Question

two bodies of masses m1 and m2 kept on a frictionless surface are pushed by a force F one after the other which produces the acceleration of 4m/s^2 and 6m/s^2 in them.what would be the acceleration if the same force is applied when these bodies are tied together.

Answer 1

Ask if any dount
It is because of f=ma

Answer 2

Given that,

Mass of first body = m₁

Mass of second body = m₂

Acceleration of first body = 4 m/s²

Acceleration of second body = 6 m/s²

We need to calculate the ratio of their masses

Using newton's second law for both bodies

$F_{1}=m_{1}\times a_{1}$

$F_{1}=m_{1}\times 4$.....(I)

$F_{2}=m_{2}\times a_{2}$

$F_{2}=m_{2}\times 6$.....(II)

If the same force is applied when these bodies are tied together.

So, $F_{1}=F_{2}$

Put the value of F₁ and F₂

$m_{1}\times4=m_{2}\times6$

$\dfrac{m_{1}}{m_{2}}=\dfrac{6}{4}$

$\dfrac{m_{1}}{m_{2}}=\dfrac{3}{2}$

The ratio of their masses is 3:2.

So, the total mass will be

$M=m_{1}+m_{2}$

Put the value into the formula

$M=3+2$

$M=5\ kg$

We need to calculate the force F₁

Using equation (I)

$F_{1}=m_{1}\times a_{1}$

Put the value into the formula

$F_{1}=3\times4$

$F_{1}=12\ N$

These bodies are tied together then we consider as a system.

We know that,

$F_{1}=F_{2}=F$

We need to calculate the acceleration

Using newton's second law

$F=MA$

$A=\dfrac{F}{M}$

Put the value into the formula

$A=\dfrac{12}{5}$

$A=2.4\ m/s^2$

Hence, The acceleration of the system would be 2.4 m/s².