Example: A 20 kg block is fired horizontally across a frictionless surface. The block strikes a platform that is attached to a spring at its equilibrium position. If the spring has a spring constant of 1200 N/m and is compressed by 10 cm before the block stops, what speed did the block strike the platform with? v Work done by the block on the spring Work done on the block by the spring to change the speed of block 0 0 Work done on a system is considered positive work - system gains energy Work done by a system is considered negative work - system loses energy

Power It is sometime more useful to discuss the rate at which the energy is transferred. This is called power. Whenever you hear rate it means changing with respect to time. P – Power [W] W – Work [J]  E – Change in energy [J]  t – Time interval [s] [P] = W = Watts = J/s = Nm/s = kgm 2 /s 3 1 horsepower (hp) = 746 W

CH 6: Potential Energy and energy Conservation

Potential Energy What is potential energy? Energy stored in a system The energy is stored when conservative forces do work on a system. The energy can be released and then stored again without the system permanently losing energy to the environment. Gravitational Potential Energy We will discuss two common conservative forces, gravitational forces and elastic forces. Work is done against gravity to store energy in a system. The force, which is equal to the gravitational force, must be applied to the system to move it a vertical distance against gravity. 1 0 If we define the initial vertical position to be zero. Work is done to change the potential energy of the system. U g – Gravitational potential energy [J] m – mass [kg] g – gravitational acceleration [m/s 2 ] h – height above what is defined to be zero height [m] This expression is only valid near the surface of the Earth!

Example: Determine the potential energy of the 10 kg cart for each case. a) The cart is at point A and the reference is point E. b) The cart is at point B and the reference is point E. c) The cart is at point A and the reference is point C. d) The cart is at point E and the reference is point D. A B C D E A is 20 m above E B is 10 m above E C is 15 m above E D is 5 m above E a) b) c) d)

Elastic Potential Energy Energy is stored in a spring when a force is applied against the restoring force of the spring to stretch or compress the spring. The force required to stretch the spring would be equal in magnitude to the restoring force. 0 If we define x 0 to be the equilibrium position which is zero. Work is done to change the potential energy of the system. U s – Elastic potential energy [J] k – spring constant [N/m] x – distance from equilibrium [m] The result obtained for the elastic potential energy describes a similar situation as can be described for gravitational potential energy. The work done by an applied force to move an object a distance from their equilibrium position against a pre-existing force will store energy within the specified system.