You are driving in your car at a constant speed. At the very top of a circular h

Question

You are driving in your car at a constant speed. At the very top of a circular hill with a radius of 39 m, you feel 1/3 as heavy as usual. What is your actual weight as you go over the top of the hill?

A. (1/3) mg, downward
B. mg, downward
C. (4/3) mg, upward
D. (2/3) mg, downward
E. (1/3) mg, upward

What is the normal force acting on you as you go over the top of the hill?

A. (2/3) mg, upward
B. (1/3) mg, upward
C. (4/3) mg, upward
D. mg, upward

What is the total force acting on you as you go over the top of the hill?

A. mg, upward
B. (1/3) mg, upward
C. (2/3) mg, downward
D. 0
E. (4/3) mg, upward

What is your acceleration as you go over the top of the circular hill??

A. v2/r, upward
B. v2/r, downward
C. mg, downward
D. mg, upward
E. 0

How fast are you moving at the top of the hill? (in m/s) A: 0.0 B: 11.3 C: 16.0 D: 19.5 E: 22.6

Explanation / Answer

(i) Weight of me = m*g

At the top of the hil, actual weight = weight / 3 = mg/3 in the downward direction.

hence, option (A) is the correct answer.

(ii) Normal force is opposite to the actual force.

hence option (B) is the correct answer.

(iii) Total balaced force = 0

hence option (D) is the correct answer.

(iv) Option (B) v^2/r is the correct answer.

(v) mv^2/r = mg/3

=> v^2/r = g/3

=> v^2 = (10*39)/3 = 130

=> v = 11.4 m/s

Hence option (B) is the correct answer.

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