Section 6-3 Gravitational Potential Energy

Warm-Up #1 A sailboat is moving at a constant velocity. Is work being done by a net external force acting on the boat? No work is being done. If work was being done on the boat, the KE would change, which means the velocity would change.

Warm-Up #2 A ball has a speed of 15 m/s. Only one external force acts on the ball. After this force acts, the speed of the ball is 7m/s. Has the force done A. positive work B. zero work C. negative work on the ball?

6.3 Gravitational Potential Energy Work done by the Force of Gravity W gravity = F * d = mg (h o - h f ) Where: W = work m = mass of the object h o = initial height above a surface h f = final height above a surface

6.3 Gravitational Potential Energy Work done by the Force of Gravity W gravity = F * d = mg (h o - h f ) Notice that W may be positive or negative. Also notice that it is the change in height that determines the Work done. This means that h 0 and h f do not need to be measured from the earths' surface.

6.3 Gravitational Potential Energy Work done by the Force of Gravity W gravity = F * d = mg (h o - h f ) This equation is valid for any path. The work depends only on the difference in vertical distance (h o -h f )

Example 1

Gravitational Potential Energy Gravitational PE is the energy than an object has by virtue of its position. For an object near the surface of the earth, the gravitational PE is PE gravity = m g h ∆PE = m g h f - mgh o Where: h = height above an arbitrary zero level.

Example 2 A child's mass is 18 kg. She has climbed up into a tree and is now frightened and cannot get back down. She is 3.7 m above the ground when she calls for help. Find her gravitational potential energy. PE = J

Total Work

Conservative vs. Non-conservative Forces The gravitational force has an interesting property that when an object is moved from one place to another, the work done by gravity is NOT dependent upon the path it takes; it merely depends upon the change in height.

Conservative vs. Non-conservative Forces

Gravity obeys both of these ‘rules’ and is therefore a conservative force. Examples of non-conservative forces include: Kinetic frictional force (more and more energy is lost if the path increases) Air resistance (more and more energy is lost if the air conditions change = path dependent) Thrust

Conservative vs. Non-conservative Forces

Assignment p. 187 Focus on Concepts #11 p. 190 #29, Use Energy to solve these problems, not kinematics!