There is one speed vcritical at which friction is not needed to keep the car on the track. What is that speed in terms of θ and R? Express your answer in terms of the variables R, θ, and the acceleration due to gravity g.

1. jay fills a wagon with sand (about 20 kg) and pulls it with a rope 30 m along the beach. he holds the rope 25° above the horizontal. the rope exerts a 20-n tension force on the wagon. how much work does the rope do on the wagon?