Notes

Outline

Chapter 3, Energy and Conservation Laws Physics 2001, Professor Ray Merry

Conservation Laws:  What does it mean for a physical quantity to be conserved? It means: The amount of that thing does not change. E.G. Conservation of mass, means the amount of mass in a system stays constant. Take the example of a burning cigarette. Cigarette before burning weighs 10 g. After burning the butt plus the ash weighs 5 g. What happened?  Is mass conserved?

Burning Cigarette

What is the Closed System Note for all the conservation laws we must include all the parts of the system! For example, not considering the air in the cigarette example led to an error. This is the secret to good scientific analysis.  What is the total environment or system?

Linear momentum, p: The mass of an object times its velocity.  p = mv  Note since v is a vector so is p! Example, m = 5 kg, v = 10 m/s what is p?  p = 5 x 10 kg m/s = 50 kg m/s Note units are kg m/s or mass x vel. Units.

Newton’s Second Law w Impulse F= D(mv)/Dt  is another way of stating Newton’s second law, in terms of D(mv), change in momentum and Dt time for the change to occur. We can also state this as F Dt = D(mv)  Where F Dt is the impulse of a force.

Impulse Diagram-Ball Hitting Floor

Impulse Problem Suppose a ball of .1 kg is in contact with a bat for .2 s, and the force the bat exerts is 5 n.  What would the speed of the ball be?  F Dt = D(mv)  since original velocity of the ball is 0, D(mv) = m x final vel.(vf) 5n x .2s = .1kg x v final Vf = 1 ns/.1kg = 10 m/s (n=kg m/s/s  nxs = kg m/s  n/kg = m/s2)

Law of Conservation of Linear Momentum: The total linear momentum of an isolated system is constant. Remember this is a vector relationship If all velocities are in the same direction it is simple, if not we must use vectors to solve total mv before = total mv after

1 D Momentum Problem A 200lb boy moving at 10 ft/sec hits  2 50 kg midgets  at rest.  Both go off together, but how fast ? Momentum before = momentum after Mom.before =200 kg x 10m/s   = 2000 kgm/sec Mass after = 50 +50 + 200 = 300 kg After mom =   300 x V2;  2000 = 300 V2 V2 = 2000/300  = 6.6 m/s

Work The force that acts times the distance moved in the direction of the force. Work = F x d  (Joules =Newtons x meters) Work units are Joules, same as energy. E.G. Force of 10 N moves 5 m W = 10 N x 5 m = 50 Nm or 50 J Note Force is a vector but work is a scalar!c

Force vs Work Note work = force x distance in direction of force. If Force is perpendicular to motion or displacement no work is done! Examples circular motion, moving parallel to floor

Gravitational Work When we lift a body we do work against gravity, but when a body falls, gravity does work on it.  If the distances are equal so are the works. Work = F x d F = weight = W=mg W=Wd = mgd Example 10kg falls 5m, what is the work? W = 10kg x 9.8m/s/s x 5m =490J

Energy (E) The measure of a system's capacity to do work. That which is transferred when work is done. Energy is measured in Joules,  which are Newtons x meters.

Define kinetic energy: Kinetic energy (KE) Energy due to motion. Energy that an object has when it is moving KE = ½ mv2 Example, 20 kg mass moving at 15 m/s KE = ½ x 20 kg x (15)2 =10 x 225 = 2250 J

Potential Energy Potential energy (PE) is Energy due to an object's position or configuration. A stretched spring has potential energy. A raised object has gravitational energy.

Gravitational Potential Energy Energy due to position, PE Gravitational PE = mgd

Other PE’s elastic potential energy stretched out rubber band or spring. internal energy unburned fuel, battery

PE Problem We can calculate the potential energy of a given situation if we know the force. Since work against gravity is weight x height lifted.   mgd, PE is the same, mgd. W = m g d.  Lift 10 kg, 2 meters W = 10kg x 9.8 m/s/s x 2 m W = 196 J;  PE stored = same, 196 J

Work and Potential Energy

Law of Conservation of Energy: Energy cannot be created or destroyed, only converted from one form to another.  The total energy in an isolated system is constant. Eo = Ef (original energy = final energy) In terms of PE and KE: PE + KE = constant

Conservation of Energy Problem A man does a work against gravity of 98 Joules lifting an object. What is its KE before it strikes if it falls back down?

Energy Conversion and Conservation Many common devices convert energy from one form to another. For example your radio converts chemical energy from a battery to electrical to sound energy. Although the law of conservation of energy holds, some of the energy ends up in forms we do not need or want, for example as heat.

Energy Conservation in Society When we talk about energy conservation in society we mean Don’t waste energy Renewable energy is energy that we can recover soon, like wood, or solar energy Fossil fuels like coal and oil take millions of years to replenish

Elastic collision Collision in which the total kinetic energy of the colliding objects is the same before and after the collision. I.E. KE is conserved. ½ mv2  before = ½ mv2  after

Inelastic collision Collision in which the total kinetic energy of the colliding bodies after the collision is not equal to the total kinetic energy before.

Torque (levers) Torque is the rotational analog of force. Torque = force times lever arm Example teeter totter

Inclined Plane Inclined plane increases distance moved but decreases force needed.

Power Power (P): The rate of doing work. The rate at which energy is transferred or transformed. Work done divided by the time. Energy transferred divided by the time. Unit of power is the watt (joule/s)

Power Problem 20 Joules of work is done in 5 s. What is the power? P = W/t = 20J/5s = 4 watts

Angular momentum The mass of an object times its speed and times the radius of its path. mvr

Law of conservation of angular momentum The total angular momentum of an isolated system is constant.  mvr= constant

Ice Skater Spinning When the skater brings their arms in, since angular momentum is constant and r is decreasing, v must increase.

Navigation: Back To Web Raymerry Home Back to Classes Back to Physics