17.0.0: ENERGY
17.0.0: ENERGY:
Energy is the ability to do work. Energy is a scalar quantity.
UNIT OF ENERGY:
The s.I.unit of energy is joule.
OTHER UNITS OF ENERGY:
Energy can also be measured using other units. The units are obtained from the combination of the unit of each quantities that make up the formula the energy.
FORM OF ENERGY:
Energy is classified into two forms:
Substitution: P.E = 0.25kg x 12.3m x 9.8m/s²
Potential Energy = 30.135 Joules
2. An object of mass 10.25kg has 26.3 J of energy at a particular height. Calculate the height. ( g = 9.8 m/s² )
SOLUTION:
Data given in the question:
Mass = 10.25 kg, P.E = 26.3 J, g = 9.8 m/s², h = ?
Formula: P.E = m x h x g
Substitution: 26.3 = 10.25 x h x 9.8. Make h the subject of the formula.
h = 26.3 / ( 10.25 x 9.8 ). ➡ h = 0.26 meters
KINETIC ENERGY K.E:
Kinetic energy is the type of energy that is process by a moving object. The unit of kinetic energy is Joule. The symbol of kinetic energy is K.E. the symbol of Joule is J.
FORMULA FOR CALCULATING KINETIC ENERGY:
Kinetic Energy K.E = ½ x mass x Velocity²
Kinetic Energy = ½ x m x V²
Remember that, Velocity = distance / time
therefore, K. E = ½ x mass x ( distance / time )²
APPLICATION OF FORMULA TO SOLVE PROBLEMS:
EXAMPLES:
1. Calculate the K.E of a car of mass 12.5 kg if the car moves at the speed of 5 m/s.
SOLUTION:
Data given in the question:
Mass = 12.5 kg, speed/ velocity = 5 m/s
Formula: Kinetic. Energy = ½ x m x V²
Substitution: Kinetic Energy = ½ x 12.5 x 5²
Kinetic Energy = 156.25 Joules
2. The Kinetic Energy of a car is 251 J. I the mass of the car is 1.75 kg, calculate the velocity of the car.
SOLUTION:
Data given in the question:
Mass = 1.75 kg, K. E = 251 J
Formula: K.E = ½ x m x V
Substitution: 251 = ½ x 1.75 x V².
Then make velocity subject of the formula. Then,
Velocity² = ( 251 x 2 ) / 1.75. ➡ Velocity ² = 304 / 1.75 = 173.714
Velocity² = 173.714 ➡. Velocity = √ 173.714
Velocity = 13.180 m/s
MORE WORKED EXAMPLES:
CONSERVATION LAW OF MECHANICAL ENERGY:
The conservation law of mechanical energy states that in an isolated system, the total energy of the system not be created nor destroyed, but can only be transformed from one form into another. Of it states that the total energy content of a system remain constant.
EXPLANATION OF CONSERVATION LAW OF MECHANICAL ENERGY:
The conservation law of mechanical energy can be explained using the following:
Let the initial position be point A,
EXERCICES:
More questions coming
17.0.0: ENERGY:
Energy is the ability to do work. Energy is a scalar quantity.
UNIT OF ENERGY:
The s.I.unit of energy is joule.
OTHER UNITS OF ENERGY:
Energy can also be measured using other units. The units are obtained from the combination of the unit of each quantities that make up the formula the energy.
FORM OF ENERGY:
Energy is classified into two forms:
- Potential energy
- Kinetic energy
POTENTIAL ENERGY:
Potential energy is the type of energy possess by any object that is at rest or a stationary object. The unit of potential energy is Joule.
FORMULA FOR CALCULATING POTENTIAL ENERGY:
potential Energy P.E = mass x height x acceleration due to gravity
Potential Energy P.E = m x h x g
APPLICATION OF FORMULA TO SOLVE PROBLEMS:
EXAMPLES:
1. Calculate the potential energy of a mango fruit at the top of a tree 12.3m high if the mass of the mango is 0.25 kg. ( g = 9.8 m/s² )
SOLUTION:
Data given in the question:
Mass = 0.25kg, height = 12.3 m, g = 9.8 m/s²
Formula: P.E = m x h x gSOLUTION:
Data given in the question:
Mass = 0.25kg, height = 12.3 m, g = 9.8 m/s²
Substitution: P.E = 0.25kg x 12.3m x 9.8m/s²
Potential Energy = 30.135 Joules
2. An object of mass 10.25kg has 26.3 J of energy at a particular height. Calculate the height. ( g = 9.8 m/s² )
SOLUTION:
Data given in the question:
Mass = 10.25 kg, P.E = 26.3 J, g = 9.8 m/s², h = ?
Formula: P.E = m x h x g
Substitution: 26.3 = 10.25 x h x 9.8. Make h the subject of the formula.
h = 26.3 / ( 10.25 x 9.8 ). ➡ h = 0.26 meters
KINETIC ENERGY K.E:
Kinetic energy is the type of energy that is process by a moving object. The unit of kinetic energy is Joule. The symbol of kinetic energy is K.E. the symbol of Joule is J.
