POTENTIAL ENERGY DIAGRAM
In physics the terms of mechanical energy usually refers to Potential energy (U) and Kinetic Energy (K). In the absence of non-conservative, or dissipative forces, these energies obey the law of conservation of energy, or ΔU + ΔK = 0. That is, when a system is only acting under the influence of conservative forces its total energy content never changes, the energy just converts between forms.

At any point in the cycle, the total energy is constant, U + K = Umax = Kmax. Remember our two relationships involving work

The work done by a conservative force decreases an object's potential energy while it is increasing its kinetic energy

Defining the initial potential energy Uo = 0, gives us

Using the calculus, we see that our desired expression of the instantaneous restoring force being equal to the negative derivative of the potential energy function.
See also this Potential Energy diagram.

The curve represents the value of potential energy U as a function of the particle's coordinate x. The horizontal line above the curve represents the constant value of the total energy of the particle E. The total energy E is the sum of kinetic ( K) and potential ( U) energies of the particle. ( U <= E)

In the slope of zero, F=0, is said to be the state of equilibrium. This terms means the net force act on the object is zero and initially There are two kinds of equilibrium: * Stable equilibrium means that small deviations from the equilibrium point create a net force that accelerates the particle back toward the equilibrium point (think of a ball rolling between two hills). * Unstable equilibrium means that small deviations from the equilibrium point create a net force that accelerates the particle further away from the equilibrium point (think of a ball on top of a hill) * Neutral equilibrium occur when the force is zero for some distance. If it is displaced to one side the force is still zero

...Experiment 4: Work, Power and Energy
Maria Isabela Mendoza, Carmela Miranda, Arianne Nagrampa, and Vivien Oreo
Department of Biological Sciences
University of Santo Tomas
España, Manila, Philippines
Abstract
The experiment performed involved work, power and energy. On the first activity, the time it took for each member to go up and down the stairs was recorded. Afterwards, the work and power done were computed. The most powerful member in the group was student number 2 with power outputs of 239.4 W and 266.0 W when going up and down respectively. On the second activity, the graphs of the potentialenergy vs. time, kinetic energy vs. time, and mechanical energy vs. time of a ball thrown vertically were all predicted. Finally, the ball was tossed on the motion detector and the graphs of potential, kinetic, and mechanical energies vs. time were all produced using the Logger Pro.
Introduction
Work is said to be an act of exerting force. Whatever it is that can make us tired is considered work. The similarity between the conventional meaning and the mathematical meaning of Work is movement. Mathematically, work is defined as W = Fd, where F is the magnitude of the force applied and d is the displacement of the object where force was applied on. Work can be positive or negative; this is due to the positive or negative nature of F and d. When work is...

...PotentialEnergy
• Definition and Mathematics of Work
• Calculating the Amount of Work Done by Forces
• PotentialEnergy
• Kinetic Energy
• 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 potentialenergy. 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 potentialenergy. Potentialenergy is the stored energy of position possessed by an object.
Gravitational PotentialEnergy
The two examples above illustrate the two forms of potentialenergy to be discussed in this course - gravitational potentialenergy and elastic potentialenergy. Gravitational potential...

...the transfer of energy; work is done on an object when an applied force moves it through a distance. The link between work and energy is work done equals energy transferred. The units for the two are also the same (joules). E.g. 500J of work = 500J of kinetic energy.
Work is calculated with the formula: work done=force x distance moved
For example, if a force of 10 newton (F = 10 N) acts along point that travels 2 meters (d = 2 m), then it does the work W = (10 N)(2 m) = 20 N m = 20 J. This is approximately the work done lifting a 1 kg weight from ground to over a person's head against the force of gravity. Notice that the work is doubled either by lifting twice the weight the same distance or by lifting the same weight twice the distance.
Examples:
Force is measured in newton’s (N)
Distance is measured in meters (M)
Work done is measured in joules (J)
Examples of work done:
How much work is done by a person who uses a force of 27.5N to move a grocery buggy 12.3m?
W = F x d = (27.5N) (12.3m) = ?
Equation
W = 338.25J
Answer
55, 000J of work is done to move a rock 25m. How much force was applied?
F = W = 55,000J = ?
d 25m
Equation
F = 2200J
Answer
You and 3 friends apply a combined force of 489.5N to push a piano. The amount of work done is 1762.2J. What distance did the piano move?
Equation
d= W = 1762.2J =
F 489.5N
Answer
d = 3.6m...

