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

Momentum 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 Force Force causes an acceleration. Acceleration = a change in an object’s velocity = a change in its momentum.

Momentum 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 Impulse Impulse = Force x time Impulse = Change in Momentum Force x time = Change in Momentum Ft = Δ (mv)

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

Impulse Changes Momentum Extending the time of an impact reduces the force of an impact.

Impulse 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 cut off about 25 km from port. What makes the momentum of a supertanker so enormous that it needs considerable time to stop. 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 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. What is the momentum of the ball before it is brought to rest? 1.4 kg·m/s 2.4 N 3.6 kg·m/s 4.6 N 5.15 kg·m/s 6.15 N

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 caught and brought to rest? 1.12 kg·m/s 2.6 kg·m/s 3.0 kg·m/s 4.4 kg·m/s

Automobiles were previously manufactured to be as rigid as possible, where as today’s autos are designed to crumple upon impact. Why? 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 times as long by riding with the punch. By how much is the force of the impact reduced? 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 duration of the impact by half, then how much is the force of the impact changed? 1.4 times as much 2.Twice as much 3.Half as much 4.No change

1.The train locomotive. 2.The squirrel. 3.They have the same momentum. Which has a greater momentum? A 50,000 kg train locomotive traveling at 1 m/s or a 1 kg squirrel traveling at 50,000 m/s.

Energy The universe is composed of both matter and energy. –Matter is substance –Energy is the mover of substance

Energy 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 Work Whenever work is done: 1)Application of a force 2) Movement of something by that force

Energy and Work Work = Force X Distance W = Fd Units of work: Newton-meter (N·m) or Joules (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.

Potential 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 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 Energy Gravitational Potential Energy = weight X height PE = mgh (weight = mg) (h = height)

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

Kinetic 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 velocity 2 KE = ½ mv 2

Potential and Kinetic Energy

Work-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 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 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 Transformations

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

Efficiency In any energy transformation, some energy is dissipated to thermal energy (heat). Efficiency = useful energy output / total energy input.

Power 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

Power 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).

Power The human heart uses slightly more than 1 W of power in pumping blood.The human heart uses slightly more than 1 W of power in pumping blood. 3 main engines of a space shuttle can develop 33,000 MW of power when fuel is burned at a rate of 3,400 kg/s.3 main engines of a space shuttle can develop 33,000 MW of power when fuel is burned at a rate of 3,400 kg/s.

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