A force of 750N keeps a 70kg pilot in circular motion if he is flying a small plane at 35 m/s in a circular path. What is the radius of the circular path?

Ac = centripetal acceleration inward = v^2/R

Finward = m Ac
so
750 = 70 (35)^2 / R

To determine the radius of the circular path, we can use the formula for centripetal force:

F = (m * v^2) / r

Where:
F is the centripetal force
m is the mass of the pilot
v is the velocity of the plane
r is the radius of the circular path

From the problem, we know that:
F = 750N
m = 70kg
v = 35m/s

We can rearrange the formula to solve for r:

r = (m * v^2) / F

Substituting the given values:

r = (70kg * (35m/s)^2) / 750N

Calculating this:

r = (70 * 1225) / 750

r ≈ 114.67 meters

Therefore, the radius of the circular path is approximately 114.67 meters.

To find the radius of the circular path, you can use the centripetal force formula:

Fc = (mv^2) / r

Where:
Fc is the centripetal force
m is the mass of the pilot
v is the velocity of the plane
r is the radius of the circular path

Now, let's plug in the given values:

Fc = 750N
m = 70kg
v = 35 m/s

750N = (70kg * (35 m/s)^2) / r

To solve for r, we can rearrange the formula:

r = (m * v^2) / Fc

Substituting the values:

r = (70kg * (35 m/s)^2) / 750N

Calculating the expression:

r = (70kg * 1225 m^2/s^2) / 750N

r = 171500 m^2/kg/N / 750N

r ≈ 228.67 meters

Therefore, the radius of the circular path is approximately 228.67 meters.