...WORK and ENERGY
Work done by a constant force
1- The drawing shows a plane diving toward the ground and then climbing back upward. During each of these motions, the lift force acts perpendicular to the displacement , which has the same magnitude, 1.7 × 103 m, in each case. The engines of the plane exert a thrust , which points in the direction of the displacement and has the same magnitude during the dive and the climb. The weight of the plane has a magnitude of 5.9 × 104 N. In both motions, net work is performed due to the combined action of the forces , and .
a. Is more net work done during the dive or the climb? Explain.
b. Find the difference between the net work done during the dive and the climb.
Answer:
a. More net work is done during the dive.
b. 6.8 × 107 J
2- Find the work done by a force through a displacement of 3m in the positive x direction
Work-Energy theorem and kinetic energy
3- The mass of the space probe is 474-kg and its initial velocity is 275 m/s. If the 56.0-mN force acts on the probe through a displacement of 2.42×109m, what is its final speed?
Answer:
4- Example 2: Skier
Gravitational PotentialEnergy, Conservative versus Nonconservative Forces
5- The gymnast leaves the trampoline at an initial height of 1.20 m and reaches a maximum height of 4.80 m before falling back down. What was the initial speed of the...

...displacement, the work done is negative.
Summary
LearnNext Video
Table of Contents[Show]
The energy of an object is its ability to do work. Energy is the cause and work is its effect. Therefore both work and energy have the same units, which is joule (J) in the SI system and erg in the CGS system. Energy is also a scalar quantity. Energy exists in many forms.
Examples
Mechanical energy which is either in the form of potentialenergy or kinetic energy or a combination of the both, electrical energy, light energy, thermal energy, nuclear energy and sound energy etc.
Potentialenergy is the energy possessed by a body by virtue of its position or state. It is further classified into gravitational potentialenergy (GPE) and elastic potentialenergy (EPE). GPE is by virtue of height of a body from a reference level, it can be expressed as GPE = mgh (m being mass of the body, g is acceleration due to gravity and h the height of the body from the reference level) whereas, EPE of a body is by virtue of its stretched state. Kinetic energy (KE) is the energy possessed by a body by virtue of its motion and is given by, K.E = ½mv2.
The law of conservation of...

...the gravitational force is greater than that done by the tension force.
C) The work done by the tension force is zero joules.
D) The work done by the gravitational force is zero joules.
E) The net work done by the two forces is zero joules.
3. A helicopter (m = 3250 kg) is cruising at a speed of 56.9 m/s at an altitude of 185 m. What is the total mechanical energy of the helicopter?
A) 3.91 × 107 J D) 6.91 × 107 J
B) 5.26 × 107 J E) 1.12 × 107 J
C) 2.27 × 108 J
4. The power needed to accelerate a projectile from rest to its launch speed v in a time t is 50 W. How much power is needed to accelerate the same projectile from rest to a launch speed of 3v in a time of 3t ? Assume no change in height before launch. |
A. 50 W B. 100 W C. 150 W D. 300 W E. 400 W |
The next 2 questions refer to the diagram below:
A string is tied to a doorknob 0.72 m from the hinge as illustrated in the figure. At the instant shown, the force applied to the string (F) is 5.0 N. This is a top-down (bird’s eye) view.
5. What is the line of action in this diagram?
A) The dashed line opposite the 57° angle
B) The solid line opposite the 33° angle.
C) The top of the door
D) The circumference of the circle made by swinging the door open.
6. What is the magnitude of the torque on the door?
A) 3.60 N m D) 4.19 N m
B) 3.02 N m E) 0.60 N m
C) 1.96 N m...

...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 kinetic energy through the experiment conducted.
Back ground:
Kineticenergy is said to be the energy of motion. Kinetic energy 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.
Potentialenergy is the energy associated with the forces that depend on the position of the object. However, there are specific types of potentialenergy and in this lab we will consider gravitational potentialenergy. Gravitational potentialenergy 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...

...Tutorial – Work, Energy
(Assume the acceleration due to gravity, g = 9.81 m/s2 )
1. Calculate the work done when a force of 40 N pushes an object a distance of
500 m in the same direction as the force.
2. Calculate the work done when a mass is lifted vertically by a crane to a height of 5 m, the force required to lift the mass being 98 N.
3. A spring, initially in a relaxed state, is extended by 100 mm. Determine the work done by using a workdiagram if the spring requires a force of 0.6 N per mm of stretch.
4. A spring requires a force of 10 N to cause an extension of 50 mm. Determine the work done in extending the spring (a) from zero to 30 mm, and (b) from 30 mm to 50 mm.
5. Calculate the work done when a mass of 20 kg is lifted vertically through a distance of 5.0 m. Assume that the acceleration due to gravity is 9.81 m/s2 .
6. Water is pumped vertically upwards through a distance of 50.0 m and the work done is 294.3 kJ. Determine the number of litres of water pumped. (1 litre of water has a mass of 1kg).
7. Determine the work done when a force of 50 N pushes an object 1.5 km in the same direction as the force.
8. Calculate the work done when a mass of weight 200 N is lifted vertically by a crane to a height of 100m.
9. A spring requires a force of 50 N to cause an extension of 100 mm. Determine the work done in extending the spring (a) from 0 to 100 mm, and (b) from 40 mm to 100 mm.
10. A...

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