Question

Calculate the acceleration of the masses and the tension in the string for each system

Answer 1

Given data:

Mass m1=9 kg

Mass m2=13 kg

To find:

Acceleration of the masses and the tension in the string for each system.

Solution:

By applying the newton's second law,

For mass m1, The equation can be written as,

`T-m_1g=ma---(1)_{}_{}`

For the mass m2, the equation is

`m_2g-T=m_2a---(2)`

By adding these two equation we can get a formula to find acceleration,

`\begin{gathered} (m_2-m_1)g=(m_1+m_2)a \\ a=((m_2-m_1)g)/((m_1+m_2)) \end{gathered}`

Here, by substituting the known values we can get

`\begin{gathered} a=((13-9)9.8)/((9+13)) \\ a=(39.2)/(22) \\ a=1.78m/s^2 \end{gathered}`

Thus the acceleration is 1.78m/s^2.

Now, to calculate the tension,

`\begin{gathered} m_2g-T=m_2\frac{(m_2-m_1)g}{(_{}m_1+m_2)} \\ T=(2m_1m_2g)/((m_1+m_2)) \\ T=(2\ast9\ast13\ast9.8)/(9+13) \\ T=(2293.2)/(22) \\ T=104.24\text{ N} \end{gathered}`

Thus, the tension in s string is 104.24 N