Kinematics problem — Calculating displacements around a circle

[SSG-E]

Homework Statement

Radius = 7 m
Distance covered at point A = 2 m
Distance covered at point B = 25 m
Find the displacement of the object from:
a. Initial position to point A
b. Intial position to point B

Relevant Equations

d = 2r

 

[Lnewqban]

What does the phrase "distance covered" means in this problem?

 

[SSG-E]

What does the phrase "distance covered" means in this problem?

It was just written in the book. All I have to do is find displacement from initial position to A and from initial position to B

 

[Lnewqban]

It was just written in the book. All I have to do is find displacement from initial position to A and from initial position to B

How would you do that?
I believe that some information is missing.

 

[etotheipi]

I assume from the numbers given that the thing is walking around the perimeter of the circle, and the distance covered is the arc length traversed.

If the initial point is denoted O, then the displacements $\mathbf{OA}$ and $\mathbf{OB}$ will be vectors. You will need to use the equations for arc length and the cosine rule to determine the magnitudes of these.

 

[SSG-E]

I assume from the numbers given that the thing is walking around the perimeter of the circle, and the distance covered is the arc length traversed.

If the initial point is denoted O, then the displacements $\mathbf{OA}$ and $\mathbf{OB}$ will be vectors. You will need to use the equations for arc length and the cosine rule to determine the magnitudes of these.

how?

 

[etotheipi]

how?

I can give you the formulae, but I won't do it for you . The length of an arc which subtends an angle $\theta$ is $s = r\theta$, whilst the cosine rule you probably know.

Draw some triangles!

 

[SSG-E]

I can give you the formulae, but I won't do it for you . The length of an arc which subtends an angle $\theta$ is $s = r\theta$, whilst the cosine rule you probably know.

Draw some triangles!

As chord OA = displacement; therefore chord length=displacement = 1.99 m
Is it correct?

 

[etotheipi]

That looks good.

How about part 2? Make sure to be careful with your angles!

 

[SSG-E]

That looks good.

How about part 2? Make sure to be careful with your angles!

will a triangle also be constructed in part b?

 

[etotheipi]

will a triangle also be constructed in part b?

Sure! If O is the initial position and C the centre, try considering the triangle defined by the edges OC, OB, BC.

 

[SSG-E]

Sure! If O is the initial position and C the centre, try considering the triangle defined by the edges OC, OB, BC.

Displacement = 13.7 m Is this correct?

 

[etotheipi]

I think that's also correct, yes.

Technically if it asks you for the displacement, you should establish a coordinate system and write out the components. I don't know whether this is required for your assignment.

 

[SSG-E]

I think that's also correct, yes.

Technically if it asks you for the displacement, you should establish a coordinate system and write out the components. I don't know whether this is required for your assignment.

Yes its also required how do i do that?

 

[etotheipi]

Then suppose you establish a Cartesian coordinate system with the $\hat{x}$ vector horizontal. You will need to first work out what angle each vector makes with the horizontal.

 

[Lnewqban]

Just for future alike assignments:
https://en.wikipedia.org/wiki/Law_of_cosines#Applications

 

[SSG-E]

Then suppose you establish a Cartesian coordinate system with the $\hat{x}$ vector horizontal. You will need to first work out what angle each vector makes with the horizontal.

Yes I get it. That is all for my assignment. Thanks for the help ; )