Answer to Question #176115 in Mechanics | Relativity for Akinola Agboola

Question

A body of mass 600g moves round a track of area 154cm² in 4secs. Calculate the total time taken to make expend 0.25KJ of energy

Answer 1

m = 600 gm = 0.6 Kg

t = 4 sec.

Area of circular track = 154 sq. cm

pi r² = 154

$r^2 = \frac{154}{pi}$

$r^2 = \frac{154}{3.14}$

r = 7 cm. = 0.07 m

Distance covered = perimeter of circular track = 2 pi r = 2 x 3.14 x 0.07 = 0.44 m

$Speed = \frac{Dist}{time} = \frac{0.44}{4} = 0.11 m/sec.$

$Kinetic Energy = \frac{1}{2} m v^2$

KE per unit round in 4 sec. = $\frac{1}{2} m v^2 = \frac{1}{2} 0.6 x 0.11^2 = 0.00363 J$

$No. of rounds for 0.25 KJ = \frac{0.25 * 1000}{0.00363} = 68870.52$

$Time for 68870.52 rounds = \frac{68870.52}{4} = 17217.6 seconds.$

Final Answer:

Total time taken to make expend 0.25KJ of energy = 17217.6 seconds