WORK AND ENERGY 1

Work Work as you know it means to do something that takes physical or mental effort But in physics is has a very different meaning Think about the following:  A heavy chair held at arms length for several minutes  A student carries a bucket of water carried along a horizontal path at a constant velocity 2

In both cases no work was done on the chair of the bucket even though both required effort What conclusions can you draw from the two examples about how work is defined in physics? 3

Equation for work When a constant force is applied to an object: Work is equal to the magnitude of the applied force times the magnitude of the displacement of the object W=Fd Work is not done unless the object is moved with the action of a force, parallel to the direction of the force. Since the heavy chair doesn’t not move vertically no work is done on the chair 4

Example How much work is done when a box is pushed with a force of 8 N over a distance of 4 meters? 32 N m Or, 32 Joules (32 J) 5

Two types of work 1) work done against another force (ex: gravity, shooting a bow, friction) 2) work done to change the speed of an object (ex: speeding up or slowing down in a car) 6

Do we always push or pull objects directly horizontal? Components of the forces will have to be found If the force applied is at an angle to the horizontal, the component that is parallel to the movement will do work on the object No work is done on the bucket being carried because all the force being applied to the bucket is perpendicular to the displacement. 7

The sign of work is important Work is a scalar quantity (no direction) It can be positive of negative It is positive when the direction of displacement is in the same direction as the force It is negative when the direction of the displacement is in the opposite direction of the force (i.e. a car slowing down) Work done by friction would be negative! 8

Net Work Many forces can be acting on an object making it move In this case each individual force can be doing work on the object And together the forces can produce a net work: W net = F net d 9

ENERGY 10

Kinetic Energy If an object is moving, it is capable of doing work This is called energy of motion, or Kinetic Energy If you do work on an object and get it moving, it can then do work on other objects 11

Kinetic Energy Equation Kinetic energy = work required to bring an object up to speed from rest, or to bring to rest from a certain speed….therefore KE=W=Fd where KE is Kinetic Energy Using Newton’s 2 nd law, this equation can be derived into it’s final form- Fd=1/2mv 2 or KE =1/2mv 2 12

Work-Kinetic Energy Theorem The net work on an object is equal to the change in the kinetic energy of the object. W net =ΔKE=KE f -KE i Or, W net =1/2mv f 2 -1/2mv i 2 13

Example On a frozen pond, a person kicks a 10.0 kg sled, giving it an initial speed of 2.2 m/s. How far does the sled move if the coefficient of kinetic friction between the sled and the ice is 0.10? Given: m=10.0 kg v i = 2.2 m/s v f = 0 m/s µ k =

Equations: W net =F net d, W net =ΔKE=1/2mv f 2 -1/2mv i 2 F f =µ k F N What forces are acting on the sled as it slows down? Only friction so: F net = F f =0.10·10.0kg·9.81m/s 2 = 9.8 N Since v f = 0, W net =-1/2mvi 2 =-1/2· 10.0kg·(2.2m/s) 2 =-24 J 15

So finally, since W net = F net d -24J=9.8N·d d=2.4 m TA DA! 16

Potential Energy 17

Potential Energy Consider an arrow loaded on a bow. Once the arrow is released it will have kinetic energy Because of the arrows position (pulled back on the bow) it has potential to move, it has potential energy 18

Gravitational Potential Energy The energy associated with an object due to the object’s position relative to the gravitational source is called gravitational potential energy Given by this equation PE g =mgh 19

Elastic Potential Energy Most common objects that have elastic potential energy are springs When springs are compressed or stretched they have elastic potential energy stored  When the force holding the spring in position is removed the spring will return to its equilibrium position Length of spring with no external forces is called relaxed length The amount of energy depends on distance compressed or stretched from its relaxed length 20

21 Elastic Potential can be found using the following equation PE elastic =1/2kx 2 Where – k is the spring constant, of force constant Spring constants have units of N/m

Example 22 When a 2.00 kg mass is attached to a vertical spring, the spring is stretched 10.0 cm such that the mass is 50.0 cm above the table. The spring constant of the spring is N/m. What is the total potential energy of this system? Given: m=2.00 kgk=400.0 N/mg=9.81 m/s 2 h= 50.0 cm = m x= 10.0 cm = m

Solution 23 PE tot = PE g +PE elastic PE g =mgh PE elastic =1/2kx 2 PE g =2.00kg·9.81 m/s2·0.500m = 9.81 J PE elastic =1/2·400.0 N/m·(0.100 m) 2 = 2.00 J 9.81 J J = J

24 Conservation of Energy

Energy is Conserved 25 Something is conserved when it remains constant Like matter, energy cannot be created or destroyed Energy gets transferred or transformed in to other types of energy

Mechanical Energy 26 Many objects have both mechanical and potential energy For example a swinging pendulum At the highest point of its swing it has all gravitational potential energy At the bottom of the pendulum it has all kinetic energy. Everywhere in between it has both PE g + KE=Total Energy

27 As the pendulum falls from its highest point it gains speed, therefore it is gaining KE As it falls it is also decreasing its height, therefore PE g is decreasing

28 Mechanical energy is the sum of the potential energy and the kinetic energy associated with an object ME = KE + ΣPE(Σ = sum) Conservation of Mechanical Energy: In the absence of friction, the total mechanical energy remains the same ME i =Me f

29 POWER

Power 30 Rate at which work is done Rate of energy transfer Equation: P=W/t Or, P=Fv (this one is less commonly used, but just in case…) The unit for power is the Watt