Question

A small block of mass 100 g moves with uniform speed in a horizontal circular groove, with vertical side walls of radius 25cm. If the block takes 2.0 s to complete one round, find the constant force by the side wall of the groove.

Answer 1

The constant force by the side wall of the groove is :- 0.2467N

• Force in the radial direction is given by MV²/R or Mω²R

• As the block takes 2 seconds to complete on complete circle ω = 2π/2 = π rad/sec
• By putting the values of mass , angular velocity and radius we get the force (0.25*π²*0.1N = 0.2467N)

Answer 2

Given:

Mass of block $m = 0.1$ kg

Radius of circle $r = 25 \times 10^{-2}$

Time $t = 2$ sec

To Find:

Constant force by the side wall of the groove,

 $F = ma$

Now find the velocity,

  $v = \frac{2\pi r }{t}$

  $v = 0.785$ $\frac{m}{s}$

But centripital acceleration is given by,

  $a = \frac{v^{2} }{r}$

  $a = \frac{(0.785)^{2} }{25 \times 10^{-2} }$

  $a = 2.46$ $\frac{m}{s^{2} }$

So force is given by,

 $F=0.1 \times 2.46$

 $F = 0.246$ N

Therefore, the constant force by the side wall of the groove is 0.246 N