Energy: Work

Page 5

This text is meant to accompany class discussions. It is not everything there is to know about energy. It is meant as a prep for class. More detailed notes and examples are given in the class notes, presentations, and demonstrations (click here.)

Changing the Total Energy due to Conservative Forces

In order to change the kinetic energy of an object, work must be done on the object. This is called the work-kinetic energy theorem. When you identify the energy due to gravity, springs and any other energies associated with conservative forces, you are accounting for the work due to these forces. It just wasn't called work. We called it potential energy instead. When we talk about all of the energy as being conserved we are talking about all of the energy due to conservative forces. The energy associated with non-conservative forces use the generic equation of Fd or it can be found from a graph.

If the world only contained conservative forces then we always could use

But the real world is more interesting than that and so the second law of thermodynamics comes into play. This just expands the first law to contain the energy moved about by non conservative forces. The conservation of energy can be rewritten as:

This basically states that you begin with a certain amount of energy and either add to it with "positive" work or you remove energy with "negative" work. What you are left with is the final amount of energy. Forces that travel in the same direction as the displacement add work. Forces that point in the opposite direction of the displacement remove work. Below are four examples to see how this works.

Example 10

Question
Solution on Paper
Video Solution

An 88.0 kg skydiver drops out of a plane and free falls for 404 m before opening his parachute. As he falls he feels an average resistive force of 555 N. How fast is he moving when his parachute opens up? Use energy methods to solve

Content 2

This video can be viewed on YouTube at http://goo.gl/tYcngS

Example 11

Question
Solution on Paper
Video Solution

A 1001 kg car is traveling at 22.00 m/s when it applies the brakes for 10.0 m and slows down to 14.0 m/s. How much force is applied by the brakes?

This video can be viewed on YouTube at http://goo.gl/oMv8Rq

Example 12

Question
Paper Solution
Video Solution

Yves Rossy has invented jet powered wings that strap onto his back so he can fly
On one flight he is traveling at 40.0 m/s. His jet engines generate 4000.0 N of thrust for 30.0 m as he climbs upwards. At this point he begins to glide to an additional height of 20.0 m. During the entire 50.0 m climb he experienced the work due to drag of 12500J. If Yves and his jet wings have a combined mass of 165 kg, then how fast is he traveling at this highest point?

This video can be viewed on YouTube at http://youtu.be/rjk9PJpnafU

Example 13

Question
Solution on Paper
Video Solution

A 75 kg human cannon ball is shot by a force of 9500 N across a distance of 7.0 m. He starts from rest at the bottom of the barrel. An average resistive force of 303 N acts against him across the first 10.0 m. During this time he is shot up 9.00m above his starting point. How fast is he traveling at this point?

Watch this video on YouTube at http://goo.gl/mtJ6Yu

Work from a graph of force and displacement

Finding the work from a graph is still the change in kinetic energy. Work is found a different way. (In calculus class this is called integration.)

The outline of this graph's "curve" is the shape of a rectangle. The area, A, of a rectangle is calculated from height times width, "A=hw." From this graph, the height is the force and the width is displacement. Instead of "A=hw," "A=Fd." Work is Fd. This means that the area under a "curve" from a graph of force versus displacement is the work. For this example, the work is (300 N)(30 m)=9000 J. This idea of "area" means the method for calculating the area is used. It does not mean that the answer is in squared distance units like m².

Note: The shaded area stops at the axis. This is beacuse the "height" is measure from zero to a given force. It stops at the axis because zero is the axis.

This time the height, or force axis, is negative. This is because the car's brakes are applying a force opposite the displacement's direction to slow it down. Work is being done "on" the car by the brakes. The work is (–200N)(45m) = –9000 J. Work is removing 9000 J of kinetic energy from the car.

Note: When the curve is under the x-axis, the area is defined as from the curve up to the axis. Like the example above, the height is measued from zero to a given force. The x-axis is zero. The area's height must go from the axis to the given force.

The space between the curve and the axis on a graph of force versus displacement represents the work done on or by the body. The size of the space is determined by calculating the area as shown above. This means a force does not have to be constant as in the formula W=Fd. Now work can vary over time and distance the amount of energy transfered trough work can be calculated.

Example 14

picture to go along with the example problem

A, 202 kg, motorcycle stuntman is completing a jump. He lands on the ramp as shown. He only applies the brakes for 12 of the 20 meter landing ramp before passing out. The graph of his braking force is shown above. What is his velocity at the bottom of the ramp? (The mass is the combined mass of the stuntman and the motorcycle.)

Solution

This video is here, http://youtu.be/x2dMbL_saDE

by Tony Wayne ...(If you are a teacher, please feel free to use these resources in your teaching.)

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