Question

A track consists of two circular points ABC and CDE of equal radius 100 m and joined smoothly as shown. Each part subtends a right angle at its centre. A cyclist weighing 100 kg together with the cycle travels at a constant speed 1 km h^-1 on the track. Find the normal force between the road and the cycle just before and just after the cycle crosses C.

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

Answer 1

Answer: (D)

682, 732 N

Answer 2

just before crossing C

N = mg cos 45 – mv²/r

= 100 × 10 × .707 - $\frac{100 \times 5^{2}}{100}$ = 682 N

just after crossing CN = mg cos 45 + $\frac{mv^{2}}{r}$ = 707 + 25

= 732 N