Energy Conservation AP

Energy Conservation AP

Manicouagan Reservoir seen from space shuttle; formed almost 1 million years ago when a large meteorite hit Earth Earth did work on meteorite to change its kinetic energy

energy can be changed from one form to another, but can never be destroyed (Conservation of Energy Law, also called the First Law of Thermodynamics) mechanical energy is the sum of the kinetic and potential energy of an object

in an isolated system, the mechanical energy does not change (is conserved) isolated system: a system that no mass can enter or leave and that has no external net forces

Elastic collision KE before collision = KE after collision Both vehicles came to a stop very shortly after the collision

in a swinging pendulum, Ep and Ek are constantly being changed from 1 to the other At every point, the sum of Ep and Ek remains the same

a force is conservative if the mechanical energy of an object does not depend on the path taken or if mechanical energy is conserved

Example The human cannon ball (m = 75.0 kg) leaves the ground with 6.3 x 10 4 J of kinetic energy. How high is he when he is moving at 5.9 m/s? Ignore air resistance

Solution All energy on ground = all energy at point B 6.3 x 10 4 J = E k B + E p B 6.3 x 10 4 J = ½ mv + E p B 6.3 x 10 4 J = ½(75.0 kg)(5.9 m/s) + E p B 38044.65 J = E p B = mgh h = 51.7 m

P 310: 6, 7, 8 Practice

Loss of Mechanical Energy Mechanical energy is not conserved when friction & air resistance are present Friction, etc. converts kinetic energy to heat energy

Example A 45.0 kg box is initially at rest when it begins to slide down a 5.00 m high slope that is 1.5 m long. Determine the force of friction if the box reaches the bottom at 5.00 m/s.

Solution E top = E bottom E p top + E k top = E p bottom + E k bottom + W frict E p top + 0 = 0 +E k bottom + W friction W friction = E p top E k bottom F = 13 N

Example A 0.50 kg ball starting from position A, 7.5 m above the ground is pushed down an incline as shown. Friction produces 10.7 J of heat energy. The ball leaves the incline at position B and reaches a height of 13.0 m above the ground. Determine the initial speed of the ball at position A.

W friction = 10.7 J Speed at A?

E A = E highest Solution E p A + E k A = E p highest + E k highest + W friction E p A + E k A = E p highest + E k highest + 10.7 J

Example A 0.0 kg ball is rolling on a floor at.0 m/s when it collides elastically with a stationary 0.10 kg ball. The 0.0 kg ball comes to a stop. Calculate the speed of the 0.10 kg ball after the collision.

Solution E k before = E k after (definition of elastic collision) ½ m. v. = ½ m.1 v.1 ½ 0.0 kg x (.0 m/s) = ½ (0.10 kg) v.1 0.40 J = ½ (0.10 kg) v.1

P 315, 316:, 3, 4a Practice

Example A 5.0 g pellet is placed in a toy gun and a spring (k = 50 N/m) is compressed 0.0 m. Calculate the maximum speed of the pellet when fired horizontally.

Solution Loss of spring energy = gain in kinetic 1 1 kx mv In AP terms: v kx m - U s = K v 50 N / m 0.0m 5.0x10 3 kg

Example A 0.450 kg object is attached to the end of a horizontal spring (k = 19.0 N/m) and displaced 0.00 m. The spring is released. Determine the speed of the mass when the displacement is 0.155 m. Position 1 Position

Solution E 1 = E E p1 = E p + E k 1 1 1 kx kx mv 1 0.380J 0.8J 0.1518J 1 mv 1 mv v = 0.81 m/s

Solution # 1 1 1 E 1 = E kx kx mv 1 E p1 = E p + E k kx kx mv 1 mv kx kx 1 kx kx v 1 m v kx kx 1 m v = 0.81 m/s

Practice A wheel of radius 0.0 m has a moment of inertia 0.40 kg m. A massless cord wrapped around the wheel is attached to a 4.0 kg box. Some time after being released, the box has 5.0 J of kinetic energy. Determine how far the box has dropped.

Solution Speed of box = 1.581 m/s Tangential speed of wheel = speed of box Angular speed of wheel = 7.905 rad/s

Solution E p = E k + K rot E p = 5.0 J+ ½ I E p = 17.50 J h = 0.45 m

Review While traveling in its elliptical orbit around the Sun, Mars gains speed during the part of the orbit where it is getting closer to the Sun. Which of the following can be used to explain this gain in speed? A. As Mars gets closer to the Sun, the Mars Sun system loses potential energy and Mars gains kinetic energy. B. A component of the gravitational force exerted on Mars is perpendicular to the direction of motion, causing an acceleration and hence a gain in speed along that direction.

Practice A 1800 kg UFO is initially at rest 400 km above Earth s surface. The UFO falls straight down and generates 8.3 x 10 8 J of heat energy while descending to an altitude of 100 km. Determine its final velocity, v T.

Practice P 33-333: 5, 6, 7, 8