A hang glider and its pilot have a total mass equal to 120 kg. While executing a 360 degree turn, the glider moves in a circle with an 8-m radius. The gliders mass is 10 m/s.
a) what is the net force on the hang glider?
b) What is the acceleration?
To find the net force on the hang glider, we need to consider two forces acting on it: the gravitational force and the centripetal force.
a) The gravitational force on the hang glider can be found using the formula:
F_gravity = mass * acceleration due to gravity
Given that the mass of the hang glider and pilot is 120 kg and the acceleration due to gravity is approximately 9.8 m/s^2, the gravitational force is:
F_gravity = 120 kg * 9.8 m/s^2 = 1176 N
The centripetal force, which keeps the glider moving in a circle, can be obtained using the formula:
F_centripetal = mass * (velocity^2 / radius)
Given that the mass of the glider is 10 kg and the radius of the circle is 8 m, and the velocity is 10 m/s, the centripetal force is:
F_centripetal = 10 kg * (10 m/s)^2 / 8 m = 125 N
The net force on the hang glider is the vector sum of the gravitational force and the centripetal force:
Net force = F_gravity + F_centripetal
= 1176 N + 125 N
= 1301 N
Therefore, the net force on the hang glider is 1301 N.
b) The acceleration of the hang glider can be calculated using the equation:
Acceleration = Net force / mass
Given the net force as 1301 N, and the mass of the glider as 10 kg, we have:
Acceleration = 1301 N / 10 kg = 130.1 m/s^2
Therefore, the acceleration of the hang glider is 130.1 m/s^2.