What is the Change in Velocity of a Model Airplane in a Circular Motion?

[aham925925]

Homework Statement

A model airplane is controlled to fly in a horizontal circle of radius 24 metres with a constant speed of 20ms-1. An observer beneath the plane notices that the plane is flying anticlockwise. Find the magnitude of the change in velocity of the plane after:
a- a full revolution
b- a quarter of a revolution
c- a half revolution

Homework Equations

I have no idea on any equations. We haven't started the study of circular motion yet.

The Attempt at a Solution

I really don't know where to start here. I guessed that the change in velocity after a full revolution would be 0 and that was correct (displacement =0) but I am not sure on the other ones (B and C). They seem like random answers. Any ideas??

 

[Shooting Star]

After half a rev, in which direction do you thing the plane is moving?

 

[aham925925]

Well, the plane would be flying downwards..

 

[Shooting Star]

No, no, the plane is flying in a horizontal circle.

 

[aham925925]

ahh yes...see I'm not really sure what that means...which is probably part of the reason why I don't know where to start...

 

[Shooting Star]

Can you visualize a model car going round in circles on the floor? Well, the floor is a horizontal plane. Just visualize the whole thing taking place up in the air.

 

[aham925925]

hmm i see what you're getting at but i still don't know the direction that the airplane will be moving...

I thought all circles were the same...

 

[Shooting Star]

Tell me in which direction the model car would be moving on the floor after it has completed half a revolution, that is, when it is at point diametrically opposite to its starting point?

 

[aham925925]

Sorry but would it be moving in the same direction?

 

[Shooting Star]

No. Take some object at hand, pretend it's a car, and identify the front and the back -- that is to say, it'll move to the front. Then just roll or slide it along the floor in a circle like a toy car. Now see how it's moving when you have completed half the circle.

 

[aham925925]

It would always be moving forward...

I'm sorry...like i said...I haven't done circular motion yet and we have just started holidays here in Australia so i can't ask my teacher...

 

[Shooting Star]

Isn't it going in exactly the opposite direction in which it started? I mean, if it was going, say, north when it started, isn't it going exactly south now?

 

[aham925925]

ohh yes of course... ha ha thank you for that

how would you find the change in velocity now that we finally have that figured out??

 

[Shooting Star]

Tell me first, if the initial velocity was 20 m/s towards north, what is the velocity after half the revolution?

Give speed and direction.

 

[aham925925]

Well...it's not -20ms-1 because the answer at the back of the book says that it's 28ms-1 (at 135 degrees anticlockwise to original motion direction)

In order to get the answer, would you have to go about resolving vectors or anything?

 

[Shooting Star]

(It's not supposed to be -20 m/s, but -40 m/s.)

1. Have you checked the answer to the correct question?

2. Was there any other information in the problem which you have not written down? Like how much high the plane was?

 

[rl.bhat]

the answer at the back of the book says that it's 28ms-1 (at 135 degrees anticlockwise to original motion direction
This answer is for ( b) i.e for quarter revolution when the initial velocity and final velocity are perpendicular. To find the change in the velocity, vf - vi, Change the direction of the initial velocity vi and find the resultant with vf

 

[aham925925]

Yes sorry I was looking at the wrong question

So if it is traveling at 20ms-1, what would it be traveling at a quarter revolution (then you cold work out change in velocity)

So the change in velocity at half a revolution would be final velocity(-20) minus the initial velocity(20) equals -40 ms-1? Thats what the book says..

Still having trouble with the quarter revolution...

 

[Shooting Star]

Have you done cartesian vectors i, j, k?

 

[aham925925]

cartesian vectors?

nope, don't think I've heard of those before.

 

[Shooting Star]

Anyway, you have understood that the velocity becomes -20 m/s from +20 m/s, so the change is -40 m/s with respect to the the original direction. The speed remains the same.

For a quarter revolution, better wait till you do the cartesian vectors. All right?

 

[aham925925]

I just worked out my value for part b to be 28.28 ms-1 (answer at the back is 28ms-1..yay!)

I just need to find the angle now...i got 45 degrees but the book says 135 degrees (180-45)

this is the last part i need.

 

[Shooting Star]

If two st lines make an angle of x deg, then they also make an angle of 180-x deg. The angle is supposed to be measured positive in the anticlockwise direction. If you draw a diagram, you'll immdtly understand.

 

[rl.bhat]

If the plane moves in anticlockwise direction and initially towards north (vi), after quarter rotation it will be moving towards west (vf). Change in velocity = vf - vi, -vipoints towatds south. Hence the resultant is towards south-west direction. What is the angle between the north and south-west direction?

 

[aham925925]

yes, of course it would be 135 degrees as we are dealing with a change in velocity...since it is moving from a north direction to a south westerly one...the angle would have to be large like 135 degrees..

OK i have solved this problem now...Thanks everyone for your help...

 

[Shooting Star]

From not understanding how to do anything to solving it, all within one hour, that's very good.