You plan to fly a model airplane of mass 0.655 kg that is attached to a horizontal string. The plane will travel in a horizontal circle of radius 5.50 m. (Assume the weight of the plane is balanced by the upward "lift" force of the air on the wings of the plane.) The plane will make 1.15 revolutions every 4.50 s. (a) Find the speed at which you must fly the plane. m/s (b) Find the force exerted on your hand as you hold the string (assume the string is massless). N
angular speed = 2 pi(1.15/4.5) = omega
v = omega * r = omega * 5.50
F = m a = m v^2/r = .655(v^2)/5.50
To find the speed at which you must fly the plane, we can use the formula for the speed of an object in circular motion:
v = (2πr) / T
where v is the velocity (speed), r is the radius of the circle, and T is the time for one revolution.
(a) First, let's calculate the time for one revolution using the given information that the plane makes 1.15 revolutions every 4.50 seconds:
T = 4.50 s / 1.15 = 3.913 s
Now, we can substitute the values into the formula to calculate the speed:
v = (2π * 5.50 m) / 3.913 s = 8.86 m/s
So, the speed at which you must fly the plane is 8.86 m/s.
(b) To find the force exerted on your hand as you hold the string, 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 plane, v is the velocity, and r is the radius of the circle.
Since the weight of the plane is balanced by the upward "lift" force, the only force acting on the plane is the centripetal force. Therefore, the centripetal force exerted on the plane is equal to the force exerted on your hand.
Substituting the given values, we can calculate the force:
F = (0.655 kg) * (8.86 m/s)^2 / 5.50 m = 10.64 N
So, the force exerted on your hand as you hold the string is approximately 10.64 Newtons.