Question

8) A stone is dropped down a well. When it hits the bottom of the well, it is travelling at 20 m s-1. The mass of the stone is 20 g.
a. Calculate the kinetic energy of the stone as it hits the bottom of the well.
b. What is the gravitational potential energy of the stone at the top of the well?
c. Calculate the height of the well.

Answer 1

Given:-

•Velocity ,v = 20m/s

• Mass ,m = 20/1000kg = 0.02 Kg

• Acceleration due to gravity ,g = 10m/s²

To Find:-

(a.) Calculate the kinetic energy of the stone as it hits the

bottom of the well.

(b.) What is the gravitational potential energy of the stone at the top of the well?

(c.) Calculate the height of the well.

Solution:-

[a]

• KE = 1/2mv2

Where,

KE is the Kinetic Energy

m is the mass

v is the speed/velocity

Substitute the value we get

→ KE = 1/2×0.02 ×20²

→ KE = 1/2× 0.02 ×400

→ KE = 0.02 × 200

→ KE = 4 J

Therefore, kinetic energy of the stone is 4Joule.

____________________________________________

[b]

According to Work Energy Theorem .

Gravitational potential energy of the stone at the top of the well is 4 Joule .

_______________________________________________

[c]

We have to calculate the height of the well .

• PE = mgh

where,

PE is Potential Energy

m is the mass

g is the acceleration due to gravity

h is the height

Substitute the value we get

→ 4 = 0.02 × 10 × h

→ 4 = 0.2 × h

→ h = 4/0.2

→ h = 20m

Therefore, the height of the well is 20 metres .

Answer 2

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8) A stone is dropped down a well. When it hits the bottom of the well, it is travelling at 20 m s-1. The mass of the stone is 20 g.

a. Calculate the kinetic energy of the stone as it hits the bottom of the well.

b. What is the gravitational potential energy of the stone at the top of the well?

c. Calculate the height of the well.

${ { \underbrace{ \mathbb{ \red{GiVeN\ }}}}}$

• $Velocity (v) =20m/s$
• $Weight (m) = \frac{20}{1000}=0.02kg$
• $Acceleration\: cause \:of \:gravity =10m/{s}^{2}$

${ { \underbrace{ \mathbb{ \red{To\:PrOvE\ }}}}}$

• $A) Calculate \:the \:kinetic \:energy \:of\: the\\ stone \:as\: it \:hits\: the\: bottom \:of \:the\: well.$
• $B) What \:is \:the \:gravitational\:\\ potential \:energy \:of \:the\: stone\: at\: the\\ top \:of \:the\: well?$
• $C) Calculate\: the\: height\: of\: the \:well.$

$\star\underbrace{\mathtt\red{⫷❥ᴀ} \mathtt\green{n }\mathtt\blue{S} \mathtt\purple{W}\mathtt\orange{e} \mathtt\pink{R⫸}}\star\:$

______________________________________

$\huge{A)}$

${\boxed {\boxed {KE= \frac{1}{2} m{v}^{2}}}}$

• $KE=Kinetic\: Energy$
• $m=weight$
• $v=velocity$

$substitute \: the \: values$

$KE=\frac{1}{2} \times 0.02\times {20}^{2}$

$KE=\frac{1}{2} \times 0.02\times 400$

$KE=0.02 \times 200$

${\boxed {\boxed {KE=4J}}}$

$\therefore Kinetic \:energy\: of\: the\: stone\: is\\ {\boxed {\boxed {4J}}}$

______________________________________

$\huge{B)}$

$according \: to \: work \: energy \: theorem$

$\therefore the \:gravitational\:\\ potential \:energy \:of \:the\: stone\: at\: the\\ top \:of \:the\: well\:is \\{\boxed {\boxed {4\:Joule}}}$

______________________________________

$\huge{C)}$

${\boxed {\boxed {PE=mgh}}}$

• $PE= Potential energy$
• $m=weight$
• $g=Acceleration\: cause \:of\:gravity$
• $h=height$

$substitute \: the \: values$

$4=0.02 \times 10 \times h$

$4=0.2 \times h$

$h=\frac{4}{0.2}$

${\boxed {\boxed {h=20m}}}$

$\therefore the \:height \:of \:the \:well\: is {\boxed {\boxed {4m}}}$

$\blue{\boxed{\blue{ \bold{\fcolorbox{red}{black}{\green{Hope\:It\:Helps}}}}}}$

${\mathbb{\colorbox {orange} {\boxed{\boxed{\boxed{\boxed{\boxed{\colorbox {lime} {\boxed{\boxed{\boxed{\boxed{\boxed{\colorbox {aqua} {@suraj5069}}}}}}}}}}}}}}}$