FORMULA FOR CALCULATING KINETIC ENERGY:
Kinetic Energy K.E = ½ x mass x Velocity²
Kinetic Energy = ½ x m x V²
Remember that, Velocity = distance / time
therefore, K. E = ½ x mass x ( distance / time )²
APPLICATION OF FORMULA TO SOLVE PROBLEMS:
EXAMPLES:
1. Calculate the K.E of a car of mass 12.5 kg if the car moves at the speed of 5 m/s.
SOLUTION:
Data given in the question:
Mass = 12.5 kg, speed/ velocity = 5 m/s
Formula: Kinetic. Energy = ½ x m x V²
Substitution: Kinetic Energy = ½ x 12.5 x 5²
Kinetic Energy = 156.25 Joules
2. The Kinetic Energy of a car is 251 J. I the mass of the car is 1.75 kg, calculate the velocity of the car.
SOLUTION:
Data given in the question:
Mass = 1.75 kg, K. E = 251 J
Formula: K.E = ½ x m x V
Substitution: 251 = ½ x 1.75 x V².
Then make velocity subject of the formula. Then,
Velocity² = ( 251 x 2 ) / 1.75. ➡ Velocity ² = 304 / 1.75 = 173.714
Velocity² = 173.714 ➡. Velocity = √ 173.714
Velocity = 13.180 m/s
MORE WORKED EXAMPLES:
CONSERVATION LAW OF MECHANICAL ENERGY:
The conservation law of mechanical energy states that in an isolated system, the total energy of the system not be created nor destroyed, but can only be transformed from one form into another. Of it states that the total energy content of a system remain constant.
EXPLANATION OF CONSERVATION LAW OF MECHANICAL ENERGY:
The conservation law of mechanical energy can be explained using the following:
- motion of object that is falling freely under the influence of gravity
- motion of object that is undergoing simple harmonic motion
EXPLANATION OF CONSERVATION LAW USING MOTION OF OBJECT THAT IS FALLING UNDER THE INFLUENCE OF GRAVITY
Let the mid point of the line be point B
Let the final position be point C.
EXPLANATION:
Total energy of the object at point A:
From the conservation law of energy,
From the conservation law of energy,
Total energy = kinetic energy + potential energy
Total energy = ½*m*v² + m*g*h
Conditions at point A:
At point A, velocity = 0 m/s because the object is at rest.h
height h = h ( i.e maximum h).
Let us put the conditions into the formula and solve it , therefore,
Total energy = ½*m*(0)² + m*g*h
Total energy = 0 + mgh
Total energy = mgh
Therefore,
total energy of the object at point A = only Potential energy
Total energy of the object at point B:
Total energy = Kinetic energy + Potential energy
Total energy = ½*m*v² + m*g*h
Conditions at point B:
As the object falls from point A , its velocity increases from zero to a particular value, while the height of the object reduces as the object is falling down.
Therefore, V is not equal to zero and h is not equal to zero.
V = v , h = h.
Let us substitute these conditions into the formula for total enery. Therefore,
Total energy = ½ *m*V² + m*g*h
Note that since neither V nor h was zero, non of the energy in the formula become zero.
Therefore,
Total energy of theV )object at point B = potential energy h
kinetic energy
energy of the object at point C:
Total energy= kinetic energy + potential energy
Total energy = ½*m*V² + m*g*h
Conditions at point C:
As the object falls from point B to point C, its velocity continue to increase to maximum while its height reduces to zero as the object hits the ground. Therefore,
V = maximum just before the object hits the ground, ( V = Maximum V )
h = zero when the object hits the ground. ( h = 0 meter )
Put the conditions into the formula and solve.
Total energy= kinetic energy + potential energy
Total energy = ½*m*V² + m*g*h
Total energy = ½*m*(Vmax)² + m*g*(0)
Total energy = ½*m*(Vmax)² + 0
Total energy = ½*m*(Vmax)²
Total energy at point C = only kinetic energy.
From the above explanation of the conservation law of energy, you can see that the total energy of a system remain constant. The energy only change from one form to another as the object moves from one position to another.
At position A, the total energy of the object is only Potential energy. As the object moves downward from position A, its potential energy reduces while kinetic energy started to build up as some of the potential energy changes to kinetic energy. As the object moves downward, it height h reduces while its initial velocity v which was zero started increasing.
At position B, the height h of the object has reduced to half of what it was initially while its velocity which was initially zero has also build up to certain value V. At this point B, the velocity V of the object is not equal to zero and the height of the object at this point is not equal to zero, though it has reduced to half.
When these values of v and h which were not equal to zero where substituted in the formula for total energy of a system, you could see that the object pocess both potential energy and kinetic energy at point B. Some of the potential energy at point A is converted into kinetic energy at point B. Therefore, the object has both potential energy and kinetic energy at position B.
