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The legislation of conservation of energy states that power cannot be developed or destroyed. In other words, the complete energy that a system remains constant. This is critical concept come remember when managing energy problems. The two simple forms of energy that we will emphasis on room kinetic energy and also potential energy.

Kinetic Energy

Kinetic energy is power that comes from motion. In various other words, objects that space moving have something that is described as kinetic energy. Because kinetic power is based upon motion, the is always a confident value. If that is no in motion, the kinetic energy of the object is zero. Kinetic energy can never be a an adverse value. Kinetic power can be quantified together one fifty percent of the mass time the velocity squared (KE = 1/2*m*v²). In SI units, the mass must be in kilograms (kg), and the velocity in meters per second (m/s). In English units, the mass need to be either lb mass (lbm) or slug, and the velocity in feet per second (ft/sec).

Potential Energy

Potential energy is just like it sounds, it is energy that is related to an object’s potential. Potential energy can it is in quantified as mass times gravity times elevation (PE=m*g*h). The unit because that mass need to be either kilogram or lb mass relying on the unit system. Heaviness is a constant, 9.81 m/s² in SI units or 32.2 ft/sec² in English units. Gravity is one acceleration, it deserve to be described as meter or feet per 2nd per 2nd or the adjust in velocity per second. Lastly, the height, has actually units of meter in SI units and also feet in English units. That is crucial to note that height is thought about a relative quantity. In various other words, once looking at potential energy, the an initial step is to develop a datum or origin. Meaning, one elevation where the height is zero needs to it is in defined. Because that example, the floor deserve to be characterized as a elevation of zero. However, the zero point (datum) walk not have to be the floor, it deserve to be any point, but it need to not be readjusted once it is defined. It is likewise important to keep in mind that potential power can be positive, zero or negative. For example, if the datum is identified as the top of a table, and the object is on the floor, the object has a negative potential energy due to the fact that the height below the top of the table.

Now the the kinetic energy and potential power have to be defined, we deserve to now use the law of preservation of Energy. In other words, the kinetic power plus the potential energy equals a consistent (KE+PE=Constant).

Let’s imagine a basic energy problem. There is things that travels from one point to another. We will call the first point the starting point (1), and also the 2nd point the ending point (2). Without considering noþeles else we can collection up the basic equation as KE1+PE1=KE2+PE2. Let’s leveling this also more; let’s say the object starts at rest (KE1=0) and also let’s speak we define the datum at the ending point (PE2=0). Currently we deserve to say the PE1=KE2. The power has literally to be converted native potential energy to kinetic energy. Note that the total energy at point 1 is equal to the power at allude 2, the energy has adjusted forms, however was not produced or destroyed.

It is also great to recognize that energy is taken into consideration path independent. In other words, it does not matter what course the object took to acquire from point 1 to allude 2, the power at point 1 and allude 2 did not change. The only thing that matters is the distinction in height of the 2 points; as lengthy as the elevation does not adjust from scenario to scenario, the solution does not change.

Kinetic and also Potential power Examples

Imagine a round rolling across the floor from one allude to another.

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Let’s say the ball has a fixed of 3 kg and is travel at 2 m/s

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At point 1:the kinetic energy = 1/2mv12 = 1/2(3kg)(2m/s)2=6 kg*m2/s2 = 6 N*m = 6 Jwhere m = mass in kilogramsv = velocity in m/sm = unit the length, meter = unit that time, secondN = unit that force, Newton1 N = 1 kg*m/s2J = unit of energy, Joule1 J = 1 N*m

Also, the potential power = mgh1 = 0, due to the fact that h = 0g = acceleration as result of gravity = 9.8m/s2h1 = elevation relative to datum (origin), in meters

At suggest 1 the full energy = KE1 + PE1 = 6 + 0

= 6 Joules

Note at allude 2:

PE2 also = 0, because of this KE2 = 6PE2 = 0 because h2 = 0 since floor is level.If KE2 = KE1 and also mass does no change,

v2 = v1 = 2m/s

Another example

Now let’s say h1≠h2, let’s to speak h2 = -2m

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h2 = -2m method that suggest 2 is 2 meter below suggest 1.A, B, and C represent three feasible paths. Note: the course taken has actually no affect on the solution.

