Question

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UICO
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3. The work done by a person in carrying a box of mass 15 kg
through a vertical height of 5m is 4900J. What is the mass of
the person?​

Answer 1

Given :-

Mass of the box = 15 kg

Height the object is being raised = 5 m

Work done by the person = 4900 J

To Find :-

The mass of the person.

Analysis :-

Here we are given with the mass of the box, height and potential energy of the person.

In order to find the height substitute the given values from the questions  such that work done is equal to mass (of both the object) into gravity into height and find the mass of the person accordingly.

Solution :-

We know that,

• m = Mass
• PE = Potential energy
• w = Work done
• h = Height
• g = Gravity

Using the formula,

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

Given that,

Mass (m₁) = 15 kg

Gravity (g) = 10 m/s

Height (h) = 5 m

Potential energy (PE) = 4900 J

Substituting their values,

⇒ 4900 = (15 + m₂) × 10 × 5

⇒ 4900 = (15 + m₂) × 50

⇒ m₂ = (4900/50) - 15

⇒ m₂ = 98 - 15

⇒ m₂ = 83 kg

Therefore, the mass of the person is 83 kg.

Answer 2

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

• Mass of the object (m₁) = 15 kg
• Height reached (h) = 5 m
• Potential energy (PE) = 4900 J

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

• The mass of the person (m₂) = ?

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

We know that:-

$\qquad\bull\:\sf{Potential \: Energy=Mass \times Gravity \times Height }$

${:} \implies \sf{4900 = \bigg(15 +m₂ \bigg) \times 10 \times 5 }$

${:} \implies \sf{4900 = \bigg(15 +m₂ \bigg) \times 50}$

${:} \implies \sf{4900 =750 + 50m₂ }$

${:} \implies \sf{4900 - 750 = 50m₂ }$

${:} \implies \sf{4150 = 50m₂ }$

${:} \implies \sf{ \cancel\dfrac{4150}{50} = m₂ }$

${:} \implies \boxed {\frak \pink{ m₂ = 83 }}$

$\qquad \therefore \: \underline {\sf{The \: mass \: of \: the \: person =83 \: kg}}$