Answer to Question #217687 in Classical Mechanics for Haseeb

Question

A trolley with mass m1 of 3.3 kg is connected to a light string with a weight of mass m2 of 2.2 kg.
The cord runs through a pulley (a small wheel where the cord runs freely)
a) Calculate the vehicle acceleration
b) Calculate the clamping force in the card

Answer 1

Mass of trolley $(m_1)=3.3 kg$

Mass of connected weight $(m_2)=2.2kg$

Now, Let the common acceleration be a and the clamping force be T (tension in the string).

Now,

$T=m_1a....(i)$

$m_2g-T=m_2a...(ii)$

From equation (i) and (ii)

$a=\frac{m_2g}{m_1+m_2}$

Now, substituting the values,

$\Rightarrow a =\frac{2.2\times 10}{3.3+2.2}m/s^2$

$\Rightarrow a = \frac{22}{5.5}m/s^2$

$\Rightarrow a = 4m/s^2$

hence, the required tension in the string or the clamping force

$T=m_1a = 3.3\times 4 N$

$\Rightarrow T= 13.2N$