Energy• Energy is the ability of a body or object to produce a

change in itself or the environment; in other words, it is the capacity to perform a work over or by an object.

Kinetic Energy• Energy of an object due to movement.

Ek= kinetic energy (J)

m= mass (kg)

v= velocity (m/s)

Example

A baseball ball of 0.14kg is thrown by a pitcher at a speed of 35m/s. Determine:• The kinetic energy of the ball.• The work performed over the ball so that it reaches the

given speed, if you assume that it began at resting state.

Potential Energy• Energy that can be associated to a body or conservative

system because of its position or configuration.• Gravitational Potential Energy: Energy associated to the

position of a body in a gravitational field and with the degree of separation between two bodies, which attract through a gravitational force.

Ep= potential energy (J)

m= mass (kg)

g= gravity acceleration (9.81 m/s2)

h= height (m)

Example• A combat plane takes off vertically and has a mass of

6200kg without load. If it elevates 18m over the runway platform before accelerating horizontally, determine the minimum work it performs supposing it does it at constant velocity.

Conservation of energy• The total amount of mechanical energy, in a closed

system in the absence of dissipative forces (e.g. friction, air resistance), remains constant.

• This means that potential energy can become kinetic energy, or vice versa, but energy cannot “disappear”

Conservation of energyA roller coaster car has a mass equal to 120kg and a velocity of 2.5m/s in the point A with a height of 10m. Determine:• The total energy of the car in the point A.• The velocity that a car goes at in the point B.

2.- A 65 kg girl is running with a speed of 2.5 m/s. How much kinetic energy does she have? She grabs on to a rope that is hanging from the ceiling, and swings from the end of the rope. How high off the ground will she swing? Answer h = 0.32 m

Exercises

1.- During a flood a tree trunk of mass 100 kg falls down a waterfall. The waterfall is 5 m high. If air resistance is ignored, calculate the magnitude of the velocity of the tree trunk at the bottom of the waterfall. (9.9 m/s)

• 2.- A skier glides down a frictionless hill of 100 meters, the ascends another hill, of height 90 meters, as shown in the figure below. What is the speed of the skier when it reaches the top of the second hill? A=the final velocity of the skier is 14 m/s.

3.- A student lifts his 2.0 kg pet rock 2.8 m straight up. He then lets it drop to the ground. Use the Law of Conservation of Energy to calculate how fast the rock will be moving (a) half way down and (b) just before it hits the ground. Answers          a) 5.2 m/s        b) 7.4 m/s

4.-  A 2-kg ball has a potential energy of 6400 J at a point A above the ground. What will its velocity be when it strikes the ground after being released from point A? (80 m/s)

 

5.- Kathy is changing the tire of her car on a steep hill 20 m high. She trips and drops the 10 kg spare tire, which rolls down the hill with an initial speed of 2 m/s. What is the speed of the tire at the top of the next hill, which is 5 m high? (17.4 m/s)

6.- Frank, a San Francisco hot dog vender, has fallen asleep on the job. When an earthquake strikes, his 300 kg hot dog cart rolls down Nob Hill and reaches point A at a speed of 8 m/s. How fast is the hot dog cart going at point B when Frank finally wakes up and starts to run after it? (21.5m/s)

7.- While on the moon, the Apollo astronauts enjoyed the effects of a gravity much smaller than that on the earth. If Neil Armstrong jumped up in the moon with an initial speed of 1.51 m/s to a height of 0.7 m, what amount of gravitational acceleration did he experience?