Question

Physics Questions (Class 9) :-

Some Numericals!

(i) How much work should be done to a bicycle of mass 20 kg to increase its speed from 3m/s to 5 m/s?

(ii) What is the power of a pump which takes 10 seconds to lift 100 kg of water to a water tank situated at a height of 20m?




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Answer 1

Answer:

• We know that whenever work is done, an equal 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 from 2 m/s to 5 m/s. Now, Work done = Change in kinetic energy. Thus, the work done is 210 J.
• Here, work done W= potential energy =mgh=100×10×20=20000J

The required power P=W/t=20000/10=2×10

3

W

Answer 2

Answers:

Part 1:

★ Given:

Mass of the bicycle = 20 kg

Initial speed [u] = 3 m/s

Final speed [v] = 5 m/s

★ To Find:

The work done in order to increase the speed as said.

★ Solution:

In the first case:

Initial Speed [u] = 3 m/s

Formula to be applied:

$\sf{KE=\dfrac{1}{2}mu^2}$

$\sf{\dfrac{1}{2}\times20\times3\times3}$

$\sf{=90J}$

In the second case:

Final Speed [v] = 5 m/s

Formula to be applied:

$\sf{KE=\dfrac{1}{2}mv^2}$

$\sf{\dfrac{1}{2}\times20\times5\times5}$

$\sf{=250J}$

Work Done = Change in KE

= 250 - 90

= 160 J

Part 2:

★ Given:

Mass = 100 kg

Height = 20 m

Time taken = 10 s

Taking gravitational field as 10 m/s.

★ To Find:

The power required.

★ Solution:

The work done = mass x gravity x height [mgh]

= 20 x 100 x 10

= 20000 J

Power required = Work done/Time taken

= 20000/10

= 2000 W (or) 2 x 10³ W

★ Final Answers:

1) The work done to increase the speed is 160 J.

2) The power required by the pump to do the work is 2000 W.