Question

A stunt pilot in an air show performs a loop-the-loop in a vertical circle of radius 3.80 103 m. During this performance the pilot whose weight is 623 N, maintains a constant speed of 2.10 102 m/s. (a) When the pilot is at the highest point of the loop determine his apparent weight in N. N (b) At what speed, in m/s, will the pilot experience weightlessness

Answer 1

The apparent weight of the pilot would be 619.48 N and the speed he would experience at weightlessness is 192. 97 m/s

What is apparent weight?

Apparent weight is a property of object that co-relates to the heaviness of the object.

It differs from the weight of an object as a result of the in-balance between the force acting on the object and an equal but opposite force

How to calculate the apparent weight

Formula:

Apparent weight = Real weight (mg) - m v∧2 ÷ r

Where m = mass

g = acceleration due to gravity = 9.8 m/s²

v = constant velocity = 2. 10 × 10∧2 m/s

r = radius = 3.80 × 10∧3 m

Note that weight = mg

m = weight ÷ g = 623 ÷ 9.8 = 63. 57 kg

a. Apparent wieight = 623 - (63. 57 × 2.10 × 10∧2 × 2.10 × 10∧2) ÷ 3.80 × 10∧3)

= 623 - (63.57 × 210) ÷ 3800

= 623 - 13377 ÷ 3800

= 623 - 3. 52

= 619.48 N

b. At weightless, weight = 0

Speed, V = √g× r = √ 9.8 × 3800 = √37,240 = 192. 97 m/s

Hence, The apparent weight of the pilot would be 619.48 N and the speed he would experience at weightlessness is 192. 97 m/s

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