Download Practice questions for centripetal motion

Practice Questions for Centripetal Motion
1. In the Bohr-Rutherford model of the hydrogen atom, the electron, of mass
9.1×10-31kg, revolves around the nucleus. The radius of the orbit is 5.3×10-11m
and the period of revolution of the electron around the nucleus is 1.5×10-16s.
a) Find the magnitude of the acceleration of the electron.
b) Find the magnitude of the electric force acting on the electron.
2. James Bond is trying to escape in a car with mass 432kg moving at 160km/h.
He is approaching a corner that forms part of a circle of radius 15.0m. The
force of static friction is μs = 0.27. Will he be able to make the turn without
sliding?
3. A chestnut of mass 10g is tied to a 1.3 m long string is being swung in a vertical
circle. The chestnut makes 10 full rotations in 6.2 seconds. The radius is 0.55m.
a) What is the tension in the string at the top? What is the tension at the
bottom?
b) At what speed should you swing the chestnut in order to have zero tension
at the top (so that gravity is doing all the work at the top)?
4. A roller coaster has a circular loop with radius 20.4m. How fast should the cars
go so that the passengers feel a normal force of 2.5mg at the top (where m is
the mass of the passenger)?
5. A 77kg student is riding a Ferris Wheel of radius 67m that makes one rotation
every 65 seconds.
top
far right
bottom
FN
FN
FN
fs
FG
FG
*I chose positive direction upwards*
FG
a) What is the student’s velocity at the top?
b) What is the normal force of the seat on the student at the top?
c) What is the normal force of the seat on the student at the top?
d) What force is acting on the student at the far right, to accelerate him
towards the centre?
6. An 82kg student rides a Ferris Wheel. At the top, the normal force of the seat
on him is 620N. What will the normal force be if the velocity is doubled?
7. A car of mass 938kg travels around a banked curve of radius 91m. The
banking is at an angle of 19° to the horizontal. The coefficient of static friction
between the road and the tires is 0.32.
a) What forces provide the centripetal acceleration? What constant speed
must the car maintain to travel safely around the curve?
b) How does the required speed for a more massive vehicle, such as a truck,
compare with the speed required for this car?
8. A child with mass 35.1kg is swinging on a swing. The circular path of the swing
has a radius of 3.67m. At the lowest point, the tension in each of the chains is
205N. What is the child’s speed at this point?
9. A yo-yo on a frayed string is swinging in a vertical circle. Where is the most
likely place for the yo-yo to be when the string breaks?
10. What happens to the acceleration if the radius is doubled and the period
remains the same?
.
11. What happens to the acceleration if the radius is doubled and the velocity
remains the same?
12. What happens to the acceleration if the velocity is doubled?
13. A plane is flying in a vertical loop of radius 2.1km. If the air exerts a force of 0N on
the plane at the top of the loop, what is the plane’s speed?