Energy is the capacity to apply any force into the state of motion of any object. Work is the mechanical energy defined as: W = F∆ x.
Te unit for the work is the “joules” (J) J = (N.m)
1000 J = 1 N (1000 m)
= 1000 N (1m)
The principles of conservation are the most important statements in science: They assert that some quantity is always conserved,and they are four accepted principles of conservation:
• Momentum (movement)
• Angular momentum
1. They are very useful to predict results when the force is unknown or impossible to calculate.
2. These principles describe the intimate connection between energy and matter.
3. They are very useful to define the fundamental forces.
4. No exception is known forany of the four principles.
Work is the manifestation of energy that is designed to do a positive job. Its definition is: “the amount of energy necessary to move something; because work is a scalar quantity, we have work in any direction.”
Mathematically we have W= F∆ x where
“F” is the force needed to perform the motion but in the opposite point of view I the force that is against the motion.This means that positive work is energy gain and negative work is energy loss.
It’s important to note that “F” must be in the same direction that the displacement for example.
Calculate the work done by gravity of the tension of a cable if it is connected to an elevator of 900 kg descents 400m
W = Fy∆y
Wg = -Wt
Wg = mg400Wg = 900(-9.81)(400)
Wg = -3,531,600J
Wg = 3,531,600J
Note: If the elevator goes upwards the quantities are the same but with inverted symbols making gravity gain energy as the tension loses it.
Calculate the work done horizontally by a force equal to120N along a distance of 70m. Watch the diagram
W = Fx∆x
Fx = FcosƟ
Fx = 120 (cos20°)
V = 112.76 (70)
V = 789341 J
If in thelast problem the box is also displaced vertically calculate the work done:
W = Ft∆y
Fy = 120sin20° - 30(9.81)
Fy = -253.26N
W = 253.26(10)
W = -2532.6
An object moving over a slope has a funny result because the work is going to depend only on the height (without friction)
y = r sinƟ
W = F∆r
W = mg sinƟ
W = -mg y
W = -mg h
Calculate the work done by a force (F=150N) thatpulls a box horizontally through 100m. Consider that the friction coefficient is equal to ϻ= 0.2
Ft= 150- 39.24
Calculate the force done horizontally for the last problem if the pulling force has an angle of 10°
Fx = 147.72N
W = 14772N
Fty = mg- FsinƟ
Fty = 20(9.81) – 150 sin10°
Fty = 169.95
This is the normal force because finally this is the weight over the surface
Ff = 0.2(169.95)
Ff = 33.99N
Calculation of the net force
Mechanical energy is a very important quantity because it is conserved. Then, for mechanical systems it is a uniquecharacteristic.
In mechanics there are considered only two energies:
-Kinetic: Due by velocity of the object.
-Potential: Due by the position of the object.
In some way, work is the way the kinetic and potential energies are related.
Therefore the mechanical energy is the trade between velocity and position. Mathematically this means that both energies are inversely proportional.
∆U = -∆KFinally the mechanical energy is: E = U+K
The change of the mechanical energy is: ∆E = ∆U+∆K
And by definition: ∆U = -W
∆K = W
The equation for the mechanical energy (E) is the constant of the system and describes the capacity of work (equations of ∆U and ∆K).
For all systems, kinetic energy is always the same.
K = ½ mv2