A model airplane of mass 0.700 kg flies with a speed of 35.0 m/s in a horizontal circle at the end of a 66.0-m-long control wire as shown in Figure (a). The forces exerted on the airplane are shown in Figure (b): the tension in the control wire, the gravitational force, and aerodynamic lift that acts at ? = 20.0° inward from the vertical. Compute the radius, lift, and tension in the wire, assuming it makes a constant angle of ? = 20.0° with the horizontal. Use g=9.8 m/s2. Determine its lift, radius, and tension.

Over the holiday break you have an internship with an ice skating show. An ice skater will start from rest and slide down an ice-covered ramp. At the bottom of the ramp, the skater will glide around an ice-covered loop which is the inside of a vertical circle before emerging out onto the skating rink floor. For a spectacular effect, the circular loop will have a diameter of 30 feet. Your task is to determine the minimum height from the rink floor to the top of the ramp for the skater to make it around the loop. When barely making it around, the skater briefly loses contact with the ice at the top of the loop.

A model airplane of mass 0.75 kg flies in a horizontal circle at the end of  a 60 m control wire, with a speed of 35 m/s. Determine the tension in the wire if it makes a constant angle of 20 degrees with the horizontal. The forces exerted on the airplane are the pull of the control wire, its own weight, and aerodynamic lift, which acts at 20 degrees inward from the vertical as shown in the diagram

A student spins a rubber stopper, tied to a string, over his head in a horizontal circle. The radius of the circle is, r, meters and the stopper has a mass of, m, grams. The stopper has period of, T, seconds, which results in a tension, 6.3 N. If the radius of the swing was changed by a factor of 2.4, what would be the resulting tension? Give your answer to 3 sig figs (1 decimal place in this case)