Question

A force of 5N gives a mass m1 an acceleration of 10m/s and a mass m2 an accelaration of 20m/s2 what accelaration would it give if both masses are tied together?

Answer 1

Given,

${ \boxed{ \boxed{ \mathtt{ \large{F = 5N}}}} }\\ { \boxed{ \boxed {\mathtt{ \large{a_{1} = 10 {ms}^{ - 2} }}}}} \\ { \boxed {\mathtt{ \large{m_{1} =>F = ma }}}} \\ { \boxed {\mathtt{ \large{ \: \: \: \: \: = > 5N = (m_{1}){10ms}^{ - 2} }}}} \\ { \boxed { \boxed {\mathtt{ \large{ \: \: \: \: \: = > { \red{m_{1} = \frac{5}{10} }}}}}}}$

And,

${ \boxed{ \boxed{ \mathtt{ \large{F = 5N}}}} }\\ { \boxed{ \boxed {\mathtt{ \large{a_{2} = 10 {ms}^{ - 2} }}}}} \\ { \boxed {\mathtt{ \large{m_{2} =>F = ma }}}} \\ { \boxed {\mathtt{ \large{ \: \: \: \: \: = > 5N = (m_{2}){10ms}^{ - 2} }}}} \\ { \boxed { \boxed {\mathtt{ \large{ \: \: \: \: \: = > { \red{m_{2} = \frac{5}{20} }}}}}}}$

Now,

$= > { \boxed{\mathtt{ \large{m_{1} + m_{2} = \frac{5}{10} + \frac{5}{20} }}}} \\ = > { \boxed{\mathtt{ \large{ \: \: \: \: \: \: \: \: \: \: m_{3} = \frac{10 + 5}{20} = \frac{15}{20} }}}}$

Hence,

$=>{ \boxed{\mathtt{ \huge{ \: \: F = (m_{3}) \times (a_{3})}}}} \\ \\=>{ \boxed {\mathtt{ \huge{5N = (\frac{15}{20}) \times (a_{3})}}}} \\ \\=> { \boxed{\mathtt{ \huge{ \frac{5}{ \frac{15}{20} } = a_{3}}}} }\\ \\=> { \boxed{\mathtt{ \huge{a_{3} = \frac{5 \times 20}{15} }}}}\\ \\=> { \boxed{ \boxed{ \boxed{\mathtt{ \huge{a_{3} = { \boxed{ \red{\frac{20}{3} = 6.66 \: {ms}^{ - 2}}}} }}}}}}$