Question

A force of 20 n gives a mass m1 an acceleration of 10m/s^2 and m2 mass an
acceleration of 30 m/s^2 What acceleration would it give if both the masses are tied
together?
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Answer 1

Answer:

• Acceleration of masses when tied together = 7.5 m/s²

Explanation:

Given:-

• A force 'F' of 20 N when applied on a mass m₁ gives an acceleration 'a₁' of 10 m/s²
• Same force F when applied on a mass m₂ provides an acceleration 'a₂' of 30 m/s²

To find:-

• Acceleration on applying the same force F when the both masses are tied together; a =?

Formula required:-

• Expression for Newton's second law of motion

       Force = mass × acceleration

Solution:-

Using formula., Force = mass × acceleration

→ F = m₁ a₁  

→ 20 = m₁ × 10

→ m₁ = 2 kg

also,

→ F = m₂ a₂

→ 20 = m₂ × 30

→ m₂ = 2/3  kg

Now, since two masses are to be tied together so combined mass 'm' will be

→ m = m₁ + m₂

→ m = 2 + 2/3

→ m = 8/3 kg

Again Using Newton's second law

Calculating the acceleration of the combined masses

→ F = m a

→ 20 = 8/3 × a

→ a = 20 × 3/8

→ a = 7.5 m/s²

Therefore,

• Acceleration of both masses tied together will be 7.5 m/s².

Answer 2

Answer:

Given :-

• Force of Mass 1 (F1) = 20 N
• Acceleration of Mass 1 (A1) = 10 m/s²
• Acceleration of mass 2 (A2) = 30 m/s²

To Find :-

Acceleration would it give if both the masses are tied

together

SoluTion :-

Firstly let's find out mass of both body

$\huge \bf \: f \: = ma$

Here,

F = Force

M = Mass

A = Acceleration

$\sf \: mass \: of \: body \: 1 \downarrow$

$\sf \:20 = m \times 10$

$\sf \: 20 = 10m$

$\sf \: m = \dfrac{20}{10}$

$\bf \: mass \: of \: body \: 1 = 2 kg$

$\sf mass \: of \: body \: 2 \downarrow$

$\sf \: 20 = m \times 30$

$\sf \: 20 = 30m$

$\sf \: m \: = \dfrac{20}{30}$

$\sf \: mass \: of \: body \: 2 = \dfrac{2}{3} kg$

Now,

Both are combined. Therefore, we will find total mass

$\sf \: total \: mass \: = mass1 + mass2$

$\sf \: total \: mass \: = 2 + \dfrac{2}{3}$

$\sf \: total \: mass \: = \dfrac{6 + 2}{3}$

$\sf \: total \: mass \: = \dfrac{8}{3} kg$

Now,

We will again use newton second law

$\huge \bf \: f \: = ma$

$\sf \: 20 = \dfrac{8}{3} \times a$

$\sf \: 20 = \dfrac{8}{3} a$

$\sf \: a \: = 20 \times \dfrac{3}{8}$

Acceleration = 7.5 m/s²