Circular Motion Questions (energies, forces, angular velocities, etc.)

[lpettigrew]

Homework Statement

Hello, I have several multiple choice questions I have found for revision purposes but I am not entirely certain whether I have solved them suitably. I have attempted to give reasoning, where applicable, for my choice of selection also. For most questions I have answered them fully, I would be very grateful if anyone could check my calculations nonetheless and verify that I have used the appropriate formula. Sometimes I feel a little uncertain about rearranging formula to suit the information given which is why I would be very grateful of any help.

Question 1; A body of mass 2 kg is travelling with twice the momentum of a body of mass 4 kg. Find the ratio of the kinetic energy of the first body to the kinetic energy of the second body?
a. 2:1
b.8:1
c. 1:2
d. 4:1

Question 2;
A body moves in a circle at constant speed, and is acted upon by several forces. Which is true?
a. There is a centripetal force towards the centre in addition to the forces acting.
b. The centrifugal force is balanced by the resultant of these forces
c. The resultant of all these forces is the centripetal force making the body accelerate towards the centre.
d. The centripetal force is balanced by the resultant of all these forces

Question 3:
A rocket is recorded to eject 800 kg of gases each second, which leave at a speed of 500 m/s relative to the rocket. This causes a force on the rocket of:
a. 1.6 N
b. 50,000 N
c. 400,000N
d. 100,000,000 N

Question 4;
Spinning at 33 revolutions per minute, a disc's angular velocity is:
a. 3.45 rad/s
b. 1.73 rad/s
c. 21 rad/s
d. 0.55 rad/s

Question 5:
A 1000 kg car begins to turn on a bend of radius 40 m with a speed of 20 m/s. Find the resultant force on the car.
a. 10,000N towards the centre of the bend
b. 500 N towards the centre of the bend
c. 10,000 N towards the centre of the bend
d. 500 N away from the centre of the bend.

Question 6:
A boy is playing on a roundabout sitting 0.8 m from the centre, he has an angular velocity of 1.5 rad/s. Find the boy's acceleration towards the centre of the roundabout.

a.1.2 m/s^2
b. 1.9 m/s^2
c. 2.8 m/s^2
d. 1.8 m/s^2

Thank you to anyone who replies.

Relevant Equations

a= rω^2
F=ma=mv^2/r

Question 1:
I believe that the ratio would be b. 8:1 because by combining the formula for kinetic energy and momentum the expression Ek=p^2/2m can be obtained.
Thus, for a body of mass 2kg with twice the momentum:
Ek=2^2/2*2=1
For a body of mass 4kg with half the momentum:
Ek=1^2/2*4=1/8
Therefore, the ratio of the kinetic energy of the first body to the second is 1:1/8 which multiplying both sides by 8 would be 8:1.

Question 2:
I believe that for a body moving at constant speed in a circular path it will experience an acceleration toward the centre of the circular path; this acceleration is called a centripetal acceleration and is provided by a centripetal force. Centripetal force is the resultant force toward acting at right angles to the direction of motion, towards the centre of the circle. Thus, I think the correct answer is c.

Question 3:
F=ma=mv^2/r
Since v=2πr/T this becomes F=m(2πr/T)^2/r
Hence, F=m4π^2r/T^2

However, perhaps the above formula is not required. I do not know how to find the force without knowing the radius, or if not the radius the centripetal acceleration? This is where I am a little stuck.

Question 4:
Well, ω=2πf= 2*π*33/60
ω=3.455...
ω=3.45 rad s^-1 (answer a I believe)

Have I used the correct formula here? I have divided the number of rotations by 60 to find the number of revolutions per second.

Question 5:
F=mrω^2=mv^2/r
F=1000*20^2/40
F=10,000 N towards the centre of the bend (option c)

Question 6:
Centripetal acceleration, a, = rω^2=v^2/r
a=0.8*1.5^2
a=1.8 m/s^2 (option d)

 

[PeroK]

1) Ok, 2) Ok

3) It's a funny rocket that moves in a circle.

4) Ok, 5) Ok, 6) Ok

 

[lpettigrew]

1) Ok, 2) Ok

3) It's a funny rocket that moves in a circle.

4) Ok, 5) Ok, 6) Ok

Thank you for your reply @PeroK I really appreciate it.

3. Haha. I think I was so taken by the theme of circular motion questioning that I neglected to see this was not applicable to the situation of a rocket.
So, F=ma
F=800*500
F=400,000 N (option c)