Question

1. Can any object have momentum even if its mechanical energy is zero?
Explain.

2. The power of a motor pump is 2 kW. How much water per minute the

pump can raise to a height of 10 m? (Given g = 10 m s-²)

3. The weight of a person on a planet A is about half that on the earth. He can
jump upto 0.4 m height on the surface of the earth. How high he can jump
on the planet A?

​

Answer 1

$\large\bf{\underline{\underline{Answer\:1}}}$

$\sf\color{red}{Since,}$

$\textbf{Mechanical energy}$

$\underline{\boxed{\sf\purple{=\: potential \:energy \:+ \:kinetic\: energy}}}$

$\boxed{\sf{If \:mechanical\: energy \:=\: 0}}$

$\huge\bold{So,}$

$\sf{PE+ KE= 0}$

$\sf{PE= - KE}$

$\huge\bold{So,}$

we can say that body may have momentum, in case mechanical energy is zero

$\large\bf{\underline{\underline{Answer\:2}}}$

——————————————————————

${ \large{ \sf{ \underbrace{\underline{\bigstar \:Given,}}}}}$

$\bold{Power \:of\: pump}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀$\pink{\bigstar}★ \large\underline{\boxed{\bf\green{2kW =2000W}}}$

$\sf{Time (t) = 60sec}$

$\sf{Height (h) = 20m}$

$\underline{\boxed{\sf\purple{g = 10m/s2}}}$

As you know, power =work done per unit time.

Work done = mgh = m ×10×20 =200m

$\underline{\bf{Therefore}}$

$\large\bf{\underline{\underline{2000W = 50m/60s}}}$

$\underline{\bf{Therefore,}}$

$\large\bf{\underline{\underline{m = 600kg}}}$

$\textit{So,}$

$\textbf\color{green}{the pump can raise 600kg of water in one minute}$

——————————————————————

$\large\bf{\underline{\underline{Answer\:3}}}$

$\underline{\boxed{\sf\purple{Since, }}}$

Weight of the person on planet A is half that on the earth, acceleration due to gravity there, will be$\tt\color{orange}{1/2}$ that on the earth.

Hence he can jump$\tt\color{orange}{double}$ the height with the same muscular force

Thankyou :)

Answer 2

$\large\color{purple}\underline{\underline{{ \boxed {Answer \: 01 }}}}$

Yes, an object can have momentum even when its mechanical energy is zero because Mechanical energy is the sum of potential energy and the Kinetic energy

$\tt \: Mechanical \: Energy (M.E) = Potential energy (P.E) + Kinetic \: Energy (K.E) \\ \tt \: M.E = 0\\ \tt \: K.E + P.E = 0\\ \tt \: P.E = -K.E$

Hence,

Even if its mechanical energy is zero, the body has momentum.

$\large\color{purple}\underline{\underline{{ \boxed {Answer \: 02}}}}$

Given

• Power of pump = 2kW =2000W
• Time (t)= 60sec
• Height (h) = 10m
• g = 10m/s2

As you know

$\tt \: Power = \frac {work \: done}{ unit \: time} \\ \tt \: Work \: done = mgh \\ \tt \:= m ×10×10 =100m\\ \tt \:2000W = 100m/60s\\ \tt \:m = 1200kg$

So, the pump can raise 1200kg of water in one minute.

$\large\color{purple}\underline{\underline{{ \boxed {Answer \: 03 }}}}$

Assume

• The mass of the person = m kg
• Height jumped by him on earth = 0.4 m
• Time required to jump by him on earth = t seconds

Let

• g = acceleration due to gravity on earth
• g' = acceleration due to gravity on planet A

$\tt \: Weight \: of \: the \: man \: on \: earth = W_1-mg \\ \tt \: Weight \: \: man \: on \: A =W_2=mg' \\ \tt \: given W_2-1/2 W' \\ \tt \: mg'= \frac{1}{2} mg \\ \tt \: =g' = \frac{1}{2} g  ----(1)$

Now energy used by him to move a distance 0.4 m on earth will be 

Potential Energy= mg(0.4)

If he gives the same PE on the planet A with accl. due to gravity g' he would move a height h'

$\tt \: Or, mg'h'=mg(0.4) \\ \tt \: by \: eqn \: (1)\\ \tt \: g' = \frac{1}{2} g\\ \tt \:mg'h'=mg(0.4)\\ \tt \: = \frac{1}{2} gh' = g(0.4)\\ \tt \: or h'=0.8m$

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$\sf \: @WildCat7083$