Question 249: Work, Energy and Power & Circular Motion

Question

A body of mass $$5 \mathrm{~kg}$$ is moving with a momentum of $$10 \mathrm{~kg} \mathrm{~ms}^{-1}$$. Now a force of $$2 \mathrm{~N}$$ acts on the body in the direction of its motion for $$5 \mathrm{~s}$$. The increase in the Kinetic energy of the body is ___________ $$\mathrm{J}$$.

Accepted Answer

The increase in kinetic energy can be found using the work-energy theorem, which states that the work done on an object is equal to the change in its kinetic energy.
The work done by a force is given by the equation:
$ W = F \cdot d $
where ( F ) is the force and ( d ) is the distance over which the force is applied.
However, we don't have the distance in this problem. But we do know that the force is applied for a time of 5 seconds, and that the initial momentum of the body is 10 kg m/s. We can use these facts to find the work done.
First, we can use the equation for force, ( F = ma ), to find the acceleration of the body:
$a = \frac{F}{m} = \frac{2 \, 	ext{N}}{5 \, 	ext{kg}} = 0.4 \, 	ext{m/s}^2 $
Then, we can use the equation for distance in uniformly accelerated motion, ( $d = v_i t + \frac{1}{2} a t^2 $), where ( $v_i$ ) is the initial velocity of the body. We can find ( $v_i $) from the initial momentum and the mass of the body:
$ v_i = \frac{p}{m} = \frac{10 \, 	ext{kg m/s}}{5 \, 	ext{kg}} = 2 \, 	ext{m/s} $
Substituting ( $v_i$ ), ( a ), and ( t ) into the equation for ( d ) gives:
$ d = 2 \, 	ext{m/s} \cdot 5 \, 	ext{s} + \frac{1}{2} \cdot 0.4 \, 	ext{m/s}^2 \cdot (5 \, 	ext{s})^2 = 10 \, 	ext{m} + 5 \, 	ext{m} = 15 \, 	ext{m} $
Finally, we can substitute ( F ) and ( d ) into the equation for work to find the increase in kinetic energy:
$ \Delta KE = W = F \cdot d = 2 \, 	ext{N} \cdot 15 \, 	ext{m} = 30 \, 	ext{J} $
So, the increase in the kinetic energy of the body is 30 J.

Work, Energy and Power & Circular Motion

A body of mass $5 \mathrm{~kg} is moving with a momentum of 10 \mathrm{~kg} \mathrm{~ms}^{-1}. Now a force of 2 \mathrm{~N} acts on the body in the direction of its motion for 5 \mathrm{~s}. The increase in the Kinetic energy of the body is ___________ \mathrm{J}$.

Integer / Numeric Answer Type