Question

force of 5 n produces acceleration of 8m/s^2 on mass m1 and acceleration of 24 on mass 2 what acceleration would the same force provide if both masses are tied together
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Answer 1

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

✭ A force of 5N acts produces an acceleration of 8 m/s² on a body of mass m1

✭ The same force produces an acceleration of 24 m/s² of a body of mass m2

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

◈ The acceleration that will be produced when thetwo bodies are tired?

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

So here we are gonna use the Newton's Second Law of Motion,

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

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

So we shall first find the mass of body 1

➝ $\displaystyle\sf F = ma$

➝ $\displaystyle\sf 5 = m \times 8$

➝ $\displaystyle\sf \purple{m_1 = \dfrac{5}{8}}$

Similarly the mass of body two will be,

➳ $\displaystyle\sf F = ma$

➳ $\displaystyle\sf 5 = m \times 24$

➳ $\displaystyle\sf \green{m_2 = \dfrac{5}{24}}$

Now the Total mass will be,

›› $\displaystyle\sf Total \ mass = m_1+m_2$

›› $\displaystyle\sf Total \ mass = \dfrac{5}{8} + \dfrac{5}{24}$

›› $\displaystyle\sf Total \ mass = \dfrac{15}{24}+\dfrac{5}{24}$

›› $\displaystyle\sf Total \ mass = \dfrac{15+5}{24}$

›› $\displaystyle\sf Total \ mass = \dfrac{20}{24}$

›› $\displaystyle\sf \orange{Total \ mass = \dfrac{5}{6}}$

So then the acceleration produced will be,

»» $\displaystyle\sf F = ma$

»» $\displaystyle\sf 5 = \dfrac{5}{6} \times a$

»» $\displaystyle\sf 5\times \dfrac{6}{5} = a$

»» $\displaystyle\sf \pink{Acceleration = 6 \ m/s^2}$

$\displaystyle\therefore\:\underline{\sf When \ they \ are \ tried \ together \ acc^n \ is \ 6m/s}$

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Answer 2

Answer:

This is a beautiful problem to test whether a student actually understands Newton's 2nd law of motion.

• Force = mass × Acceleration

That simple law is all you need to solve this problem, but you need to

use it a few times.

๏ m₁ alone:

$= > \sf Force = mass \times Acceleration$

$=> \sf 5 N = m_1\times 8 \: m/s^2$

$=>\sf m_{1}= \dfrac{5 \: N }{8 \: m/s^{2} }$

$=> \underline{ \boxed{\sf m_{1}= 0.625 \:kilograms }}$

____________________....

๏ m₂ alone:

                    

$= > \sf Force = mass \times Acceleration$

$=> \sf 5 N = m_2\times 24 \: m/s^2$

$=>\sf m_{2}= \dfrac{5 \: N }{24 \: m/s^{2} }$

$=> \underline{ \boxed{\sf m_{2}= 0.208 \:kilograms }}$

_________________....

Now, we will find the total mass

$=> \sf Total \: mass = m_1 + m_2$

$=> \sf Total \: mass =0.625+ 0.208$

$=> \underline{ \boxed{ \sf Total \: mass = 0.833 \:kilograms }}$

_______________....

❍ m₁ and m₂ glued together:

$=> \sf Force = mass \times Acceleration$

$= > \sf 5 N= 0.833 \: kg \times Acceleration$

$=> \sf Acceleration = \frac{5N}{0.833 \: kg}$

$=> \underline{ \boxed{ \textsf{ \textbf{ Acceleration = 6 \: m/s ^2 }}}}$