Question

in an atwood’s machine, the larger mass is 4.2 kg and the smaller mass is 1.5 kg. Ignoring friction, what is the acceleration of the masses?

Answer 1

Answer:

a = 4.64 m/s²

Explanation:

Given that,

Larger mass, M = 4.2 Kg

Smaller mass, m = 1.5 Kg

Friction of pulley = 0

Acceleration of the masses, a = ?

In an Atwood's machine,

Tension in the string, T

Acceleration due to gravity, g

The net force on the smaller mass is, f = T - mg  ( f = ma)

The net force on the larger mass is,   F = Mg -T  (F = Ma)

Since the acceleration 'a' of the two masses remains the same, the equations can be solved to a.

Adding the above equations

                          ma + Ma = Mg -mg

                          a (m + M) = (M - m) g

                              $a = \frac{M - m}{ M + m} g$

Substituting the values in the above equation

                             $a = \frac{4.2 - 1.5}{ 4.2 + 1.5} 9.8$    

                                       = 4.64 m/s²

Hence, the acceleration of  the masses, a = 4.64 m/s²