As the object fals futher to the ground,at positon C, just before the object hits the ground, its velocity V build up or increased to maximum value while its height reduced to zero.
When these values of V which is maximum and height h which has reduced to zero were substituted into the formula for total energy, potential energy reduced to zero while kinetic energy increased to maximum.
The object has only kinetic energy at position C because the remaining potential energy at position B were converted to kinetic energy at position C. Therefore the total energy of the object at position C is only kinetic energy.
EXPLANATION OF CONSERVATION LAW USING MOTION OF OBJECT THAT IS UNDERGOING SIMPLE HARMONIC MOTION:
The figure shows the motion of an object that is undergoing simple harmonic motion.
To explain the law of conservation of energy, I am will select three positions along the path of the motion of the object. (I) position A at the maximum height level, (ii) position B at the midway between A and C (iii) position C at the the equilibrium position of the object.
Let us explain the total energy that the object process at each of the three positions thus:
Total energy of the object at point A:
From the conservation law of energy,
Total energy= kinetic energy + potential energy
Total energy = ½*m*V² + m*g*h
Conditions at position B:
kinetic energy
energy of the object at point C:
Total energy= kinetic energy + potential energy
Total energy = ½*m*V² + m*g*h
Conditions at point C:
As the object falls from point B to point C, its velocity continue to increase to maximum while its height reduces to zero as the object hits the ground. Therefore,
V = maximum just before the object hits the ground, ( V = Maximum V )
h = zero when the object hits the ground. ( h = 0 meter )
Put the conditions into the formula and solve.
Total energy= kinetic energy + potential energy
Total energy = ½*m*V² + m*g*h
Total energy = ½*m*(Vmax)² + m*g*(0)
Total energy = ½*m*(Vmax)² + 0
Total energy = ½*m*(Vmax)²
Total energy at point C = only kinetic energy.
From the above explanation of the conservation law of energy, you can see that the total energy of a system remain constant. The energy only change from one form to another as the object moves from one position to another.
At position A, the total energy of the object is only Potential energy. As the object moves downward from position A, its potential energy reduces while kinetic energy started to build up as some of the potential energy changes to kinetic energy. As the object moves downward, it height h reduces while its initial velocity v which was zero started increasing.
At position B, the height h of the object has reduced to half of what it was initially while its velocity which was initially zero has also build up to certain value V. At this point B, the velocity V of the object is not equal to zero and the height of the object at this point is not equal to zero, though it has reduced to half.
When these values of v and h which were not equal to zero where substituted in the formula for total energy of a system, you could see that the object pocess both potential energy and kinetic energy at point B. Some of the potential energy at point A is converted into kinetic energy at point B. Therefore, the object has both potential energy and kinetic energy at position B.
As the object fals futher to the ground,at positon C, just before the object hits the ground, its velocity V build up or increased to maximum value while its height reduced to zero.
When these values of V which is maximum and height h which has reduced to zero were substituted into the formula for total energy, potential energy reduced to zero while kinetic energy increased to maximum.
The object has only kinetic energy at position C because the remaining potential energy at position B were converted to kinetic energy at position C. Therefore the total energy of the object at position C is only kinetic energy.
EXPLANATION OF CONSERVATION LAW USING MOTION OF OBJECT THAT IS UNDERGOING SIMPLE HARMONIC MOTION:
To explain the law of conservation of energy, I am will select three positions along the path of the motion of the object. (I) position A at the maximum height level, (ii) position B at the midway between A and C (iii) position C at the the equilibrium position of the object.
Let us explain the total energy that the object process at each of the three positions thus:
Total energy of the object at point A:
From the conservation law of energy,
Total energy= kinetic energy + potential energy
Total energy = ½*m*V² + m*g*h
Conditions at position A:
At point A, velocity V = 0 m/s because the object is monentarily at rest.
height h = h ( i.e maximum h).
Let us put the conditions into the formula and solve it , therefore,
Total energy = ½*m*(0)² + m*g*h
Total energy = 0 + mgh
Total energy = mgh
Therefore,
total energy of the object at position A ( at maximum height) = only Potential energy
Total energy of the object at position B:
From the conservation law of energy,
From the conservation law of energy,
Total energy = Kinetic energy + Potential energy
Total energy = ½*m*v² + m*g*h
As the object is returning fact to its rest / equilibrium position, its velocity v build up and increase from zero to a particular value while its height h reduces to to a value h
Therefore, V is not equal to zero and h is not equal to zero.
V = v , h = h.
Let us substitute these conditions into the formula for total enery. Therefore,
Total energy = ½ *m*V² + m*g*h
Note that since neither V nor h was zero, non of the energy in the formula become zero.
Therefore,
Total energy of the objects at point B = potential energy + kinetic energy
EXERCICES:
More questions coming
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