We are solving series of problems on a concept work, power and energy. We know that when there is no loss of energy in any other format, the total energy is conserved. It means the total mechanical energy of the system is constant. If potential energy increases, its kinetic energy decreases and vice versa. Power is defined as the rate of change of work done. It is the ability of doing work in specified time. Power is measured with a unit called watt and it can be also expressed as the dot product of velocity and force.

**Problem**

A bomb of mass 10 kilogram projected vertically upward from the ground. At a certain point on its journey it has some potential energy and some kinetic energy and the values are given. We need to measure the velocity of the projection of the body. The problem is as shown in the diagram below.

**Solution**

We know that the total mechanical energy of any system is conserved. In the path some where the body has both potential and kinetic energy. When the same body is vertically projected from the ground it has no potential energy and its total energy is in the form of only kinetic energy. Thus we can equate the total energy to kinetic energy and the problem can be solved as shown below.

**Problem**

A boy blowing a whistle sends in air at a known mass per second with a known speed. We need to measure the power of the lung. The problem is as shown in the diagram below.

**Solution**

We know that the power is defined as the rate of change of work done or energy. Here the energy is kinetic energy and the power is rate of change of kinetic energy. In the given data, mass per unit time is given to us and we can substitute and solve the problem as shown in the diagram below.

**Problem**

If the power of a motor pump is known for us, we need to know how many liters of water it can lift from a well of depth 10 meter in one minute. The problem is as shown in the diagram below.

**Solution**

Here the energy is in the form of potential energy. Hence power is here defined as the rate of change of potential energy. We also know that one liter is thousand cubic centimeter. We can solve the problem as shown in the diagram below.

**Problem**

It is given in the problem that a bucket of mass is tied to a light rope and it is lowered at constant acceleration in downward direction. We need to measure the work done by the rope when the bucket is lowered to a certain distance. The problem is as shown in the diagram below.

**Solution**

As the bucket is tied to the rope and hence it is tight and hence it will have some tension inside it. We can measure the tension as the effective force acting in the rope. We know that the rope is moving upward and hence effective force is the difference between tension and the weight. Tension and displacement are in the opposite direction and hence we see a negative sign in the answer.We can solve the problem as shown below.

**Problem**

A ball is thrown vertically upwards with a velocity and it returns to the ground with a different velocity. We need to measure the maximum velocity reached by the body. The problem is as shown in the diagram below.

**Solution**

We can solve the problem using law of conservation of energy. The total work done is the sum of kinetic energy of the two cases as shown in the diagram below. We can get the maximum height reached by it as shown below.

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