Work is only done by a force on an object if the force causes the object to move in the direction of the force. Objects that are at rest may have many forces acting on them, but no work is done if there is no movement.

W = F·d Work, Work is a scalar quantity. by definition, is the product of the force exerted on an object and the distance the object moves in the direction of the force. W = F·d Work is a scalar quantity.

The SI unit of work is the Joule, named in honor of James Prescott Joule. One Joule, J, of work is the work done when 1.0 N of force is applied through a distance of 1.0 m.

“Force vs. Displacement” graph. Graphically, work is the area under a “Force vs. Displacement” graph. displacement, m

work = Fd(cosq), W = Fd(cos q) = (40N)(3.0 m)(cos 35) = 98 J If the force and displacement are not in the exact same direction, then work = Fd(cosq), where q is the angle between the force direction and displacement direction. F =40 N d = 3.0 m The work done in moving the block 3.0 m to the right by the 40 N force at an angle of 35 to the horizontal is ... W = Fd(cos q) = (40N)(3.0 m)(cos 35) = 98 J

Energy comes in many forms: mechanical, electrical , magnetic, solar, the ability (capacity) to do work Energy comes in many forms: mechanical, electrical , magnetic, solar, thermal, chemical, etc... The SI unit of energy is the Joule. Energy, like work, is a scalar.

KE = 1/2 mv2 Kinetic Energy energy of motion All moving objects that have mass have kinetic energy. KE = 1/2 mv2 m - mass of the object in kg v - speed of the object in m/s KE - the kinetic energy in J

Work-Energy Theorem the net work done on an object is equal to its change in kinetic energy

an object to change its KE because A net force causes an object to change its KE because a net force causes an object to accelerate, and acceleration means a change in velocity, and if velocity changes, KE changes. Learn more about the Work-Energy Theorem here and here.

PEg = mgh Potential Energy energy of position or condition gravitational potential energy PEg = mgh m - mass of object in kg g - acceleration of gravity in m/s2 h - height of object, in m, from some arbitrary reference point PE – gravitational potential energy in J

PEe = ½ kx2 Potential Energy energy of position or condition elastic potential energy PEe = ½ kx2 k – elastic constant in N/m x - elongation or compression in m PEe – elastic potential energy in J Click here to investigate elastic constants.

Law of Conservation of Energy “Energy can be neither created nor destroyed. It may only change forms.” S all types of energy before the event = S all types of energy after the event Examples: A dropped object loses gravitational PE as it gains KE. A block slides across the floor and comes to a stop. A compressed spring shoots a ball into the air.

the time rate of doing work; or the time rate transfer of energy. Power, by definition, is the time rate of doing work; or the time rate transfer of energy. P = W / t Power is a scalar quantity.

1.0 J of energy is transferred The SI unit of power is the Watt, named in honor of James Watt. One Watt, W, of power is the power achieved when 1.0 J of work is done or 1.0 J of energy is transferred in a time of 1.0 s.

Simple Machines “a device that is used to manipulate the amount and/or direction of force when work is done” A common misconception is that machines are used to do a task with less work than would be needed to do the task without the machine. They do not! In fact (mainly because of friction), you actually do more work with a machine than without it (for the same task). The major benefit of a machine is that the work can be done with less applied force, but at the expense of the distance through which the force must be applied.

Work = Force x Distance “large force x small distance = small force x large distance” For example, 1000 J of work is needed to lift 1000 N onto a table 1.0 m high. If the object were pushed up a 4.0 m ramp (inclined plane), a minimum of 250 N of force would be needed (250 N x 4.0 m = 1000 J). In reality, friction between the object and the ramp would make the necessary force greater than 250 N.

Efficiency of a Machine If a 10 m ramp were used, a minimum of 100 N of force would be needed. The greater the distance, the smaller the necessary force. Efficiency of a Machine “the ratio of useful work output to useful work input” It is impossible to get as much “useful” work or energy out of a machine as you put into it.

Consider the lever, pulley, and inclined plane as examples of simple machines: Inclined plane: decreases necessary force because of an increase in distance Lever: used to decrease force by increasing distance; changes direction of force (link) Pulley: used to decrease force by increasing distance; may change direction of force (link) Click here to perform an interesting activity on simple machines.

Click here to explore energy, work, and the Work-Energy Theorem in more depth.