Higher Engineering Mathematics, Sixth Edition

132 Higher Engineering Mathematics

velocity,v=

√

( 2 .5gr)=

√

( 2. 5 )( 9. 8 )( 1500 )

=

√

36750 = 191 .7m/s

and 191.7m/s= 191. 7 ×

60 × 60

1000

km/h=690km/h

Now try the following exercise

Exercise 60 Further problems on

centripetal force

1. Calculate the tension ina stringwhen it is used
   to whirl a stone of mass 200g round in a hor-
   izontal circle of radius 90cm with a constant
   speedof3m/s. [2N]
   2. Calculate the centripetal force acting on a
   vehicle of mass 1 tonne when travelling aro-
   und a bend of radius 125m at 40km/h. If this
   force should not exceed 750N, determine the
   reduction in speed of the vehicle to meet this
   requirement.
   [988N, 5.14km/h]
   3. A speed-boat negotiates an S-bend consist-
   ing of two circular arcs of radii 100m and
   150m. If the speed of the boat is constant at
   34km/h, determine the change in acceleration
   when leaving one arc and entering the other.
   [1.49m/s^2 ]