Question

1. I want to catapult a 10-N cannonball off a lever attached to a fulcrum. I place the lever so the cannonball is at the lever edge 9 meters from the fulcrum. If I weight 600 N, what’s the minimum lever arm on my side needed to successfully launch the cannonball?

   1. 9 meters

   2. 540 meters

   3. 15 centimeters

   4. 11 centimeters

   5. 6 meters

Answer 1

Given that fulcrum is in balanced position, So that means

Net torque on fulcrum = 0

Clockwise torque due to catapult = Counterclockwise torque due to person

We know that torque = rxF = r*F*sin

  = 90 deg, in this case since angle between rotation axis and force is 90 deg

sin 90 deg = 1

So,

r1*F1 = r2*F2

F1 = Weight of catapult = 10 N,

r1 = distance of catapult from fulcrum = 9 m

F2 = Weight of person = 600 N

r2 = distance of person from fulcrum = r1*(F1/F2)

r2 = 9*(10/600) = 9/60 = 0.15 m = 15 cm

r2 = 15 cm = distance of person from fulcrum = lever arm on person's side

Correct option is C.

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