2020 Phase-2 Laws of MotionConnected bodies with friction - pulley systems Medium Question 18 of 72 in Laws of Motion

Calculate the acceleration of the block and trolly system shown in the figure. The coefficient of kinetic friction between the trolly and the surface is 0.05. ($g=10\ m/s^2$, mass of the string is negligible and no other friction exists).

A 1.00 m/s$^2$
B 1.25 m/s$^2$
C 1.50 m/s$^2$
D 1.66 m/s$^2$

The answer is B.

Solution

For the hanging block (2 kg): $2g-T=2a$. For the trolley (10 kg) on the surface with friction: $T-\mu(10)g=10a$. Adding: $2g-\mu(10)g=12a\Rightarrow a=\dfrac{2(10)-0.05\times10\times10}{12}=\dfrac{20-5}{12}=\dfrac{15}{12}=1.25\ m/s^2$.

Concept Connected bodies with friction - pulley systems

Laws of Motion in past papers

72 questions from this chapter have appeared across 27 exam years.