KINETIC ENERGY
Objects have energy because of their motion; this energy is called kinetic energy. Kinetic energy of the objects having mass m and velocity v can be calculated with the formula given below; K=1/2mv²

Kinetic energy is a scalar quantity; it does not have a direction. Unlike velocity, acceleration, force, and momentum, the kinetic energy of an object is completely described by magnitude alone. Like work and potential energy, the standard metric unit of measurement for kinetic energy is the Joule. As might be implied by the above equation, 1 Joule is equivalent to 1 kg(m/s) 2.

Examples
1. Determine the kinetic energy of a 625-kg roller coaster car that is moving with a speed of 18.3 m/s. Answer:
KE = 0.5mv2
KE = (0.5)(625 kg)(18.3 m/s)2
KE = 1.05 x105 Joules
2. If the roller coaster car in the above problem were moving with twice the speed, then what would be its new kinetic energy? Answer:
KE = 0.5mv2
KE = 0.5(625 kg)(36.6 m/s)2
KE = 4.19 x 105 Joules

Work-Energy Theorem

Relationship between KE and W: The word done on an object by a net force equals the change in kinetic energy of the object:

Wnet = Kf - Ki
This relationship is called the work energy theorem
W = Fdcosø
When the energy of the body increases, work is positive.

Examples:

1. A boy pushes a 5.00 kg cart in a circle, starting at 0.500 m/s and accelerating to 3.00 m/s. How much work was done on the cart? Answer:

W= Kf- Ki = (0.5)m(vfinal)2 - (0.5)m(vinitial)2
W = (0.5)(5.00)(3.00)2 - (0.5)(5.00)(0.500)2
W = 21.9 J

2. A 1000.0 kg truck accelerates from 20.0 m/s to 25.0 m/s over a distance of 300.0 m. What is the average net force on the truck?

Answer:

W = Kf- Ki = (0.5)m(vfinal)2 - (0.5)m(vinitial)2
W = (0.5)(1000.0kg)(25.0m/s)2 – (0.5)( 1000.0kg)(20.0m/s)2...

...Example problems involving collisions 1) On a horizontal frictionless surface a puck of mass m initially at speed u collides head-on (without rotation) with a stationary puck of mass M. Find the velocities of both puck after the collision if: i) the collision is fully elastic ii) the collision if fully inelastic. i) momentum: kineticenergy: mu = mv+MV (+ve in direction of initial u) 1 /2 m u2 = 1/2 m v2 + 1/2 M V2
2 eqns in 2 unknowns: V = (u - v) m/M substitute in K eqn: u2 = v2 + (M/m) V2 = v2 + (M/m) (u - v)2 (m/M)2 = v2 + (u - v)2 (m/M) let ρ = (m/M) ⇒ v2 (1 + ρ) - 2ρ u v + u2 (ρ - 1) = 0 quadratic eqn: b2-4ac = 4ρ2 u2 - 4 (1 + ρ) (ρ - 1) u2 = 4ρ2 u2 - 4 (ρ2 - 1) u2 = 4u2
v = [2ρ u ± (4 u2)1/2]/{2 (1 + ρ)} = [2ρ u ± 2 u]/{2 (1 + ρ)} = u (ρ ± 1)/(1 + ρ) + ⇒ v = u , and V = 0 (no collision occurs!) - ⇒ v = u (ρ - 1)/(1 + ρ) , and V = ρ (u - v) = 2ρ2 u/(1 + ρ) e.g. ρ = 1 ⇒ v = 0, V = u . as ρ → 0 ⇒ v → - u , V → 0
ii) momentum: let ρ = (m/M) kineticenergy: ratio: then
m u = (m + M) v v = u 1/(1 + 1/ρ)
1
⇒
v = u m/(m + M)
before: K1 =
/2 m u2 ,
after:
K2 =
1
/2 (m + M) v2
K2/K1 = (1 + 1/ρ) v2/u2 = 1/(1 + 1/ρ) ⇒ v = u/2 , K2/K1 = 1/2 . as ρ → 0 ⇒ v → 0 , K2/K1 → 0
e.g. ρ = 1
2) A point mass m swings under gravity from a fixed pivot on a massless cord through an angle θ to collide with a stationary block of mass M. Assuming a fully elastic collision find the distance the...

