1. A car with mass 651 kg passes over a bump in a road that follows the arc of a circle of radius 38.8 m as shown.
2. What is the maximum speed the car can have as it passes the highest point of the bump before losing contact with the road? The acceleration due to gravity is 9.8 m/s2.
3. A bucket full of water is rotated in a vertical circle of radius 0.759 m (the approximate length of a person's arm). What must be the minimum speed of the pail at the top of the circle if no water is to spill out?
At the Six Flags Great America amusement park in Gurnee, Illinois, there is a roller coaster that incorporates some of the latest design technology and some basic physics. Each vertical loop, instead of being circular, is shaped like a teardrop (shown in the figure). The cars ride on the inside of the loop at the top, and the speeds are high enough to ensure that the cars remain on the track. The biggest loop is 35 m high, with a maximum speed of 31 m/s (nearly 69.44 mph) at the bottom. Suppose the speed at the top is 12 m/s and the corresponding centripetal acceleration is 2.3 g (where g is the free-fall acceleration).
The acceleration of gravity is 9.8 m/s2.
What is the radius of the arc of the teardrop at the top?
4. If the total mass of the cars plus people is 2638 kg, what force does the rail exert on it at the top?
5. Suppose the roller coaster had a loop of radius 17 m.
If the cars have the same speed (12 m/s) at the top, what is the centripetal acceleration at the top?
6. What is the normal force at the top in this situation?
A model airplane of mass 0.333 kg ?ies in a horizontal circle at the end of a control wire of length 33.2 m with a speed of 27.6 m/s.
The forces exerted on the airplane are the pull of the control wire, its own weight, and aerodynamic lift, which acts at 23.7o inward from the vertical as shown in the figure.
