The change in velocity betwen two points

[Sleve123]

Here's a question that I got in my mechanics tutorial.

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A particle travels on a semi-circular path from A to B -

The diameter being 200m, the time taken 80 seconds, Calculate:

a) its speed

b) average velocity from A to B

c) the change velocity from A to B

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Me and my lecturer agree that a) is 3.93 m/s, b) is 2.5 m/s (in the direction A to B), but we disagree on c).

My lecturer got 5 m/s and me 7.85 m/s, are we both wrong or are one of us right?


Also it would be helpful to expalin how you get to the answer (if I'm wrong).

 

[berkeman]

Here's a question that I got in my mechanics tutorial.

--------------------------------------------------------------------

A particle travels on a semi-circular path from A to B -

The diameter being 200m, the time taken 80 seconds, Calculate:

a) its speed

b) average velocity from A to B

c) the change velocity from A to B

----------------------------------------------------------------------

Me and my lecturer agree that a) is 3.93 m/s, b) is 2.5 m/s (in the direction A to B), but we disagree on c).

My lecturer got 5 m/s and me 7.85 m/s, are we both wrong or are one of us right?


Also it would be helpful to expalin how you get to the answer (if I'm wrong).

Can you explain your answer to c? And what is the direction of the change in velocity that you list?

 

[Sleve123]

Can you explain your answer to c? And what is the direction of the change in velocity that you list?

I worked it out like this:

I'm assuming that the velocity is always at a tangent to the circle (in this case a semi circle),
then the velocity at A and B, will be of the same magnitude (the speed 3.926 m/s) but in opposite directions, therefore the difference will be:

Change in velocity (from A to B) = Velocity at A - Velocity at B

but Velocity at B = - Velocity at A because they are opposite directions, therefore--->

Change in velocity (from A to B) = Velocity at A - - Velocity at A = 2 x (Velocity at A)

= 2 x 3.926 = 7.85 m/s

 

[berkeman]

I worked it out like this:

I'm assuming that the velocity is always at a tangent to the cricle (in this case a semi cirle),
then the velocity at A and B, will be of the same magnitude (the speed 3.926 m/s) but in opposite directions, therefore the difference will be:

Change in velocity (from A to B) = Velocity at A - Velocity at B

but Velocity at B = - Velocity at A because they are opposite directions, therefore--->

Change in velocity (from A to B) = Velocity at A - - Velocity at A = 2 x (Velocity at A)

= 2 x 3.926 = 7.85 m/s

That was my thought as well. However, you need to define a coordinate system in order to get the sign correct. Velocity is a vector quantity, with magnitude and direction. So the direction of the vectors in the coordinate system makes a difference.

 

[Sleve123]

That was my thought as well. However, you need to define a coordinate system in order to get the sign correct. Velocity is a vector quantity, with magnitude and direction. So the direction of the vectors in the coordinate system makes a difference.

Thanks - Yeah I've worked it out using vectors (gives the same answer), but you can see from a diagram that there is no horizontal components of velocity so I didn't bother in my working above.

I tried to explain this to him but he was having none of it, I'm on a teacher training course (I did an engineering degree and I am converting) but many on the course haven't done much maths, so I thought I was going nuts.

 

[berkeman]

Thanks - Yeah I've worked it out using vectors (gives the same answer), but you can see from a diagram that there is no horizontal components of velocity so I didn't bother in my working above.

I tried to explain this to him but he was having none of it, I'm on a teacher training course (I did an engineering degree and I am converting) but many on the course haven't done much maths, so I thought I was going nuts.

The orientation of the semicircle to the coordinate system does matter. If the coordinate system is x to the right and y pointing up to the top of the page, and the semicircle is drawn on the top half of the coordinate system, then the initial velocity is in the +y direction, and the final is in the -y direction, so the magnitude of the change is twice the initial magnitude, but the sign is negative (since it started positive, and ends negative).

 

[Sleve123]

The orientation of the semicircle to the coordinate system does matter. If the coordinate system is x to the right and y pointing up to the top of the page, and the semicircle is drawn on the top half of the coordinate system, then the initial velocity is in the +y direction, and the final is in the -y direction, so the magnitude of the change is twice the initial magnitude, but the sign is negative (since it started positive, and ends negative).

Thanks, I get it all now.