Constrained Motion of a Pair of Rods

In summary, the problem involves finding the velocity of points B and C along a constrained rod, and a misunderstanding of the direction of the velocity vector at point B led to an incorrect initial answer. Clarifying the angle and direction of the velocity vector led to the correct solution of ##v_C = 4 \sqrt3## m/s.
  • #1
Viraam
66
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?
 

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  • #2
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?
 
  • #3
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.
 

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  • #4
OK. But your red vector is not in the correct direction to represent the velocity of B.
 
  • #5
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?
 
  • #6
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.
 
  • #7
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.
 

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  • #8
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.
 
  • #9
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.
 
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Likes Viraam

Related to Constrained Motion of a Pair of Rods

1. What is constrained motion of a pair of rods?

Constrained motion of a pair of rods is a physical phenomenon where two rods are connected by a hinge or joint, making them move in a restricted manner relative to each other. This can be observed in various mechanical systems such as car suspensions and door hinges.

2. How does constrained motion affect the movement of the rods?

Constrained motion limits the degrees of freedom of the rods, meaning they can only move in a specific way as determined by the type of constraint. This can result in rotational or translational motion, depending on the type of connection between the rods.

3. What are the different types of constraints in a pair of rods?

There are several types of constraints that can be observed in a pair of rods, including hinge joints, sliding joints, and fixed joints. Hinge joints allow for rotational motion, sliding joints allow for translational motion, and fixed joints restrict both rotational and translational motion.

4. How is constrained motion of a pair of rods represented mathematically?

Constrained motion of a pair of rods can be represented using equations and diagrams to illustrate the relationships between the rods and their constraints. The equations of motion can be derived using principles of mechanics such as Newton's laws and conservation of energy.

5. What are some real-world applications of constrained motion of a pair of rods?

Constrained motion of a pair of rods has many practical applications, including in mechanical systems such as car suspensions, door hinges, and robotic arms. It can also be observed in biological systems, such as the movement of joints in the human body. Understanding constrained motion is essential in designing and analyzing various engineering systems.

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