Chapter 4 Acceleration and Momentum

Objectives

• 4.1 Explain how force, mass, and acceleration are related.

• 4.1 Compare rates at which different objects fall. Observe the effects of air resistance.

• 4.2 Explain why things that are thrown or shot follow a curved path. Compare motion in a straight line to circular motion.

• 4.2 Define weightlessness

Newton’s Second Law

Force equals mass times acceleration.

F = ma

Acceleration: a measurement of how quickly an object is changing speed.

What does F = ma mean?

Force is directly proportional to mass and acceleration. Imagine a ball of a certain mass moving at a certain acceleration. This ball has a certain force.

Now imagine we make the ball twice as big (double the mass) but keep the acceleration constant. F = ma says that this new ball has twice the force of the old ball.

Now imagine the original ball moving at twice the original acceleration. F = ma says that the ball will again have twice the force of the ball at the original acceleration.

More about F = ma

If you double the mass, you double the force. If you double the acceleration, you double the force.

What if you double the mass and the acceleration?

(2m)(2a) = 4F

Doubling the mass and the acceleration quadruples the force.

So . . . what if you decrease the mass by half? How much force would the object have now?

What does F = ma say?F = ma basically means that the force of an

object comes from its mass and its acceleration.

Something very small (low mass) that’s changing speed very quickly

(high acceleration), like a bullet, can still have a great force. Something

very small changing speed very slowly will have a very weak force.

Something very massive (high mass) that’s changing speed very slowly (low acceleration), like a glacier, can still have great force.

Newton’s 2nd Law shows that different masses accelerate to the earth at the same rate, but with different forces.

• We know that objects with different masses accelerate to the ground at the same rate.

• However, because of the 2nd Law we know that they don’t hit the ground with the same force.

F = ma

98 N = 10 kg x 9.8 m/s/s

F = ma

9.8 N = 1 kg x 9.8 m/s/s

If mass remains constant, doubling the acceleration, doubles the force. If force remains constant, doubling the mass, halves the acceleration.

Weight Force

Apparent Weight

How does your weight change in the following?•Elevator accelerating up•Elevator accelerating down•Car accelerating•Falling

Acceleration Caused by Gravity

• Often called Weight• F = ma• Weight is a force• Acceleration on Earth 9.8 m/s/s

Air Resistance

• Also called the Drag force• A result of moving the fluid molecules out of

the way– Size, shape, speed, density all influence the

amount of drag• Faster = More resistance

Terminal Velocity

• The fastest an object can fall– Based off of air resistance

• Parachutes lower people’s terminal velocity

Projectile Motion

• Monkey and Banana Gun Scenario– If a gun pointed at a monkey fires and the monkey

falls at the same time, does the monkey get hit?

Projectile Motion

• http://www.youtube.com/watch?v=cxvsHNRXLjw

• Monkey and Gun

Projectile Motion

• Horizontal and Vertical motion are different and independent of one another– An object thrown sideways hits ground at same

time as an object which is dropped– They are independent because the force acting on

fall is gravity, which is straight down for both

Projectile Motion

• Large angle of fire = Long time aloft (90 degrees is max time)

• 45 degree angle of fire = Farthest (in ideal world)– Air resistance makes this closer to 30 in real world

Centripetal

• Centripetal Force = Force directed Inward to pull an object in a circular path– Centripetal Acceleration: Result of force

Weightlessness

– To be in free fall or completely void of a substantial gravitational force

• What are some effects?– Human body weakens– Plants/Crystals can grow to be larger– Others?

Satellites and their Speed

• Satellites are constantly falling towards the planet they orbit (just as Earth is constantly falling towards the Sun)– In free fall

• Inertia (horizontal velocity) + Falling (centripetal acceleration) leads to orbit

Satellites and their Speed

• A balance between inertia and centripetal acceleration

End 4.1 – 4.2 Notes

• Newton’s first law and equation (Solve F = ma given 2 of 3 variables)

• Air resistance, what causes it and how does it change with speed/other factors

• Gravity, the law• Projectile motion, the independence of

horizontal and vertical motion

Satellites

• LEO: Low Earth Orbiting satellite– Move very fast, used to spy

• MEO: Medium Earth Orbiting satellite– Move moderately fast, used for gps– 12,000 miles above sea level

• GEO: Geostationary Earth Orbiting satellite– Stay at same place about earth, used for tv/radio– 22,000 miles above sea level

Newton’s Third Law

For every action there is an equal and opposite reaction.

What does this mean?

For every force acting on an object, there is an equal force acting in the opposite direction. Right now, gravity is pulling you down in your seat, but Newton’s Third Law says your seat is pushing up against you with equal force. This is why you are not moving. There is a balanced force acting on you– gravity pulling down, your seat pushing up.

Think about it . . .

What happens if you are standing on a skateboard or a slippery floor and push against a wall? You slide in the opposite direction (away from the wall), because you pushed on the wall but the wall pushed back on you with equal and opposite force.

Why does it hurt so much when you stub your toe? When your toe exerts a force on a rock, the rock exerts an equal force back on

your toe. The harder you hit your toe against it, the more force the rock exerts back on your toe (and the more your toe

hurts).

Action-Reaction Pairs

• In an Action-Reaction pair– Each object acts on the other– Each object pushes/pulls with same magnitude of

force• Tug of War is NOT an example of Newton’s 3rd Law• Mr.Love pushing the Earth away is (by jumping)• Rockets are examples (throw gas/gas throws

rocket)

Momentum

• Momentum is conserved as long as no outside forces are present– Momentum is conserved when the system is

isolated completely from outside forces• Momentum = mass (kg) * velocity (m/s)– Since it is velocity, direction matters

Impulse (Change Momentum)

• F = ma Ft = mv

• Large F over a small time = small force over a large time– Same effect. Force over time changes momentum

t

vmF

Collisions

• Momentum Before = Momentum After– 10 P to the Right before a collision, then 10 P to the

right after the collision• Problem: A ball rolling at 5 m/s to the right with a

mass of 0.25 kg collides with a ball of mass 0.5kg at rest. What is the velocity of the 0.5 kg ball if?– The 0.25 kg ball stops– The 0.25 kg ball recoils at – 1 m/s– The 0.25 kg ball keeps rolling forward at 2 m/s

Momentum Practice

Momentum of1. 100,000 kg Train at rest2. 0.01 kg bug moving at 2m/s3. You running at top speed4. Car moving at 10 m/s (25mph)