Question

(A) A body moving with 40 J of kinetic energy has mass of 20 kg. Find its speed.
(B) A person carrying a load of 20 kg climbs 4 mm in 10 sec. Calculate the work done and his power.

Answer 1

We know that in physics, the kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. On the other hand, potential energy is energy that is stored or conserved in an object or substance. This stored energy is based on the position, arrangement or state of the object or substance. We can think of it as energy that has the 'potential' to do work. Based on this concept we have to solve this question.

Complete step by step answer
(A) From the question we can say that:
Mass of a moving body (m) be 20 kg
Kinetic energy of a moving (${{E}_{k}}$) is 40 joules
Speed of a moving body (v) is what we have to find.
We know that,
${{E}_{k}}=\dfrac{1}{2}m{{v}^{2}}$
In the above expression m is the mass and v is velocity.
Now we have to put the values in the above expression to get:
$\Rightarrow 40=\dfrac{1}{2}\times 20\times {{\text{v}}^{2}}$
$\Rightarrow {{v}^{2}}=\dfrac{(40\times 2)}{20}$
On further evaluation we get:
$\Rightarrow {{v}^{2}}=\dfrac{80}{20}$
$\Rightarrow {{v}^{2}}=\dfrac{8}{2}$
$\Rightarrow {{v}^{2}}=4$
Now the value v is obtained as:
$\Rightarrow v=2m/s$

Hence, the speed is given as $2m/s$ .

(B) From the question we can say that:
Mass of load is given as 20 kg.
Height reached is given as 4 m.
Time taken is given as 10 m/s.
Gravity is taken as $10m/{{s}^{2}}$
Work done is to be calculated by us.
We can write the formula to find the work done as:
Work done = Potential energy = $m\times g\times h$.
Now we have to put the values as:
Work done $=20 \times 10 \times 4$
So, after the evaluation we get that the work done is 800 J.
Now to find the power we know that:
Power = Work done/Time
After we put the values, we get
Power = 800 / 10 = 80 W

Hence the power is given as 80 W

Note: We should know that kinetic energy is built up in an object by motion and can be defined as the energy that is needed to either slow it down or speed it up. Studies have also been done using kinetic energy and then converting it to other types of energy, which is then used to power everything from flashlights to radios and more. Energy is transferred from one object to another when a reaction takes place. Energy comes in many forms and can be transferred from one object to another as heat, light, or motion, to name a few.
On the other hand, potential energy becomes useful when it is converted to kinetic energy. Kinetic energy is used to perform work. Work occurs when force is applied to an object. Kinetic energy is useful because it allows work to be done. Potential energy is the energy by virtue of an object's position relative to other objects. Potential energy is often associated with restoring forces such as a spring or the force of gravity. This work is stored in the force field, which is said to be stored as potential energy.