Question

A box of weight 100 N is lifted to a height of 10 m above ground. How much potential energy will be stored in the box?
9800 J
1000 J
2000 J
None of the above​

Answer 1

$\large{\underline{\underline{\sf{ \maltese \: {Given:-}}}}}$

• Weight = 100 N
• Height = 10 m

$\large{\underline{\underline{\sf{ \maltese \: {To \: find:-}}}}}$

Potential energy = ?

$\large{\underline{\underline{\sf{ \maltese \: {Solution:-}}}}}$

➊ We know that:–

$\qquad \bull \bf \: {Weight = Mass \times Acceleration }$

$\begin{gathered}\begin{gathered}\qquad \quad {:} \longrightarrow\sf \: {100 = mass \times 10 } \\\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\qquad \quad {:} \longrightarrow\sf \: { \dfrac{100}{10} = mass } \\\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\qquad \quad {:} \longrightarrow\sf \: { mass = \cancel\dfrac{100}{10} } \\\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\qquad \quad {:} \longrightarrow\sf \: \underline{ \boxed {\sf{mass = 10 \: kg }}} \\\end{gathered}\end{gathered}$

➋ We know that:–

$\qquad \bull \bf \: { Potential \: energy=mass \times acceleration \times height}$

$\begin{gathered}\begin{gathered}\qquad \quad {:} \longrightarrow\sf \: {potential \: energy = 10 \times 10 \times 10 } \\\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\qquad \quad {:} \longrightarrow \underline{ \boxed{\sf \: {potential \: energy = 1000 \: J}}} \\\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\large \quad \therefore\sf \: { The \: correct \: option \: is \: \underline{\underline{1000 \: J}}} \\\end{gathered}\end{gathered}$

$\large{\underline{\underline{\sf{ \maltese \: {Answer:-}}}}}$

The potential energy is 1000 J.

Answer 2

Answer:

$\boxed{ \bold{ \sf \: \star given \star}}$

Force applied to lift the box = 100 N

Height of the box = 10 m

$\boxed{ \bold{ \sf \: \star to \: find \star}}$

The potential energy of an stored in the box.

$\boxed{ \bold{ \sf \: \star evaluation \star}}$

Here we are given with the mass and height of the box.

Firstly, using the formula of force (ie. force is equal to mass multiplied by the acceleration) find the acceleration accordingly.

In order to find the potential energy of the object substitute the values in the question such that potential energy mass into gravity into height and find the potential energy accordingly.

Solution :-

We know that,

m = Mass

h = Height

PE = Potential energy

g = Gravity

a = Acceleration

f = Force

Using the formula,

$\underline{\boxed{\sf Force=Mass \times Acceleration}}$

Given that,

Force (f) = 100 N

Acceleration (a) = 10 m/s

Substituting their values,

⇒ f = ma

⇒ 100 = m × 10

⇒ m = f/a

⇒ m = 100/10

⇒ m = 10 kg

Using the formula,

$\underline{\boxed{\sf Potential \ energy=Mass \times Gravity \times Height }}$

Given that,

Mass (m) = 10 kg

Gravity (g) = 10 m/s

Height (h) = 10 m

Substituting their values,

⇒ PE = mgh

⇒ PE = 10 × 10 × 10

⇒ PE = 1000 J

Therefore, the potential energy of an box is 1000 J.