Question

☆challenge for mods/ stars☆


Question-

A force of 5 newtons gives a mass m1 an acceleration of 8m/s^2, and a mass m2 an acceleration of 24 m/s^2 . what acceleration would it give if the masses are tried together? ​

Answer 1

GiveN :

• Force (F) = 5 N
• Acceleration of 1st object (a1) = 8 m/s²
• Mass of 1st object = m1
• Acceleration of 2nd object (a2) = 24 m/s²
• Mass of 2nd Object = m2

To FinD :

• Acceleration when masses are tied together.

SolutioN :

ㅤㅤㅤㅤㅤㅤ$\underbrace{\sf{For\ first\ object}}$

$\implies \sf{F = m_1 a_1}$

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$\implies \sf{5 = m_1 \times 8}$

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$\implies \sf{m_1 = \dfrac{5}{8}}$

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$\underline {\sf{\therefore \: Mass\ of\ First\ object\ is\ \dfrac{5}{8}\ kg}}$

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ㅤㅤㅤㅤ$\underbrace{\sf{For\ Second\ Object}}$

$\implies \sf{F = m_2 a_2}$

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$\implies \sf{5 = 24m_2}$

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$\implies \sf{m_2 = \dfrac{5}{24}}$

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$\underline {\sf{\therefore\ Mass\ of\ second\ object\ \dfrac{5}{24}\ kg}}$

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Now, if masses are tied together :

$\implies \sf{m = m_1 + m_2}$

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$\implies \sf{m = \dfrac{5}{8} + \dfrac{5}{24}}$

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$\implies \sf{m = \dfrac{5(3) + 5(1)}{24}}$

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$\implies \sf{m = \dfrac{15 + 5}{24}}$

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$\implies \sf{m = \dfrac{20}{24}}$

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Now, acceleration of objects :

$\implies \sf{F = ma}$

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$\implies \sf{a = \dfrac{F}{m}}$

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$\implies \sf{a = \dfrac{5}{\dfrac{20}{24}}}$

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$\implies \sf{a = \dfrac{24 \times 5}{20}}$

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$\implies \sf{a = \dfrac{24}{4}}$

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$\implies \sf{a = 6}$

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$\therefore$ Acceleration when masses are tied together is 6 m/s².

Answer 2

Answer:

$1)$ In the first case :

Force, $F$ = 5 N

Mass, $m$ = m1 (To be calculated)

And,

Acceleration, a = $8 m/s^2$

Now,

$F$ = m × a

So,

$5$ = m1 × 8

And, m1 =$\frac{5}{8}$kg

m1 = 0.635kg

Thus, the mass m1 is 0.625kg.

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$2)$ In the second case :

Force, $F$ = 5 N

Mass, $m$ = m2 (To be calculated)

And,

Acceleration, a = $8 m/s^2$

Now,

$F$ = m × a

So,

$5$ = m2 × 24

and, m2 =

$\frac{5}{24}$kg

m2 = 0.208kg

Thus, the mass m2 is 0.208 kg.

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$3)$ In the third case :

Force, $F$ = 5 N

Total Mass, $m$ = m1 + m2

= 0.625 + 0.208

= 0.833 kg

And, Acceleration, $a$ = ? (To be calculated)

Now,

putting these values in the relation:

$F$ = m × a

we get:

$5$ = 0.833 × a

a =$\frac{5}{0.833}$

a = $6 m/s^2$

Thus, if both the masses are tied together, then the acceleration would be $6 m/s^2$