Skip to main content

Updates ...

Visit the website for latest posts, courses, admission & more.

For guest/sponsored article(s), please check this link.

System of Masses $m_1 + m_2 + m_3 $

Three masses $m_1 , m_2 , m_3 $ kept on a smooth horizontal surface under the influence of force F have got certain acceleration (refer figure). Find the force that mass $m_1$ exerts on mass $m_2$.


Let a be the acceleration.

Taking $m_1 + m_2 + m_3 $ as system,

$F = (m_1 + m_2 + m_3)a$

$\Rightarrow a = \frac {F}{m_1 + m_2 + m_3 }$

Let N be the force that $m_1 $ exerts on $m_2 $. Taking $m_2 + m_3$ as system,

$N = (m_2 + m_3 ) a$

$\Rightarrow N = F. \frac {m_2 + m_3 }{m_1 + m_2 + m_3 } $

Interestingly, as $m_1 \to 0$, $N \to F$

Popular posts from this blog

A man starts walking from the point P (-3, 4) ....

A man starts walking from the point P (-3, 4), touches the x-axis at R, and then turns to reach at the point Q (0, 2). The man is walking at a constant speed. If the man reaches the point Q in the minimum time, then $50 [(PR)^2 + (RQ)^2 ]$ is equal to _ _ _ _ . Solution For time to be minimum at constant speed, the directions must be symmetric. In other words, the angles made by PR and RQ with the vertical must be the same just like in the law of reflection in optics. $tan \theta = \frac {MP}{MR} = \frac {NQ}{NR} $ $\Rightarrow \frac {3-r}{4} = \frac {r}{2}$ $\Rightarrow r=1 $ So, $R \equiv ( - 1,0)$ Now, $50(PR^2+RQ^2)=50[(4+16)+(1+4)]=1250$