Answer to Question #123990 in Classical Mechanics for Vidurjah Perananthan

Question #123990
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
1
Expert's answer
2020-06-29T14:13:13-0400

As per the question,

mass of the trolley (m1)=3.3kg(m_1)=3.3kg

mass connected with the trolley with the help of the string (m2)=2.2kg(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)

m1gT=m1am_1g-T=m_1a

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

and

Tm2g=m2aT-m_2g=m_2a

T2.2g=2.2a(ii)\Rightarrow T-2.2g=2.2a---(ii)

from equation (i) and (ii),

3.3g2.2g=5.5a\Rightarrow 3.3g-2.2g=5.5a

a=1.1g5.5m/sec2\Rightarrow a=\frac{1.1g}{5.5}m/sec^2

and

b)

T=2.2g+2.2a=2.2g+2.2×1.1g5.5T=2.2g+2.2a=2.2g+2.2\times \frac{1.1g}{5.5}

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

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

=2×2.64g=5.28gN=2\times 2.64g = 5.28gN


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