Newton’s Laws – Learning Outcomes Define force and give its unit.

Define momentum and give its unit.

Solve problems about momentum.

State Newton’s three laws of motion.

Demonstrate the laws of motion.

State some applications of the laws.

Derive 𝐹 = 𝑚𝑎.

Solve problems about forces.

Define friction.

Give some applications of friction.

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Define Force, Momentum A force, F is any influence that causes an object to

accelerate.

Force is measured in newtons (N).

Inertia is the tendency of an object to maintain its

current state of motion.

The mass, m of an object is how we measure its inertia,

measured in kilograms.

The momentum, p of an object is the product of its mass

and its velocity.

Formula: 𝑝 = 𝑚𝑣, measured in kg∙m∙s-1.

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Solve Problems About Momentum e.g. Caoilinn is trying to get to space by being blasted

out of a cannon. Between herself, all her protection

gear, and the sabot, the mass of the payload is 100 kg. If

she needs to reach 11 000 m∙s-1 to escape Earth, what is

the minimum momentum of the payload?

e.g. Laura fires a gun at a target. The bullet has mass 30

g and momentum 9 kg∙m∙s-1. What is the bullet’s

velocity?

e.g. Rebecca is driving along a straight par of the M50.

Her car has mass 850 kg and she is driving at 100 km/hr.

What is the car’s momentum?

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State Newton’s Laws To make sure we fully understand the correct laws of

motion, we will start with incorrect laws and identify their

problems.

1. An object with no net force on it will naturally come to

rest.

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State Newton’s Laws There are two major problems with this law.

1. Different objects come to rest at different rates. A rolling

wheel takes longer to stop than a box at the same initial

speed, with the same mass.

2. Different surfaces will slow the same object at different

rates. Objects will slide for much longer on ice than on

rubber for example.

Newton’s First Law:

An object will move at constant velocity unless acted on

by a net external force.

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State Newton’s Laws This first law is sometimes called the Law of Inertia.

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State Newton’s Laws7

State Newton’s Laws2. A net force causes an object to move with constant

velocity.

e.g. Consider a car moving along a road. It will slow

down if you take your foot off the accelerator or if the

engine turns off. To maintain velocity, the engine needs

to keep pushing the car forward.

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State Newton’s Laws There’s one big problem with this analogy:

The car slows down because there are external forces

on it. Cars face friction from the road and the air – if a

car moves with constant velocity, it’s because the

accelerator is causing a force to counteract these

things, meaning no net force.

In fact, if there is a net force on the car due to friction,

the car’s momentum changes at a constant rate:

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State Newton’s Laws Newton’s Second Law:

The rate of change of an object’s momentum is

proportional to the applied force and takes place in

that direction.

𝐹 ∝𝑝2−𝑝1

𝑡

F = force

p = momentum

t = time taken

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State Newton’s Laws3. Larger / heavier objects apply larger forces to smaller /

lighter objects.

e.g. a truck smashing into a car. The truck exerts a much

larger force on the car than the car exerts on the truck.

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State Newton’s Laws Don’t forget the second law.

A truck has more momentum (more mass and/or

velocity) than a car. To change this momentum takes a

lot of force, whereas it takes less for a car.

In fact the forces that the truck and car exert are equal,

but with momentum and inertia at play, we see the

effect of the force more on the car.

Newton’s Third Law:

When body A exerts a force on body B, B exerts a force

on A with equal magnitude but opposite direction.

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Give Applications of the Laws Rockets!

Sports.

Ball games

Seat belts

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Derive 𝐹 = 𝑚𝑎 From Newton’s second law:

𝐹 ∝𝑝2−𝑝1

𝑡

⇒ 𝐹 ∝𝑚𝑣−𝑚𝑢

𝑡

⇒ 𝐹 ∝𝑚 𝑣−𝑢

𝑡

⇒ 𝐹 ∝ 𝑚𝑎

⇒ 𝐹 = 𝑘𝑚𝑎

Define the newton so that 𝑘 = 1

⇒ 𝐹 = 𝑚𝑎

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Solve Problems About Forces The cheetah is one of the fastest land animals. Calculate

the resultant force acting on the cheetah while it is

accelerating at a rate of 7 m s-2. The mass of the

cheetah is 150 kg.

An astronaut of mass 120 kg is on the surface of the

moon, where the acceleration due to gravity is 1.6 m s–2.

What is the weight of the astronaut on the surface of the

moon?

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Solve Problems About Forces A lunar buggy designed to travel on the surface of the

moon (where acceleration due to gravity is1.6 m s-2) had

a mass of 2000 kg when built on the earth.

i. What is the weight of the buggy on earth?

ii. What is the mass of the buggy on the moon?

iii. What is the weight of the buggy on the moon?

iv. A powerful rocket is required to leave the surface of

the earth. A less powerful rocket is required to leave the

surface of the moon. Explain why.

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Solve Problems About Forces A skateboarder with a total mass of 70 kg starts from rest

at the top of a ramp and accelerates down it. The ramp

is 25 m long and is at an angle of 200 to the horizontal.

The skateboarder has a velocity of 12.2 m s–1 at the

bottom of the ramp.

i. Calculate the average acceleration of the

skateboarder on the ramp.

ii. Calculate the component of the skateboarder’s

weight that is parallel to the ramp.

iii. Calculate the force of friction acting on the

skateboarder on the ramp.

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Solve Problems About Forces A man of mass 80 kg stands on a weighing scales in a lift.

If the scales reads newtons, find the reading on the

scales when the lift:

i. is at rest.

ii. moves upwards at a constant 3 m s-1.

iii. moves downwards at a constant 4 m s-1.

iv. accelerates upwards at 2 m s-2.

v. accelerates downwards at 2 m s-2.

vi. accelerates downwards at 10 m s-2.

(use g = -10 m s-2)

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Define Friction, Give Examples Friction is a force which opposes motion.

Examples of friction:

Car brakes (press against the wheels).

Walking (keeps up from slipping).

Air resistance (causes extra fuel to be needed and slows

down spacecraft on re-entry).

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