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Work

Eg. A ball of mass 500g is moving at a velocity of 5m/s. What is the kinetic energy of the ball?

kinetic energy = 1/2 mv2 = 1/2 x 0.5 x 5 x 5 = 6.25 J

Eg. Billy has a mass of 40kg. He runs up a flight of 20 steps, each of height 0.25m. Calculate his gain in gravitational potential energy

gain in gravitational potential energy = mgh = 40 x 10 x (20 x 0.25) = 2000 J

Principle of Conservation of Energy

States that "energy can neither be created not destroyed but can be transformed from one form into another with no change in its total amount."

Eg. A ball of mass 3kg is dropped from a height of 5m.

i. calculate the gravitational potential energy of the ball before it is dropped

ii. calculate the speed of the ball on hitting the ground

iii. if the ball bounces to a height of 3m, with what speed does it leave the ground?

iv. explain why the ball does not reach its original height when it bounces up again

i. gravitational potential energy = mgh = 3 x 10 x 5 = 150J

ii. The kinetic energy of the ball on hitting the ground is equal to the ball's original gravitational potential energy so the kinetic energy of the ball on hitting the ground = 150J

If the ball hits the ground with speed v,

1/2 mv2 = 150

v2 = (150 - 2)/3 = 100

v = 10ms-1

iii. The kinetic energy of the ball on leaving the ground is equal to its gravitational potential energy on rising to its maximum height, that is 3m.

The gravitational potential energy of the ball 3m above the ground = 3 x 10 x 3 = 90 J

The kinetic energy of the ball leaving the ground = 90 J

If the ball leaves the ground with speed v,

1/2 mv2 = 90v2 = (90 x 2)/3

v = 7.746ms-1

iv. Because part of its kinetic energy is changed into other forms of energy like sound and heat when it hits the ground

Eg. A pendulum bob of mass 0.5kg is moved sideways until it has risen by a vertical height of 0.2m. Calculate the speed of the bob at its

i. highest point

ii. lowest point

i. at the highest point, the kinetic energy of the bob = 0

if the speed of the bob at its highest point is v,

1/2 mv2 = 0

1/2 x 0.5 x v = 0

v2 = 0

v = 0

ii. according to the principle of conservation of energy, the kinetic energy of at the lowest point is equal to the gravitational potential energy at the highest point.

If the speed of the bob at its lowest point is v,

1/2 mv2 = mgh

v2 = 2 x 10 x 0.2 = 4

v = 2 m/s

Power and efficiency

i. the power output of the motor driving the crane

ii. the efficiency of the motor if the power input is 5kW

i. power output = work done/time taken = (200 x 10 x 5)/4 = 2500W

ii. efficiency of motor = (power output/power input) x 100% = (2500/5000) x 100% = 50%Friction

- Work is the product of the force on a body and the distance it moves in the direction of the force

- Work done = force x distance moved in the direction of the force

- Work is done whenever energy is changed from one form into another.

- SI unit is joule (J)

- Work is a scalar quantity

- energy is defined as the capacity to do work

- SI unit is joule (J)

- Energy is a scalar quantity

- Kinetic energy is the energy a body possesses due to its movement

- kinetic energy can be classified into
- translational kinetic energy: possessed by bodies in translational motion (eg moving train) =1/2 mv2

- rotational kinetic energy: possessed by bodies in rotational motion (eg rotating merry-go-round)

- translational kinetic energy: possessed by bodies in translational motion (eg moving train) =1/2 mv2
- potential energy is the energy a body possesses due to its position or state

- potential energy can be classified into:
- gravitational potential energy: possessed by a body due to its position = mgh

- elastic potential energy: possessed by a body due to its strained state of being stretched or compressed

- gravitational potential energy: possessed by a body due to its position = mgh

Eg. A ball of mass 500g is moving at a velocity of 5m/s. What is the kinetic energy of the ball?

kinetic energy = 1/2 mv2 = 1/2 x 0.5 x 5 x 5 = 6.25 J

Eg. Billy has a mass of 40kg. He runs up a flight of 20 steps, each of height 0.25m. Calculate his gain in gravitational potential energy

gain in gravitational potential energy = mgh = 40 x 10 x (20 x 0.25) = 2000 J

Principle of Conservation of Energy

States that "energy can neither be created not destroyed but can be transformed from one form into another with no change in its total amount."

Eg. A ball of mass 3kg is dropped from a height of 5m.

i. calculate the gravitational potential energy of the ball before it is dropped

ii. calculate the speed of the ball on hitting the ground

iii. if the ball bounces to a height of 3m, with what speed does it leave the ground?

iv. explain why the ball does not reach its original height when it bounces up again

i. gravitational potential energy = mgh = 3 x 10 x 5 = 150J

ii. The kinetic energy of the ball on hitting the ground is equal to the ball's original gravitational potential energy so the kinetic energy of the ball on hitting the ground = 150J

If the ball hits the ground with speed v,

1/2 mv2 = 150

v2 = (150 - 2)/3 = 100

v = 10ms-1

iii. The kinetic energy of the ball on leaving the ground is equal to its gravitational potential energy on rising to its maximum height, that is 3m.

The gravitational potential energy of the ball 3m above the ground = 3 x 10 x 3 = 90 J

The kinetic energy of the ball leaving the ground = 90 J

If the ball leaves the ground with speed v,

1/2 mv2 = 90v2 = (90 x 2)/3

v = 7.746ms-1

iv. Because part of its kinetic energy is changed into other forms of energy like sound and heat when it hits the ground

Eg. A pendulum bob of mass 0.5kg is moved sideways until it has risen by a vertical height of 0.2m. Calculate the speed of the bob at its

i. highest point

ii. lowest point

i. at the highest point, the kinetic energy of the bob = 0

if the speed of the bob at its highest point is v,

1/2 mv2 = 0

1/2 x 0.5 x v = 0

v2 = 0

v = 0

ii. according to the principle of conservation of energy, the kinetic energy of at the lowest point is equal to the gravitational potential energy at the highest point.

If the speed of the bob at its lowest point is v,

1/2 mv2 = mgh

v2 = 2 x 10 x 0.2 = 4

v = 2 m/s

Power and efficiency

- Power is defined as the rate of doing work

- Power = work done/time taken

- SI unit is watt (W)

- Efficiency is the ratio of useful output energy to the total input energy or the ratio of useful power to the total input power.

- Efficiency = (useful output energy / input energy) x 100%

i. the power output of the motor driving the crane

ii. the efficiency of the motor if the power input is 5kW

i. power output = work done/time taken = (200 x 10 x 5)/4 = 2500W

ii. efficiency of motor = (power output/power input) x 100% = (2500/5000) x 100% = 50%Friction

- The net force that slows down moving objects

- Acts in the opposite direction of motion of objec

- related to objects which are not moving.

- amount of force applied = amount of friction

- applied force does not affect friction

- it can be affected by surface or sudden change in mass

- enables walking

- brakes of vehicles

- reduce efficiency of machinery

- energy wasted as heat

- lubricants

- ball bearings