Kinetic energy L.O.:  Calculate kinetic energy.  Calculate the speed of an object applying the principle of energy conservation.

Energy transfers: from gravitational potential energy to kinetic energy and vice versa

Gravitational potential energy When you lift an object up you increase its gravitational potential energy. change in gravitational potential energy = weight  vertical height difference

Falling If you let the object fall it loses gravitational potential energy and gains kinetic energy. kinetic energy = ½  mass  speed 2

Lifting a bag of flour Lift up a 1 kg bag of flour to a height of 2 m. change in gravitational potential energy = weight  vertical height difference = 10 N  2 m = 20 J

Now drop the bag of flour As it falls, it loses gravitational potential energy and gains kinetic energy gain in kinetic energy = loss of gravitational potential energy = 20 J

What speed does it reach? kinetic energy= 20 J ½  mass  speed 2 = 20 J mass  speed 2 = 40 speed 2 = 40 (m/s) 2 speed= √40 m/s speed= 6.32 m/s

Steps in the calculation First find the change in gravitational energy. If there is no friction, this will be equal to the gain in kinetic energy. Rearrange the equation for kinetic energy to first find the square of the speed. Now take the square root to find the speed.

Sliding down slopes If a roller coaster rolls down a slope its gravitational potential energy decreases and its kinetic energy increases by the same amount.

Sliding down slopes The change in gravitational potential energy depends only on the vertical height difference and the weight. It does not depend on the shape or length of the slope. So the gain in kinetic energy also depends only on the vertical height difference and the weight.

mass = 400 kg weight = 4000 N 10 m How much kinetic energy does it gain? change in gravitational potential energy = weight  vertical height difference = 4000 N  10 m = J gain in kinetic energy = loss of gravitational potential energy = J

mass = 400 kg weight = 4000 N 10 m How fast does it go? kinetic energy= J ½  mass  speed 2 = J mass  speed 2 = J speed 2 = J/mass speed 2 = 200 (m/s) 2 speed= 14.1 m/s

In summary When an object falls: The amount of kinetic energy it gains is equal to the amount of gravitational energy it has lost minus any energy that is wasted causing heating due to friction. If friction can be ignored: loss of gravitational potential energy = gain in kinetic energy

To do: 1) Workbook page ) worksheet 4.30