Lecture 4 Momentum and Impulse Energy and Work Potential Energy Kinetic Energy

Lecture 4Lecture 4

• Momentum and Impulse

• Energy and Work

• Potential Energy

• Kinetic Energy

MomentumMomentum

• Momentum: Inertia in motion

– Directly related to the magnitude of an object’s velocity and its mass.

– Momentum = mass x velocity

– Momentum = mv

Momentum and ForceMomentum and Force

• Force causes an acceleration.

• Acceleration = a change in an object’s velocity = a change in its momentum.

Momentum and TimeMomentum and Time• How long a force is applied will also determine

how much the momentum of an object changes.

– Applying a force for twice the time produces twice the change in momentum.

Momentum and ImpulseMomentum and Impulse

• Impulse = Force x time

• Impulse = Change in Momentum

• Force x time = Change in Momentum

Ft = Δ (mv)

Momentum and ImpulseMomentum and Impulse

• Compare the momentum of a 1 kg cart moving at 10 m/s with that of a 2 kg cart moving at 5 m/s.

• For the same force, which cannon imparts a greater impulse to a cannonball – a long cannon or a short one?

Impulse Changes MomentumImpulse Changes Momentum

• In order to increase the momentum of an object, apply the greatest force for as long as possible.

Impulse Changes MomentumImpulse Changes Momentum

• Extending the time of an impact reduces the force of an impact.

Impulse Changes MomentumImpulse Changes Momentum

Impulse Changes MomentumImpulse Changes Momentum

• Imparting a large impulse on objects in a short time produces considerable force.

To bring a super tanker to a stop, its engines are typically To bring a super tanker to a stop, its engines are typically cut off about 25 km from port. What makes the momentum cut off about 25 km from port. What makes the momentum of a supertanker so enormous that it needs considerable of a supertanker so enormous that it needs considerable time to stop.time to stop.

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1. Because they travel at a high velocity.

2. Because of the Earth’s gravitational pull on the tanker.

3. Because of the enormous mass of the tanker.

4. Because of the density of the tanker.

Momentum and ImpulseMomentum and Impulse

• A few equations to remember:

–Momentum = mv

–Impulse = Ft = Δ mv

A 0.15 kg baseball moving at a speed of 40 m/s is caught. A 0.15 kg baseball moving at a speed of 40 m/s is caught. What is the momentum of the ball before it is brought to What is the momentum of the ball before it is brought to rest?rest?

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1. 4 kg·m/s2. 4 N3. 6 kg·m/s4. 6 N5. 15 kg·m/s6. 15 N

A 0.15 kg baseball moving at a speed of 40 m/s is caught. A 0.15 kg baseball moving at a speed of 40 m/s is caught. How much impulse acts on the ball when it has been How much impulse acts on the ball when it has been caught and brought to rest?caught and brought to rest?

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1. 12 kg·m/s2. 6 kg·m/s3. 0 kg·m/s4. 4 kg·m/s

Automobiles were previously manufactured to be Automobiles were previously manufactured to be as rigid as possible, where as today’s autos are as rigid as possible, where as today’s autos are designed to crumple upon impact. Why?designed to crumple upon impact. Why?

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1. Increases the amount of time the car is brought to rest which reduces the force of impact.

2. Shortens the amount of time the car is brought to rest which reduces the force of impact.

3. The force of impact remains the same, but the impulse of the impact is reduced.

4. None of the above. They’re just saving on manufacturing material costs.

If a boxer increases the duration of impact to 3 If a boxer increases the duration of impact to 3 times as long by riding with the punch. By how times as long by riding with the punch. By how much is the force of the impact reduced?much is the force of the impact reduced?

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1. 1/3 the amount of force.2. 1/9 the amount of force.3. The amount of force

cannot be changed because the change in momentum is the same.

If a boxer moves into the punch and decreases the If a boxer moves into the punch and decreases the duration of the impact by half, then how much is duration of the impact by half, then how much is the force of the impact changed?the force of the impact changed?

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1. 4 times as much2. Twice as much3. Half as much4. No change

1. The train locomotive.

2. The squirrel.3. They have the

same momentum.

Which has a greater momentum? A 50,000 kg Which has a greater momentum? A 50,000 kg train locomotive traveling at 1 m/s or a 1 kg train locomotive traveling at 1 m/s or a 1 kg squirrel traveling at 50,000 m/s.squirrel traveling at 50,000 m/s.

