An airplane is doing a vertical loop in the air. The airplane goes at a velocity of 320 and at the top of the loop, n=500N. The pilot weighs 62kg.
calc the radius of the loop
vertical loop, given: v=320, n at the top=510N, m=62kg
i don't know what eqn i use to find the radius of the loop..
again, what is n? n is not a commonly known symbol, at least here in Texas.
n is normal force
If n is the force of the seat pushing on the pilot at the top of the loop, then
n + mg = m V^2/R, the centripetal force
Solve for R. You need to state what your units of velocity are. They should be in m/s if you expect the formula to work with Newtons, kg and meters for the other terms
To find the radius of the loop, we can use the concept of centripetal force. In this case, the centripetal force is provided by the normal force. At the top of the loop, the normal force and the weight must add up to supply the necessary centripetal force.
The centripetal force is given by the equation:
F = m * v^2 / r
where F is the centripetal force, m is the mass of the pilot, v is the velocity of the airplane, and r is the radius of the loop.
At the top of the loop, the normal force (n) must equal the sum of the weight (mg) and the centripetal force (F):
n = mg + F
Given that n = 500N and m = 62kg, we can find the weight by multiplying the mass by the acceleration due to gravity (9.8 m/s^2):
mg + F = 500
62 * 9.8 + F = 500
F = 500 - (62 * 9.8)
Now, using the formula for centripetal force, we can solve for the radius:
F = m * v^2 / r
F = (62 * 320^2) / r
(500 - (62 * 9.8)) = (62 * 320^2) / r
To calculate the radius, we rearrange the equation:
r = (62 * 320^2) / (500 - (62 * 9.8))
Please substitute the values into the equation to calculate the radius of the loop.