Question

A track consists of two circular parts ABC and CDE of equal radius $100m$ and joined smoothly as shown. Each part subtends a right angle at its center. A cyclist weighing $100kg$ together with the cycle, travels at a constant speed of $18kmph$ on the track. Find the normal force between the road and the cycle just before and just after the cycle crosses C.

• A. $682N,682N$
• B. $732N,682N$
• C. $732N,732N$
• D. $682N,732N$

Answer 1

The correct option is D $682N,732N$

Just before crossing $C$,
$N_1=mg\cos {45}^0-\frac{{mv}^2}{r}$ = $100\times 10\times \left(.707\right)-\frac{100\times 5^2}{100}=682N$
And just after crossing $C$,

$N_2=mg\cos {45}^0+\frac{{mv}^2}{r}=707+25=732N$