Question

a) Patrons on the midway ride called the Rotor stand with their backs against the wall of a revolving cylinder, while the floor drops away from beneath them. To keep from falling, they require a centripetal acceleration of about 25 m/s2. If the rotor has a diameter of 5.0 m, with what minimum frequency does it revolve.

Input your answer in terms of HZ or 1/s but do not include the unit in your answer. Round to one decimal place.

b) A 2.00 kg stone is whirled in a circle by a rope 4.00 m long, completing 5 revolutions in 2.00 s. Calculate the tension in the rope if the stone is rotated horizontally on a smooth frictionless surface.

Input your answer in Newtons but do not include the unit in your answer.

c) For the statement below indicate whether or not it represents a situation where work is done. In the answer box use a (W) if you think work is being done and a (NW) if there is no work being done.

An airbag in a car is deployed and slows down a person in the car during an accident where the car hits a light standard at an intersection.

d) An object has a velocity of 4.0 m/s, [E]. If the velocity of the object becomes 8.0 m/s, [E] then the:

I. momentum of the mass is doubled

II. momentum of the mass is four times as great

III. kinetic energy of the mass is doubled

IV. kinetic energy of the mass is four times as great.

The true statements are:

Select one:

II and IV

I and IV

III and IV

II and III

Answer 1

a) The centripetal acceleration is given as:

where, omega is the angular velocity with which the object is rotating

and r is the radius

Substituting values:

b) The tension in the rope is equal to the centripetal force:

c) No work is getting done in the situation since, after the collision the car comes to a complete stop and no further displacement of car under the impact force takes place.

d) The momentum of an object is given by:

So, if the velocity is doubled, the momentum also doubles.

The kinetic energy of an object is given by:

So, if the velocity of the object is doubled, the kinetic energy becomes 4 times.

So, the correct option is: B) I and IV.