Recall the KE = 6 J, PE = 0 JSince full energy continues to be constant

KE1 + PE1 = KE2 + PE26 + 0 = KE2 + PE2We can uncover PE2 because h2 = -2mPE2 = mgh2 = (3kg)(9.8m/s)(-2m) = -58.8J

Now 6 + 0 = KE2 – 58.8Now solve for KE26 + 58.8 = KE2KE2 = 64.8 J

To discover v2KE2 = 1/2mv22 = 1/2(3kg)(v2)2 = 64.8v22 = 2/3(64.8) = 43.2v2 = 6.57 m/sAn boost of 4.57 m/s

Other varieties of Energy

Energy is no only restricted to kinetic and potential energy. There are countless different forms of energy. However, in basic Physics, the other creates are ignored in order to simplify the subject of energy equations. The other develops of energy are usually introduced at the college level.

For example, work introduced to a system deserve to and influence the complete energy of the system. For example, imagine a piece of furniture in your ago yard. The is sit there and also not moving. Since it is not moving, it does no kinetic energy. Also, because it is top top the ground, it cannot go any kind of lower. In this case, both the potential and also kinetic energy are zero. Currently what wake up if who comes and also picks up the couch. The potential power of that couch has changed, but it did no come indigenous the kinetic energy. So whereby does that power come from? to be it created? Did we violate the law of conservation of Energy? The price is no, us did no violate any type of laws the Physics. Originally, the couch is taken into consideration as one isolated system in our example. The human is an exterior entity the introduced energy into that device by choose up the couch. In Physics terms, the human did work on the system. Occupational is thought about as a form of energy. Work can be quantified a pressure times a distance.

However, the is not that simple. The force and also distance should be pointing in the exact same direction. Because that example, a weight is a force. For example, work have the right to be done by gravity. Actually work-related done by gravity is another means to define potential energy. Weight is mass time gravity. Gravity always points down, therefore the force points under as well. For gravity to perform work, an item must either rise or fall. In this case, no work is being done if things moves next to side. This concept is much better understood by knowledge vectors.

To assist clarify a vector, we will compare velocity to speed. Rate is a magnitude, for example 60 miles per hour. Note that rate does not define a direction. Velocity is a vector, an interpretation it has a magnitude and direction. Because that example, a velocity can be 60 miles every hour in the y-direction. Vectors are best defined in projectile problems also referred to as kinematics equations.

Another instance where energy can not remain constant is in a collision problem. Let’s speak a human holds an apple at shoulder height. At this point, the apple has potential energy however no kinetic energy. Then the human releases the apple permitting it to start falling. As it is falling, the energy is gift converted native potential power to kinetic energy. Just prior to it strikes the ground, almost every one of the potential energy has to be converted to kinetic energy. But what happens as soon as it actually hits the ground? as soon as the apple hit the ground, the is actually colliding through the ground, and that kinetic power gets took in by the ground during the collision.

During a collision, momentum is conserved. Depending on the coefficient the restitution, the two objects associated in a collision in reality distribute the minute before and after the collision based upon their material properties. For example, imagine a human is holding 2 objects in your hands. In one hand, the human is hold a basketball. In the other hand, a person is stop a bag filled with sand. If the person drops both objects onto a concrete floor, the basketball will bounce, yet the bag that sand will simply plop on the ground and also lay there. During the collision, the basketball retains many of its inert while the bag of sand gives it every up. Over there is a factor why this happens; the coefficient the restitution between the concrete and the basketball is various from the coefficient that restitution between the concrete and the bag the sand.

An example Using Work

Now, let’s look in ~ the original instance again, except a pressure will be applied from allude 1 to suggest 2, prefer someone bound a string come the ball.

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Let’s speak the street from point 1 to point 2 is 20 meters and also the force is 7 Newtons.*Note the angle between the force and path of take trip is 35°.Also remind KE1 = 6 J, PE1 = 0

Again, since flat, PE1 = PE2 = 0Very important: complete energy is not continuous because the the applied force. This applied force introduce a brand-new energy v work.

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wherew = work, in JoulesF = used force, in Newtonsd = street from suggest 1 to allude 2, in meters· = dot product-> = defines values together vectors

Therefore:

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where Θ = angle between force and path.

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Finally W1-2 = <7(cos(35°))N>(20m) = 114.68J

The new equationKE1 + PE1 + W1-2 = KE2 + PE26 + 0 + 114.68 = KE2 + 0

120.68 J = KE2

Lastly, to uncover v2KE2 = 1/2mv22120.68 = 1/2(3kg)(v2)280.45 = v22v2 = 8.97 m/sAn increase of 6.97 m/s early to applied force throughout 20 m from allude 1 to point 2.