Question

How much work should be done on a bicycle of mass 20kg to increase its speed from 2ms^-1 to 4ms^-1. ​

Answer 1

$\bf{\underline{\underline{Answer:}}}$

$\bf\therefore 120J$

$\bold{\underline {Given:}}$

• Mass of bicycle = 20 kg

• Speed from 2ms¯¹ to 4 ms¯¹

$\bold{\underline {To\:Find:}}$

• Work should be done on a bicycle =?

$\bf{\underline{\underline{Step\: by\: step \:explanation:}}}$

We know that whenever work is done, an equal energy amount of energy is used up. So, the work done in this case will be equal to the change in kinetic energy of bicycle when its speed changes.

In the first case:

Mass of the bicycle, m = 20 kg

and, speed of the bicycle V = 2 ms¯¹

So, kinetic energy ,$K_E=\dfrac{1}{2}mv^2$

$= \dfrac{1}{2} \times 20 \times {(2)}^2\\ \\=10\times 4 \\ \\ =40J$

In the second case:

Mass of the bicycle, m = 20kg

And, speed of the bicycle, v = 4ms¯¹

$\sf So,\:kinetic \:energy, E_k=\dfrac{1}{2}mv^2\\ \\=\dfrac{1}{2}\times 20 \times (4)^2\\ \\ = 10 \times 16\\ \\= 160J$

•°•Change in kinetic energy = 160 - 40 = 120J

Thus,work done will be 120J.

Answer 2

initial work=1/2mv^2

=1/2×20×4=40J

final work=1/2mv^2=1/2×20×16=160J

work done =final work -initial work

=160-40

=120J