Herriman High AP Physics C Chapter 7 Work and Energy

Section 7.2 What is Energy?  Energy deals with the state of an object.  We assign an energy value to a system of objects.  Energy in a System is always conserved.  No exception to this principle has ever been found. Herriman High AP Physics C

Section 7.2 Energy Conservation  All energy in a system is constant  Work and energy are interchangeable.  Doing work on a system either changes its kinetic energy and/or stores energy as potential energy.

Herriman High AP Physics C Section 7.3 Kinetic Energy  Kinetic Energy is energy of Motion Any moving object has kinetic energy Dependent on the mass of the object and its velocity. Mathematically expressed as: E k = ½ mv 2

Herriman High AP Physics C Sample Problem  What is the kinetic energy of a car with a mass of 2000 kg moving at 30 m/s?  E k = ½ mv 2 = (½)(2000 kg)(30 m/s) 2 = 900,000 Joules

Herriman High AP Physics C Section 7.4 Work  The Physics definition of work requires a displacement, i.e. an object must be moved in order for work to be done!  The Applied force which causes the displacement contributes to the work, i.e. in order to contribute to the work, the applied force must be parallel to the displacement.

Herriman High AP Physics C Work: A Mathematical Definition  Work = (Force)(Displacement) W = Fs Work is the scalar product of two vectors.  Units of Work = (Newton)(Meter)  1 Newton Meter = 1 Joule  A Joule is a unit of Energy and it takes energy to do work and work done on an object either causes it to move (kinetic energy) or is stored (potential energy)

Herriman High AP Physics C Sample Problem  What work is done sliding a 200 Newton box across the room if the frictional force is 160 Newtons and the room is 5 meters wide? W = F f ΔX = (160 N)(5 m) 800 Joules

Herriman High AP Physics C Sample Problem 400 N 600 N A box is pulled 30 M across a floor by a rope which makes a 30° angle with the horizontal. If the force exerted on the rope is 400 N, how much work is done? Only Force in the direction of the motion does work. Hence, W = F cos θs = 400 cos 30° 30 M = Joules.

Section 7.5 Work and Kinetic Energy  Work done on an object changes its energy.  A change in kinetic energy can be set equal to the work done on the system. ½ mv f 2 – ½ mv i 2 = F x d Herriman High AP Physics C

Section 7.6: Gravitational Potential Energy  Occurs due to the accelerating force of gravity  Is determined by the position of the object in the gravitational field  Mathematically determined by: E p = mgh where m is mass, g is the acceleration due to gravity and h is the height above a determined baseline.

Herriman High AP Physics C Sample Problem  What is the potential energy of a 10 kg rock sitting on a cliff 30 meters high? The acceleration due to gravity is 9.8 m/s 2.  E p = mgh = (10 kg)(9.8 m/s 2 )(30 m) 2940 Joules

Herriman High AP Physics C Section 7.7: Work Done by Variable Forces  If the force applied in a problem varies with respect to position, then calculating the work done by that force requires integration. Hence

Herriman High AP Physics C Section 7.7: A particle on a spring  Top picture is “rest position”; x = 0 No work is done  Bottom picture is “stretched position” Work has been done stretching the spring F s = -kx

Herriman High AP Physics C Section 7.7 Particle on a Spring  Combining this with the previous equation: W =∫F(x)dx and F = -kx We get: ∫(-kx)dx = ½ kx i 2 – ½ kx f 2

Herriman High AP Physics C Sample Problem  A wooden block with a mass of 6.4 kg is hung vertically from a spring. This causes the spring to stretch meters from its equilibrium position. What work is done by the block on the spring?  Summing the forces in the problem: ∑F = mg-kx = 0; so kx = mg or k = mg/x and W = ½ kx 2 so W = ½ mgx = ½ (6.4 kg)(9.8 m/s 2 )(0.124 m) = 3.89 J

Herriman High AP Physics C Section 7.9: Power  Power = Work/time = Joules/Second  Mathematically there are two formulas for Power: or since then

Herriman High AP Physics C Sample Problem  What power is developed by a 55 kg person who does 20 chin ups, h = 3 m, in 45 seconds?  P= w/t = FΔd/t = mgh/t (20(55 kg)(9.8 m/s 2 )(3 m))/45 sec = Watts

Herriman High AP Physics C Problem Types  Work  Work at an angle  Kinetic Energy  Gravitational Potential  Elastic Potential  Conservation  Power