PROBLEMS
1. A car is driving around a skid pad on a test track, which is a circular path to test how well a car can grip the road while turning. It manages to round a 700 foot radius skid pad with a lateral (centripetal) acceleration of 1.07g (multiples of gravitational acceleration). How fast is the car going?
2. A 200 gram mass hangs from a 0.70m long string. The mass is made to rotate while tracing out a circle in the horizontal plane at 1.0m/s. What angle does the string make with respect to vertical. Hint: If you get to a place where you don't think you can solve the math, then either keep trying (it's possible by hand) or plot the function you end up with to find its roots.
3. A plane is traveling at 300 m/s at constant altitude with a banking angle of 5.0 degrees. What is the radius of the turn it is making.
4. If a car is going 3.0m/s slower than the limit from problem number 1, at what maximum rate can the driver speed up by pressing the accelerator without causing a slide.
5. How fast must a rollercoaster be traveling along a track in order for passengers to go inverted and feel momentary weightlessness if the loop has a radius of 12.0m?
6. A motorcycle rounds a banked turn of 7% with a radius of 85m. If the friction coefficient between the tires and the road surface is 1.2 and the mass of the motorcycle with rider is 260 kg, how fast can the motorcycle round the turn? Assume g=9.8m/s2.
7. If a planet orbits twice as far from the sun as earth does, what is its orbital period in earth years?
8. An amusement park ride is made of a giant cylinder with its axis perpendicular to the ground - like a giant soda can. Occupants go inside the cylinder as it begins to spin. At a high enough spin rate the occupants are stuck on the walls and don't slide down even if they lift their feet. Suppose and the cylinder's radius is 8.0m. What angular velocity is needed to allow occupants to stick to the walls while seemingly defying gravity?
9. What centripetal acceleration do we undergo at the equator with respect to earth's center on account of its daily rotation about its axis? The radius of earth is
10. What centripetal acceleration do we undergo with respect to the sun on account of earth's orbit around the sun. Assume it's a circular orbit of radius
ANSWERS
1. 47.3 m/s (using g=9.8m/s2)
2. 21.6 degrees (using g=9.8m/s2)
3. 103,000 m = 103km
4. (using g=9.8m/s2)
5. 11 m/s
6. 34m/s
7. 2.83 yr
8. 1.75 rad/s
9.
10.