Answer to Question #123990 in Classical Mechanics for Vidurjah Perananthan

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

As per the question,

mass of the trolley $(m_1)=3.3kg$

mass connected with the trolley with the help of the string $(m_2)=2.2kg$

chord runs through the pulley,

Let the acceleration of the trolley = a and tension in the string is T,

Now,

a)

$m_1g-T=m_1a$

$\Rightarrow 3.3g-T=3.3a----(i)$

and

$T-m_2g=m_2a$

$\Rightarrow T-2.2g=2.2a---(ii)$

from equation (i) and (ii),

$\Rightarrow 3.3g-2.2g=5.5a$

$\Rightarrow a=\frac{1.1g}{5.5}m/sec^2$

and

b)

$T=2.2g+2.2a=2.2g+2.2\times \frac{1.1g}{5.5}$

$\Rightarrow T=2.2g+0.44g=2.64gN$

Hence , clamping force on the card$=2T$

$=2\times 2.64g = 5.28gN$