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Standard XII

Physics

Calculation for Varying Direction

An air puck o...

Question

An air puck of mass $m_{1}$ is tied to a string and allowed to revolve in a circle of radius R on a frictionless horizontal table. The other end of the string passes through a small hole in the centre of the table, and a load of mass $m_{2}$ is tied to the string? The suspended load remains in equilibrium while the puck on the tabletop revolves.
a. Find the tension in the string.
b. Find the radial force acting on the puck.
c. Find the speed of the puck.
d. Qualitatively describe what will happen in the motion of the puck if the value of $m_{2}$ is somewhat increased by placing an additional load on it.
e. Qualitatively describe what will happen in the motion of the puck if the value of $m_{2}$ is instead decreased by removing a part from the hanging load.

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Solution

a) $T = m_{2} g$
b) $F =$ Centrifugal force $= \frac{{m V}^{2}}{r}$ .
c) $m_{2} g = \frac{m_{1} V^{2}}{r}$
$V = \sqrt{\frac{m_{2}}{m_{1}} g r}$
d) $m_{2}$ will start moving downwards and radius of $m_{1}$ will decrease.
e) $m_{2}$ will go upward and the value of $R$ will increase.

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a) T=m2gb) F= Centrifugal force =mV2r.c) m2g=m1V2r V=√m2m1grd) m2 will start moving downwards and radius of m1 will decrease.e) m2 will go upward and the value of R will increase.

a) $T = m_{2} g$
b) $F =$ Centrifugal force $= \frac{{m V}^{2}}{r}$ .
c) $m_{2} g = \frac{m_{1} V^{2}}{r}$
$V = \sqrt{\frac{m_{2}}{m_{1}} g r}$
d) $m_{2}$ will start moving downwards and radius of $m_{1}$ will decrease.
e) $m_{2}$ will go upward and the value of $R$ will increase.