Chapter 4 Work and Energy Additional Concepts For Describing Motion

PSC 150 Exercise "Conservation of Energy" Results and Conclusions

1.) Based on your table, as the object moves UPWARD its kinetic energy: Questions: Decreases 2.) Based on your table, as the object moves UPWARD its gravitational potential energy: 3.) Based on your table, as the object moves DOWNWARD its kinetic energy: 4.) Based on your table, as the object moves DOWNWARD its gravitational potential energy: 5.) Based on your table, as the object moves UPWARD its total mechanical energy: 6.) Based on your table, as the object moves DOWNWARD its total mechanical energy: 7.) As the object moves the only force acting on it is: Decreases Increases Remains Constant Gravitational Force

If the only force acting on an object is the gravitational force the kinetic and gravitational potential energies may change but the total mechanical energy remains constant. Conclusion

8.) Based on your table, as the pendulum swings DOWNWARD its kinetic energy: Questions 9.) Based on your table, as the pendulum swings DOWNWARD its gravitational potential energy: 10.) Based on your table, as the pendulum swings UPWARD its kinetic energy: 11.) Based on your table, as the pendulum swings UPWARD its gravitational potential energy: 12.) Based on your table, as the pendulum swings UPWARD or DOWNWARD its total mechanical energy: 13.) As the pendulum swings the two forces acting on it are: Increases Decreases Remains Constant Gravitational Force and Tension Tension is always perpendicular to the direction of motion.

Conclusion If the only force acting on an object is the gravitational force or if there are other forces which are always perpendicular to the direction of motion the kinetic and gravitational potential energies may change but the total mechanical energy remains constant.

14.) At what point(s) (A,B,C,D) does the kinetic energy have its maximum value? 15.) At what point(s) (A,B,C,D) does the gravitational potential energy have its maximum value? 16.At what point(s) (A,B,C,D) does the pendulum have both kinetic and potential energy? C A & D B

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Questions: 17.) Based on your table, as the object moves its kinetic energy: 18.) Based on your table, as the object moves its gravitational potential energy: 19.) Based on your table, as the object moves its total mechanical energy: 20.) As the object moves the applied force was in the SAME OPPOSITE direction as the motion. 21.) The units of Force X Displacement are: 22.) The units of Force X Displacement are the same as the units of mechanical energy: 23. As the object moves the change in its total mechanical energy, E, approximately equals the product of the applied force and the displacement. Increases Remains Constant Increases Same True

Conclusion When a net external force acts on an object in the same direction as its motion the total mechanical energy increases. The change in the object’s total mechanical energy equals the product of the net force and the object’s displacement.

Questions: 17.) Based on your table, as the object moves its kinetic energy: 18.) Based on your table, as the object moves its gravitational potential energy: 19.) Based on your table, as the object moves its total mechanical energy: 20.) As the object moves the frictional force was in the SAME OPPOSITE direction as the motion. 23. As the object moves the change in its total mechanical energy, E, approximately equals the product of the applied force and the displacement. Decreases Remains Constant Decreases Opposite True

Conclusion When a frictional force acts on an object in the opposite direction as its motion the total mechanical energy decreases. The change in the object’s total mechanical energy equals the product of the frictional force and the object’s displacement.

Work-Energy Theorem “When a net force causes an object to accelerate, the work done on or by the object equals the change in the object’s kinetic energy.” The Work-Energy Theorem can be derived from Newton’s Second Law.

Another Type of Energy Define: Gravitational Potential Energy is something an object has because of its position. GPE is a Scalar!

“When an external force (equal to the object’s weight) lifts an object at a constant velocity, the work done by that force equals the change in the object’s Gravitational Potential Energy.” If  GPE is positive, the gravitational Potential Energy has increased. If  GPE is negative, the gravitational Potential Energy has decreased.

Total Mechanical Energy, E The Total Mechanical Energy of an object is defined as the sum of its Kinetic Energy and Gravitational Potential Energy. E = KE + GPE Extended Work-Energy Theorem “The work done by any force other than the gravitational force equals the change in Total Mechanical Energy.”

What if the only force acting on an object is the gravitational force? Work done by the gravitational force does NOT change the total mechanical energy it does cause a conversion between kinetic energy and gravitational potential energy. If the work done by the gravitational force is positive… the gravitational force is in the same direction as the displacement, gravitational potential energy is converted into kinetic energy. The gravitational force is called a Conservative Force. If the work done by the gravitational force is negative… the gravitational force is in the opposite direction as the displacement, kinetic energy is converted into gravitational potential energy.

The Law of Conservation of Energy “If the only force acting on an object is the gravitational force, or if there are other forces acting on the object but they do no work, the kinetic and gravitational energies may change but the total mechanical energy remains constant.”

Net Force Lifting Force greater than weight e.g.,Friction Lifting Force Less than weight