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EnergyEnergy

• The universe is composed of both matter and energy.

– Matter is substance

– Energy is the mover of substance

EnergyEnergy

• Energy: the property of a system that enables it do work (produce changes on another system).

– When work is done by one system on another, energy is transferred.

– We usually only observe energy when it is being transferred or being transformed.

Energy and WorkEnergy and Work

• Whenever work is done:

1) Application of a force

2) Movement of something by that force

Energy and WorkEnergy and Work

Work = Force X Distance

W = Fd

Units of work: Newton-meter (N·m) orJoules (J).

• Units of Energy: Joules (J).

– Heating 1g of water one degree C = 4.2 J

– 1 nutritional Calorie = 4.2 kilojoules (KJ)

– 1 kilowatt-hour = 3.6 megajoules (MJ)

– Recommended human diet = 9 megajoules (MJ)

– 1 large pizza = 16 megajoules (MJ)

– 1 gallon of gasoline = 120 megajoules (MJ)

– 1 ton of TNT = 4.2 gigajoules (GJ)

Mass-Energy Equivalence Matter is a condensed form of energy.

1 gram of mass = energy released by 21.5 kilotons of TNT or the combustion of 568,000 gallons of gasoline.

1 gram of mass = 89.9 Terajoules.1 gram of mass = 89.9 Terajoules.

Potential EnergyPotential Energy

• Potential Energy (PE): stored energy or the potential for doing work.

• Examples:– Stretched Springs– Chemical energy in fuels and food– Electric potential or voltage– Buildup of stress along a fault in Earth’s crust– Gravitational potential energy

• Whenever work is done, energy is exchanged.

Potential EnergyPotential Energy

• Gravitational Potential Energy (PE): the potential energy due to elevated positions.

• Amount of PE possessed by an elevated object = work done against gravity in lifting it.

Potential EnergyPotential Energy

• Gravitational Potential Energy = weight X height

PE = mgh(weight = mg)(h = height)

Potential EnergyPotential Energy

• The PE of an elevated object does not depend on the path taken to get it there. Only vertical distance matters.

Kinetic EnergyKinetic Energy

• Kinetic Energy (KE): the energy of motion.

– Depends on the mass of an object as well as its velocity.

Kinetic energy = ½ mass X velocity2

KE = ½ mv2

Potential and Kinetic EnergyPotential and Kinetic Energy

Work-Energy TheoremWork-Energy Theorem

• KE of a moving object is equal to:

– the work required to bring it from rest to a speed.

– the work the object can do while being brought to rest.

Work-Energy TheoremWork-Energy Theorem

• Work = Change in Kinetic Energy.

Work = ΔKE

Fd = ΔKE

• If there is no change in an object’s energy, then no net work was done on it.

• If you push a crate horizontally with 100 N across 10 m, and the friction between the crate and the floor is a steady 70 N, how much KE is gained by the crate?

• For the same force, why does a longer cannon impart more speed to a cannonball?

Energy TransformationsEnergy Transformations

The Law of Conservation of Energy:

Energy cannot be created or destroyed; it may be transformed from one form into another, but the total amount of energy never changes.

Energy TransformationsEnergy Transformations

Energy TransformationsEnergy Transformations

What is the ultimate source of energy What is the ultimate source of energy stored in fossil fuels such as coal?stored in fossil fuels such as coal?

EfficiencyEfficiency

• In any energy transformation, some energy is dissipated to thermal energy (heat).

• Efficiency = useful energy output / total energy input.

PowerPower

• Power: the measure of how fast work is done.

Power = work done / time interval

• Example: An engine that delivers twice the power can accomplish twice the amount of work in the same amount of time.

– Greater power = greater acceleration

PowerPower• Power is also the rate at which energy is changed from

one form to another.

• Unit of power: joule per second or the watt (W).

– 1 W of power is used when 1 J of work is done in 1 second (J/s).

– 1 W of power represents 1 J of energy that is converted each second (J/s).

PowerPower

• The human heart The human heart uses slightly more uses slightly more than 1 W of power in than 1 W of power in pumping blood.pumping blood.

• 3 main engines of a 3 main engines of a space shuttle can space shuttle can develop 33,000 MW develop 33,000 MW of power when fuel is of power when fuel is burned at a rate of burned at a rate of 3,400 kg/s.3,400 kg/s.

The Grand Coulee Dam can produce up to approximately 7,080 Megawatts or power.