Evans SPH 4U1

Unit 4: Energy & Momentum

Note 1B: Work/Conservation of Energy

Reference: Chapters 4.3, 4.4 and 6.3

Gravitational Potential Energy (measurd in Joules):    Energy due to elevation above the ground.

NEAR THE EARTH  you can use the following formula (for distances greater than 100km the error becomes large):

~ where is the vertical displacement in metres.

~ Note: to use this equation g (9.8 m/s2)must not change over the vertical displacement.

~ are positive if vertical displacement is up (and negative if it is down).

~ When objects are lifted up, kinetic energy is converted to gravitational potential energy

~ When objects are dropped, gravitational potential energy is converted to kinetic energy. (i.e. roller coasters)

FARTHER AWAY FROM THE EARTH (Chapter 6.3)

The work to change the separation of 2 masses from r1 to r2 is the gravitational potential energy

To escape the gravitational field (the gravitational well),  r2 becomes infinite. At this point the energy is defined as 0. To escape a gravitational field (i.e. to get to the 0 energy level) an object  has to take on energy so by definition we define the energy level in the gravitational well as negative and the formula becomes:

Law of Conservation of Energy:

Energy can be converted into different forms but it cannot be destroyed.

So far we've only talked about Eg and Ek so you are used to working with...... and

but there are many more forms of energy (see text page 198).

You should also know that ...Work done on a moving object by kinetic friction results in the conversion of kinetic energy to thermal energy, Eth

Example 1:

Text page 201 #6 angle is 17.5 degrees

Example 2:

A 40 kg boy on a sled slides down a hill at a 15 degree angle to the horizontal.  A kinetic friction force of 60N is between the sled and the hill. His speed is 3.0 m/s near the top.  What is his speed after going 50m down the hill? 10.3 m/s

Example 3:

A skier (m=50kg) slides down the slope of a hill inclined at 20 degrees.  The skier starts from rest and slides 8.0m along the slope to reach the bottom of the hill.  The coefficient of kinetic friction is 0.14.

a) Draw a free-body diagram of the skier.

b) With what speed does the skier reach the bottom of the hill? (Note: Although this could be done resolving forces on inclined planes as we did last chapter, solve it this time using energies.  Hint total energy is potential energy at the beginning and gets converted to kinetic energy and thermal energy). 5.7 m/s

Homework:

Page 191 #4, 5

Page 194 #3, 4