Constrained Motion of a Pair of Rods

AI Thread Summary
The discussion revolves around the constrained motion of two rods and the calculation of velocities at points B and C. Initially, the user calculated the velocity of point B as 4 m/s but was confused about the velocity of point C, which was given as 4√3 m/s. Clarifications were made regarding the angles involved, specifically that the velocity vector at point B is perpendicular to rod AB. After addressing the angle discrepancies, the user correctly derived the relationship between the velocities, confirming that v_B cos 30° equals v_C cos 60°. The final conclusion was that the correct velocity for point C is indeed 4√3 m/s.
Viraam
Messages
66
Reaction score
2

Homework Statement


?temp_hash=1f2fdf21cbbbcf9ce9961180ca82225e.png

Homework Equations


## v = r \omega##

The Attempt at a Solution


Velocity of point B= ##v_B = 4 \times \omega = 4 ## m/s
Since the separation between B and C is constrained to be a constant, Velocity of B along rod = Velocity of C along the rod
## \Rightarrow v_B \cos \theta = v_C \cos \theta ##
## v_B = v_C = 4 ##m/s

However the answer provided is ## v_C = 4 \sqrt 3 ## m/s. Where did I go wrong?
 

Attachments

  • Capture.PNG
    Capture.PNG
    14.8 KB · Views: 466
  • ?temp_hash=1f2fdf21cbbbcf9ce9961180ca82225e.png
    ?temp_hash=1f2fdf21cbbbcf9ce9961180ca82225e.png
    14.8 KB · Views: 647
Physics news on Phys.org
Please define which angle you are denoting by ##\theta##.

Do the velocities of points B and C make the same angle with respect to rod BC?
 
TSny said:
Please define which angle you are denoting by ##\theta##.

Do the velocities of points B and C make the same angle with respect to rod BC?
Oops... Forgot to mention that. Sorry.
 

Attachments

  • Capture.PNG
    Capture.PNG
    3 KB · Views: 464
OK. But your red vector is not in the correct direction to represent the velocity of B.
 
TSny said:
OK. But your red vector is not in the correct direction to represent the velocity of B.
Ohh I get it. I took the wrong vector. Isn't the red vector supposed to be tangential to AB?
 
Viraam said:
Ohh I get it. I took the wrong vector. Isn't the red vector supposed to be tangential to AB?
##\vec {v}_ {_B}## is not tangential to rod AB. Rod AB is rotating about A.
 
TSny said:
##\vec {v}_ {_B}## is not tangential to rod AB. Rod AB is rotating about A.
What is meant to ask is if the vector ##
\vec {v}_ {_B}## at an angle of ## 90^ \circ## to AB? Like in the figure here.
 

Attachments

  • Capture.PNG
    Capture.PNG
    2.7 KB · Views: 467
Viraam said:
What is meant to ask is if the vector ##
\vec {v}_ {_B}## at an angle of ## 90^ \circ## to AB? Like in the figure here.
Yes. We would say the velocity is perpendicular to rod AB.
 
TSny said:
Yes. We would say the velocity is perpendicular to rod AB.
Thanks. I got the right answer now. The angle between the velocity vector and the rod is ##30^\circ##.
## v_B \cos 30^\circ = v_C \cos 60^\circ##
## v_C = 4 \sqrt3##
 
  • #10
Looks good.
 
  • Like
Likes Viraam
Back
Top