...Experiment 7: Work, Power and Energy
Laboratory Report
John Karl Macrohon
Department of Math and Physics
College of Science, University of Santo Tomas
España, Manila Philippines
Abstract
The experiment is subdivided into two activities: Power and Energy of a Tossed Ball (Physics with Computers). The work done by gravity on each member when going up and downstairs of the second and third floors of the Main Building and the power output of each member of the group in each case was computed in activity 1 (Power), while in activity 2 (Energy of a Tossed Ball),a ball was thrown vertically up from a height of 50.0cm from the motion detector to compare the graphs the it collected from the predicted graphs of the group . The results obtained from the experiment clearly demonstrated conservation of mechanical energy, the change in kinetic and potential energies as a ball moves in free fall and the power output when going up and downstairs.
1. Introduction
Long ago, people used to trade by only exchanging products when the concept of 'money' was yet to be introduced. Now we do know the concept of money. But if we were to define money, it would not be an easy task. But we do know it can manifest itself in many forms. Money is a concept imagined by man and it plays a very big role in the present world.
The concepts of work, energy and power play the same role in...

... Power and Energy
Arlie Bamiano, Jealine Marie Bernabe, Petrenne Clarice Caimbon, Jhia Caso
Department of Biological Sciences
College of Science, University of Santo Tomas
España, Manila Philippines
Abstract
The experiment deals primarily with computing the work done by gravity on each member in two scenarios (going up and down the stairs of the second floor and the third floor of the Main Building) wherein weight was also considered and following this, the power output of each member was also computed. Using the Logger Pro, the kinetic and potential energies of a ball in free fall were graphed and compared. At the end of the experiment, it was said that member #2 was the most “powerful” among the group since she had the highest power output both in going up and going down the stairs and in the second activity, the results were obtained and the predictions made were correct.
1. Introduction
Work, power and energy are three words that are commonly used in a man’s
activity involving a force and movement in the direction of the force. Energy is the ability to do work. Power is the rate of doing work or the rate of using energy.
This experiment was designed to demonstrate the conservation of mechanical energy, to measure change in kinetic and potential energies as a ball moves in free fall and to determine power...

...conservation of mechanical energy
Section: 8
Name: Ahmed Atari
University ID: 201103848
Instructor: Ahmed Zainelabdin
Submission date: May 1, 2014
Objective: the purpose of this lab is to investigate the law of conservation of energy. This can be achieved by measuring both potential and kineticenergy through the experiment conducted.
Back ground:Kineticenergy is said to be the energy of motion. Kineticenergy can be defined through this equation:
KE=12mv2 (equation 1)
Where m is the mass of the object in motion, and v is the velocity of the moving object.
Potential energy is the energy associated with the forces that depend on the position of the object. However, there are specific types of potential energy and in this lab we will consider gravitational potential energy. Gravitational potential energy is the energy possessed by the objected due to earth's gravity. This can be specifically defined by the equation:
PEgrav=mgy (equation 2)
Where m is the mass of the object, g is the acceleration due to gravity and y is the height of the object.
With these energies defined, total energy of the system is the sum of its kinetic...

...the point of action of the force and the pivot point). |
Figure 2 Tangential and radial components of force F |
There may be more than one force acting on an object, and each of these forces may act on different point on the object. Then, each force will cause a torque. The net torque is the sum of the individual torques.
Rotational Equilibrium is analogous to translational equilibrium, where the sum of the forces are equal to zero. In rotational equilibrium, the sum of the torques is equal to zero. In other words, there is no net torque on the object.
* Note that the SI units of torque is a Newton-metre, which is also a way of expressing a Joule (the unit for energy). However, torque is not energy. So, to avoid confusion, we will use the units N.m, and not J. The distinction arises because energy is a scalar quanitity, whereas torque is a vector.
Torque
If a net force is applied to an object’s center of mass, it will not cause the object to rotate. However, if a net force is applied to a point other than the center of mass, it will affect the object’s rotation. Physicists call the effect of force on rotational motion torque.
Torque Defined
Consider a lever mounted on a wall so that the lever is free to move around an axis of rotation O. In order to lift the lever, you apply a force F to point P, which is a distance r away from the axis of rotation, as illustrated below.
Suppose the lever is very heavy and...

