Tag Archives: Laws of Motion
The two blocks, each of mass M kg, are connected …
The string between mass m and 2m is inextensible and light …
Weighing Machine in Elevator
A man inside an elevator uses weighing machine to weigh himself. With what acceleration should the elevator descend so that the weighing machine reports the weight of the man to be half of its true value?
The reading of the weighing machine depends on the force by which the machine is pressed. Let us say the machine is pressed downwards by force N. The machine will exert an equal upward force N on the man.
Let m be the mass of the man. For the man system,
mg – N = ma
$mg – \frac{{mg}}{2} = ma$
$ \Rightarrow a = \frac{g}{2}$
Pulley + Block + Rope
A uniform rope of linear mass density $\lambda $ is used to release block m with uniform acceleration a. Find the tension at a point P on the rope at a distance l from the block as shown in the figure.
Solution
Let mass m and the rope of length l above the block be the system.
Mass of rope of length $l = \lambda l$
For the system under consideration, $(m + \lambda l)g – {T_P} = (m + \lambda l)a$
$ \Rightarrow {T_P} = (m + \lambda l)(g – a)$
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 $m_2$.
Solution
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 $m_1 \to 0$, $N \to F$
Laws of Motion ~ Quote
“The laws of motion dictate that a pebble thrown upwards and a planet orbiting a star are both governed by the same principles, reminding us that the universe is interconnected and bound by a set of fundamental rules.”