A force of 750 N keeps a 70-kg pilot in circular motion if he is flying a small plane at 35m/s in a circular path.What is the radius of the circular path?
Applying F=ma towards the center of the circle
750=ma (m-mass of the pilot)
a=(v^2)/r (r- radius of the circle)
750=m(v^2)/r
r= [m(v^2)]/750
How?
To find the radius of the circular path, we can use the formula for centripetal force:
F = (m * v^2) / r
Where:
F = force (750 N)
m = mass of the pilot (70 kg)
v = speed of the plane (35 m/s)
r = radius of the circular path (unknown)
Rearranging the formula to solve for r:
r = (m * v^2) / F
Substituting the given values:
r = (70 kg * (35 m/s)^2) / 750 N
Calculating:
r = (70 * 1225) / 750
r = 17150 / 750
r = 22.87 m
Therefore, the radius of the circular path is approximately 22.87 meters.
To find the radius of the circular path, we can use the equation for centripetal force:
F = (m * v^2) / r
Where:
F = centripetal force (in Newton)
m = mass of the object (in kg)
v = velocity of the object (in m/s)
r = radius of the circular path (in meters)
In this case, the mass of the pilot (m) is 70 kg, the velocity (v) is 35 m/s, and the centripetal force (F) is 750 N. We can rearrange the equation to solve for r:
r = (m * v^2) / F
Substituting the given values:
r = (70 kg * (35 m/s)^2) / 750 N
Now we can calculate the radius:
r = (70 kg * 1225 m^2/s^2) / 750 N
r = 85750 kg·m^2/s^2 / 750 N
r = 114.33 m
Therefore, the radius of the circular path is approximately 114.33 meters.