...Part B
Now, suppose that Zak's younger cousin, Greta, sees him sliding and takes off her shoes so that she can slide as well (assume her socks have the same coefficient of kinetic friction as Zak's). Instead of getting a running start, she asks Zak to give her a push. So, Zak pushes her with a force of 125 \rm N over a distance of 1.00 \rm m. If her mass is 20.0 \rm kg, what distance d_2 does she slide after Zak's push ends?
Remember that the frictional force acts on Greta during Zak's push and while she is sliding after the push.
F= Fp-Fr
E= F*Lp= (Fp-Fr)*Lp= Fr*Lr
Lr= Lp*((Fp/Fr)-1)
Lr= 1*((125/(20*9.8*0.25))-1)= 1.6 m
Mark pushes his broken car 150 m down the block to his friend’s house. He has
to exert a 110 N horizontal force to push the car at a constant speed. How much
thermal energy is created in the tires and road during this short trip?
thermal energy is created in the tires and road
= 110 * 150
=16500 J
A 30 kg child slides down a playground slide at a constant speed. The slide has a height of 4.0 m and is 7.0 m long.
Using energy considerations, find the magnitude of the kinetic friction force acting on the child.
The friction force F is parallel to the slope and is constant in magnitude, so its work is
W = - F d
with d = length of the slide.
ΔU = m g Δh
Therefore:
- F d = m g Δh
F = - m g Δh / d = - 30 x 9.8 x (- 4.0) / 7.0 = 168N
A block of weight w = 15.0 N...

...Potential Energy
• Definition and Mathematics of Work
• Calculating the Amount of Work Done by Forces
• Potential Energy
• KineticEnergy
• Mechanical Energy
• Power
An object can store energy as the result of its position. For example, the heavy ball of a demolition machine is storing energy when it is held at an elevated position. This stored energy of position is referred to as potential energy. Similarly, a drawn bow is able to store energy as the result of its position. When assuming its usual position (i.e., when not drawn), there is no energy stored in the bow. Yet when its position is altered from its usual equilibrium position, the bow is able to store energy by virtue of its position. This stored energy of position is referred to as potential energy. Potential energy is the stored energy of position possessed by an object.
Gravitational Potential Energy
The two examples above illustrate the two forms of potential energy to be discussed in this course - gravitational potential energy and elastic potential energy. Gravitational potential energy is the energy stored in an object as the result of its vertical position or height. The...

...system. |
| | It would take less time to reach its bound orbit. |
| | It would orbit the earth at a faster velocity. |
| | | | |
Question 7 | 1.61 points | Save |
| When energy is converted from one form to another, a tiny amount is inevitably lost. | | | | |
| | True |
| False |
| | | | |
Question 8 | 1.61 points | Save |
| There is no gravity in space. | | | | |
| | True |
| False |
| | | | |
Question 9 | 1.61 points | Save |
| The Moon is slowly moving away from the earth. | | | | |
| | True |
| False |
| | | | |
Question 10 | 1.61 points | Save |
| Which of the following statements correctly describes the law of conservation of energy? | | | | |
| | | The total quantity of energy in the universe never changes. |
| | An object always has the same amount of energy. |
| | It is not really possible for an object to gain or lose potential energy, because energy cannot be destroyed. |
| | Energy can change between many different forms, such as potential, kinetic, and thermal, but it is ultimately destroyed. |
| | The fact that you can fuse hydrogen into helium to produce energy means that helium can be turned into hydrogen to produce energy. |
| | | | |
Question 11 | 1.61...