Question

A force of 6N gives a mass m1 an acceleration of 18 m/s2

and a mass m2 an acceleration of 24 m/s2

. What acceleration would it give if both the masses were tied together????​

Answer 1

Explanation:

force = 6N

for m1, f= m1a

m1 = f/a= 6/18 = 1/3 kg

fir m2 , f=m2a

m2 = f/a = 6/24 = 1/4 kg

combined mass = 1/4+1/3 = 7/12 kg

f = m.a

a = f/m

= 6/(7/12) = 12 *6/7

so , new acceleration = 72/7 ms^-2

Answer 2

Given:-

• Force = 6N
• Acceleration of 1st body = 18 m/s²
• Acceleration of 2nd body = 24 m/s²

To find:-

Acceleration of the body is both the masses are tied together.

Solution:-

For the 1st body:-

Force = 6N

Acceleration = 18 m/s²

We know,

$\sf{Force = Mass \times Acceleration}$

= $\sf{6 = m_1 \times 18}$

=> $\sf{m_1 = \dfrac{6}{18}\:kg}$

=> $\sf{m_1 = \dfrac{1}{3}\:kg}$

For the 2nd body:-

Force = 6N

Acceleration = 24 m/s²

Now,

$\sf{Force = Mass\times Acceleration}$

= $\sf{6 = m_2 \times 24}$

= $\sf{m_2 = \dfrac{6}{24}}$

= $\sf{m_2 = \dfrac{1}{4}\:kg}$

Now,

$\sf{Total \:mass \:of \:both \:the \:bodies = \dfrac{1}{3} + \dfrac{1}{4}\:kg}$

=> $\sf{m = \dfrac{3 + 4}{12}\:kg}$

=> $\sf{m = \dfrac{7}{12}\:kg}$

Now,

We have,

$\sf{Force = 6N}$

$\sf{Mass = \dfrac{7}{12}\:kg}$

$\sf{Acceleration = ?}$

Therefore,

= $\sf{Force = Mass \times Acceleration}$

=> $\sf{6 = \dfrac{7}{12} \times a}$

=> $\sf{6 \times\dfrac{12}{7} = a }$

=> $\sf{a = 10.29\: m/{s}^{2}}$

Therefore if both the masses are combined then the body would give an acceleration of 10.29 m/s².