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.