplane encounters less drag than faster boats or airplanes.

• wide boats and airplanes must push aside more fluid than narrow crafts

• For slow motion

through water, drag

is proportional to

the speed of the

object.

Air Drag

• In air, drag at most speeds is proportional to the square of the speed

• So if an airplane doubles its speed it encounters four times as much drag

• At very high speed,

however, the simple

rules break down when

the fluid flow becomes

erratic and such things

as vortices and shock

waves develop.

• Friction between the tire and the ground is nearly the same whether the tire is wide or narrow.

• The purpose of the greater contact area is to reduce heating and wear.

Check Yourself

• 1. What net force does a sliding crate experience when you exert a force of 110 N and friction between the crate and the floor is 100 N?

• 2. A jumbo jet cruises at constant velocity of 1000 km/h when the thrusting force of its engines is a constant 100,000 N. What is the acceleration of the jet? What is the force of air resistance on the jet?

Lubricants

• reduce friction by keeping the two sliding

surfaces apart with a thin layer of fluid.

• Friction is no longer rubbing the surfaces

but instead rubbing the lubricant.

Another way to reduce friction is to roll an object over a surface.

• This is called rolling

frictional force instead of

kinetic frictional force.


Friction and Air Resistance

Friction and air resistance are forces opposing motion.

Sliding friction

• Force between surfaces in relative motion

• less that static friction

Friction

• The force of friction does not depend on speed.

• Once an object is sliding, the friction force remains approximately the same.

• Unlike the friction between solid surfaces, fluid friction depends on speed.

• A very common form of fluid ?(liquid or gas) friction for something moving through air is air resistance, also called air drag.

friction does not depend on the area of contact.

• If you slide a smaller

surface, all you do is

concentrate the same

weight on a smaller area

with the result that the

friction is the same.

• Stopping distance when

brakes are applied is not

affected by the number of

tires

the force of friction does not depend on speed

• It may be more when

the crate is at rest and

on the verge of

sliding

• Once sliding the

friction force remains

approximately the

same.

friction does not depend on the area of contact

• Slide the crate on its

smallest surface and

all you do is

concentrate the same

weight on a smaller

area with the result

that the friction is the

same

• the friction between a truck and the ground is the same

• # of tires do not matter

• (More tires spreads the load and reduces the pressure and wear per tire).

• stopping distance is not affected by the number of tires

Coefficients of Friction Equations

• Static force=Coefficient of static x Normal

Force (Weight)

• Fs = us x N

• Kinetic Force=Coefficient of kinetic x Normal Force

(Weight)

• Fk = uk x N

A crate made of wood weighs 85 lbs is on a concrete floor.

• What force is required to get it moving?

• Fs = us x N

• us ; Page 176

• us = .6

• Fs = .6 x 85 = 51

Same crate is now moving, what force is needed to keep it moving at a constant speed?

• Fk = uk x N

• uk ; Page 176

• uk = .4

• Fk = .4 x 85 = 34

Three identical blocks are pulled, as shown, on a

horizontal frictionless surface. If tension in the rope held by the hand is 30 N, what is the tension in the other ropes?

• Use F = ma to the whole system• if the mass of a block is "m"

30 = 3mathereforea = 30/3m=10/m

• The tension on the rope between Block 3 and 2 is "T 1“

•using F = ma

• T1 = m *10/mT1 = 10 N

• if the tension between block 2 and 1 is T2

then using F= ma for both the block 3 and 2T2 = 2m * 10/mT2 = 20 N

• If forces are equal but opposite, they are balanced.

• If one force is greater than the opposite force, than it is an unbalanced force.

What happens when forces aren’t balanced—when net forces do not equal zero.

(Mechanical equilibrium, ΣF = 0, where forces are balanced.)

•The net force on a kicked soccer ball, for example, is greater than zero, and the motion of the ball changes abruptly.

•Its path through the air is not a straight line but curves downward due to gravity—again, a change in motion

the combination of forces acting on an object is the net force

• To increase the acceleration of an object, you must increase the net force acting on it.

• Doubling the force doubles the acceleration• The object’s acceleration is directly

proportional to the net force acting on it.• We write acceleration net force ( directly ∼

proportional to) • It means any change in one is the same

amount of change in the other.

Volume The quantity of space an object occupies.

Newton’s second law The acceleration of an object is directly proportional to the net force acting on the object, is in the direction of the net

force, and is inversely proportional to the mass of the object.

Force Any influence that can cause an object to be accelerated, measured in newtons (or in pounds, in the British system).

Free fall Motion under the influence of gravitational pull only.

Terminal speed The speed at which the acceleration of a falling object

terminates because air resistance balances its weight. When direction is specified, then we speak of terminal velocity.

• A large rocks resistance to

a change in motion (its

mass) is 100 times that of

the pebble. The greater

force offsets the equally

greater mass.

The acceleration of free fall is independent of an object’s mass

• The ratio of weight (F) to mass (m) is the same for

all objects in the same locality; so, their

accelerations are the same in the absence of air

resistance.

The ratio of weight (F) to mass (m) is the same for

the large rock and the small feather; similarly, the

ratio of circumference (C) to diameter (D) is the

same for the large and the small circle.

When Acceleration Is g—Free Fall

• The greater the mass of an object, the

greater the gravitational force of

attraction between it and the Earth.

• the acceleration of an object depends

not only on the force—in this case, the

weight—but also on the object’s

resistance to motion, its inertia.

• inertia is a resistance to acceleration.

• use the symbol g, rather a, to denote

that acceleration is due to gravity alone.


Free Fall Acceleration

Newton’s Second Law explains why all objects fall with same acceleration.

Ratio of weight/mass always the same since weight depends on mass.

Analogy with ratio of circumference / diameter always equals pi (3.1415…).

• A 65 kg person stands on a scale, what is the force of gravity on the person?

• FG = m x g

• g = 9.8 m/s2

• FG = 65 kg x 9.8 m/s2

• FG = 637 N

Wind tunnel

• http://www.grc.nasa.gov/WWW/K-12/airplane/wrong1.html

Newton’s Laws 2nd

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