1. ## Hard A-Level Question

A particle of mass 4kg rest on a smoothplane inclined at 60(degrees) to the horizontal. The particle is attached to one end of a light inelastic string which passes over a fixed smooth pulley at the top of the plane and carried a particle of mass 2kg at the other end.
Find
a)the acceleration of the system
b)the tension in the string

Thanks

2. Originally Posted by helpishere
A particle of mass 4kg rest on a smoothplane inclined at 60(degrees) to the horizontal. The particle is attached to one end of a light inelastic string which passes over a fixed smooth pulley at the top of the plane and carried a particle of mass 2kg at the other end.
Find
a)the acceleration of the system
b)the tension in the string

Thanks

$\displaystyle F_1=m_1g \sin(\theta)-T=m_1a$

$\displaystyle F_2=T-m_2g=m_2a$

Since the acceleration of the system is constant we can solve the above equations for "a" and set them equal to each other.

$\displaystyle g\sin(\theta)-\frac{T}{m_1}=\frac{T}{m_2}-g$

We can clear the fractions by multiplying by $\displaystyle m_1m_2$

$\displaystyle m_1m_2g\sin(\theta)-m_2T=m_1T-m_1m_2g$

$\displaystyle m_1m_2g(1+\sin(\theta))=(m_1+m_2)T$

$\displaystyle T=\frac{m_1m_2(1+\sin(\theta))}{m_1+m_2}$

Just plug in and finish from here.

I hope this helps and good luck.