132 Higher Engineering Mathematics
velocity, v =
(2.5 gr) =
(2.5)(9.8)(1500)
=
√
36750 = 191.7 m/s
and 191.7 m/s= 191.7 ×
60 × 60
1000
km/h = 690 km/h
Now try the following exercise
Exercise 60 Further problems on
centripetal force
1. Calculate the tension in a string when it is used
to whirl a stone of mass 200 g round in a horizontal circle of radius 90 cm with a constant
speed of 3 m/s.
[2 N]
2. Calculate the centripetal force acting on a
vehicle of mass 1 tonne when travelling around a bend of radius 125 m at 40 km/h. If this
force should not exceed 750 N, determine the
reduction in speed of the vehicle to meet this
requirement.
[988 N, 5.14 km/h]
3. A speed-boat negotiates an S-bend consisting of two circular arcs of radii 100 m and
150 m. If the speed of the boat is constant at
34 km/h, determine the change in acceleration
when leaving one arc and entering the other.
[1.49 m/s 2 ]