Work and Potential Energy

Outline what is meant by change in gravitational potential energy. State and apply how Work is equivalent to Potential Energy. Solve problems involving Work, Energy and Power. List the different forms of potential energy and describe examples of work’s relation to potential energy. Assessment Standards

A 750 gram soccer ball is shot with a velocity of 12.5 m/s from the player towards the goal. It hits the goal net and causes it to move 75 cm in stopping the ball. What is the average force exerted on the ball? What was the acceleration of the ball? What is the time it takes to come to a stop? Examples

Energy is the capacity to do work Potential Energy: Stored capacity to do work Gravitational potential energy (perched on cliff) Elastic potential energy (like in compressed spring) Chemical potential energy (stored in bonds) Nuclear potential energy (in nuclear bonds) Energy can be converted between types Work = Energy

Potential energy that is dependent on height is called gravitational potential energy. Gravitational Potential Energy

Energy that is stored due to being stretched or compressed is called elastic potential energy. Elastic Potential Energy

If you stand on a 3 m diving board, you have 3 times the E P, than you had on a 1 meter diving board. Gravitational Potential Energy depends upon position with respect to some reference point. Gravitational Potential Energy

“The bigger they are the harder they fall” is not just a saying. It’s true. Objects with more mass have greater Gravitational PE. Gravitational Potential Energy

The energy that a mass has due to its position relative to the surface of the Earth. The height is measured relative to an arbitrary zero point. Unit: kg(m/s 2 )m = Nm = J (Joule) Gravitational Potential Energy

An object's gravitational potential energy is not a "fixed" quantity but rather a "relative" quantity. The gravitational potential energy of a body is always measured "relative" to some convenient baseline, such as the Earth's surface; however, all convenient reference levels are equally valid. The expression mg  h, for the gravitational potential energy of an object, is nothing more than an expression of the work required to raise an object of mass m kilograms to a height of h meters. Gravitational Potential Energy

Work = W = F (5 m) = PE = mgh = mg (1 m) Gravitational Potential Energy

Ramp 10 m long and 1 m high Push 100 kg all the way up ramp Would require mg = 980 N (220 lb) of force to lift directly (brute strength) Work done is (980 N)  (1 m) = 980 N·m in direct lift Extend over 10 m, and only 98 N (22 lb) is needed  Something we can actually provide  Excludes frictional forces/losses Example: Ramp

The energy that an object has due to its amount of stretch or compression. The amount of stretch or compression is from its natural equilibrium position. Unit: N/mm 2 = Nm = J (Joule) Elastic Potential Energy

An archer does work in pulling back the bow, this gives the arrow Potential Energy. When the archer releases the arrow, the Potential Energy which was stored is then released into Kinetic Energy. Elastic Potential Energy

When you pull on (stretch) a spring, it pulls back (top picture) When you push on (compress) a spring, it pushes back (bottom) Thus springs present a restoring force:   x is the displacement (in meters)  k is the “spring constant” in Newtons per meter (N/m)  the negative sign means opposite to the direction of displacement Elastic Potential Energy

Do work on a spring to compress it or expand it from equilibrium. Hooke’s law Work = Potential Energy – therefore the spring now has stored potential energy due to how much the spring has changed in length ( Δ x). Elastic Potential Energy

Person does work W = F s Δ x in pulling the box and stretching the spring. This gives the box Elastic Potential Energy. Therefore: W =  E p F  s=1/2k  x 2 Elastic Potential Energy

The amount of work or potential energy can be determined from a graph of Force vs. stretch of a spring by taking the area under the graph. Since F = kx for a spring it shows that E p = ½ k  x 2. Elastic Potential Energy

You are 1.80 m tall. A 0.1 kg apple, which is hanging 1 m above your head, drops on you. How much potential energy does it loose? 0 J 0.49 J 0.98 J 4.9 J Gravitational Potential Energy

In a hydroelectric power plant one ton of water is passing through the turbines per second. The water is falling 100 meters before hitting the turbines. 1 ton = 907 kg = 2000 lbs Assuming 100% efficiency, how much electrical power can the turbines generate? Examples

A 30 cm long crank attached to a winch, a simple machine that lifts a 200 kg load. The crank turns through 400 complete revolutions by the application of a 15 N force applied perpendicular to the crank arm. How high does the winch lift the load? examples

Batman uses a spring loaded catapult device to shoot his bat rope up and over the side of the building so he can use his special boots to scale the building. The device has a spring constant of 7500 N/m and it compresses 40 cm. If the mass of the end is 3 kg, how high of a building can Batman scale? examples