Question

A force of 10 N produces an acceleration of 5 m/s2 when it acts on one body and 2 m/s2 when it acts on another body. If two bodies are tied together and the same force is applied, what will be the acceleration produced?  

Please explain it step by step.

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Answer 1

Explanation:

• A force of 10 Newtons produces an acceleration of 5 m/s^2 on the first body hence the mass of the first body is 2 kg ( by using the equation force = mas * acceleration )

• The force of same magnitude acts on the another body and produces the acceleration of 2 m/s^2 , hence the mass of the body is 5 kg .

• When these two bodies of mass 2 kg and 5 kg are placed together the total mass will be 7 kg . We have to find the acceleration of these two bodies when a force of 10 N is applied on them.

• Hence by using the Newtons equation F = m*a , we get 10 = 7*a

• therefore the acceleration of the two bodies together is a = 10/7 m/s^2 i.e 1.42 m/s^2.

Answer 2

$\displaystyle\large\underline{\sf\red{Given}}$

✭ A force of 10 N is applied

✭ There are two bodies

• Body 1 = Produces an acceleration of 5 m/s²
• Body 2 = Produce an acceleration of 2 m/s²

$\displaystyle\large\underline{\sf\blue{To \ Find}}$

◈ The acceleration when these two bodies are tied together

$\displaystyle\large\underline{\sf\gray{Solution}}$

So here we may primarily use,

$\displaystyle\underline{\boxed{\sf F = ma}}$

• F = Force
• m = Mass
• a = Acceleration

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$\underline{\bigstar\:\textsf{According to the given Question :}}$

Body 1

• Force = 10 N

• Mass = ?

• Acceleration = 5 m/s²

Substituting the given values,

➝ $\displaystyle\sf F = ma$

➝ $\displaystyle\sf 10 = m \times 5$

➝ $\displaystyle\sf 10 = 5a$

➝ $\displaystyle\sf \dfrac{10}{5} = m$

➝ $\displaystyle\sf \purple{Mass_1 = 2 \ kg}$

Body 2

• Force = 10 N

• Mass = ?

• Acceleration = 2 m/s²

»» $\displaystyle\sf F = ma$

»» $\displaystyle\sf 10 = m\times 2$

»» $\displaystyle\sf 10 = 2m$

»» $\displaystyle\sf \dfrac{10}{2} = m$

»» $\displaystyle\sf \green{Mass_2 = 5 \ kg}$

So now when they are tired together,

➳ $\displaystyle\sf F = (m_1+m_2)\times a$

➳ $\displaystyle\sf 10 = (2+5)\times a$

➳ $\displaystyle\sf 10 = 7\times a$

➳ $\displaystyle\sf 10 = 7a$

➳ $\displaystyle\sf \dfrac{10}{7} = a$

➳ $\displaystyle\sf \pink{Acceleration = 1.43 \ m/s^2}$

$\displaystyle\sf \therefore\:\underline{When \ they \ are \ tied \ Acc^n \ will \ be \ 1.43 m/s^2}$

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