Question

A force of 5 N produces an acceleration of 8 ms-2 on a mass m1 and an acceleration of 24 ms-2 on a mass m2. What acceleration would the same force provide if both the masses are tied together?

Answer 1

Given:

Force applied,F= 5 N

Acceleration produced in mass m₁, a₁= 8 m/s²

Acceleration produced in mass m₂, a₂= 24 m/s²

To Find:

Acceleration produced be given force when applied to both masses as a whole(or tied)

Solution:

We know that,

• Expression of force F is given by

$\pink{\underline{\boxed{\bf{F=ma}}}}$

where,

m is mass of body

a is acceleration of body

$\rule{190}{1}$

For mass m₁,

$\longrightarrow\rm{F=m_{1}a_{1}}$

$\longrightarrow\rm{5=m_{1}\times8}$

$\longrightarrow\rm{8m_{1}=5}$

$\longrightarrow\rm{m_{1}=\dfrac{5}{8}\ kg}$

For mass m₂,

$\longrightarrow\rm{F=m_{2}a_{2}}$

$\longrightarrow\rm{5=m_{2}\times24}$

$\longrightarrow\rm{24m_{2}=5}$

$\longrightarrow\rm{m_{2}=\dfrac{5}{24}\ kg}$

Let the combined mass of both the masses after tying be M

So,

$\longrightarrow\rm{M=m_{1}+m_{2}}$

$\longrightarrow\rm{M=\dfrac{5}{8}+\dfrac{5}{24}}$

$\longrightarrow\rm{M=\dfrac{15+5}{24}}$

$\longrightarrow\rm{M=\dfrac{20}{24}}$

$\longrightarrow\rm{M=\dfrac{5}{6}\ kg}$

Now, let the acceleration produced in combined mass after applying force be A

So,

$\longrightarrow\rm{F=MA}$

$\longrightarrow\rm{5=\dfrac{5}{6}\times A}$

$\longrightarrow\rm{\dfrac{5A}{6}=5}$

$\longrightarrow\rm{A=\dfrac{5\times6}{5}}$

$\longrightarrow\rm\green{A=6\ m/s^{2}}$

Hence, the required acceleration is 6 m/s².

Answer 2

Answer:

Given:

Force applied,F= 5 N

Acceleration produced in mass m₁, a₁= 8 m/s²

Acceleration produced in mass m₂, a₂= 24 m/s²

To Find:

Acceleration produced be given force when applied to both masses as a whole(or tied)

Solution:

We know that,

Expression of force F is given by

where,

m is mass of body

a is acceleration of body

For mass m₁,

For mass m₂,

Let the combined mass of both the masses after tying be M

So,

Now, let the acceleration produced in combined mass after applying force be A

So,

Hence, the required acceleration is 6 m/s².

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