Newton Law's of motion question

In summary, the problem involves finding the velocity of end B of a rigid rod placed between two smooth vertical walls, given that end A of the rod moves with velocity 'u' along the vertical direction. Two methods are suggested - using the relation L^2 = x^2 + y^2 and differentiating the equation to find the velocities of B and A. Ultimately, the solution relies on the fact that the relative velocity between the two ends along the rod should be 0 since the rod is rigid.
  • #1
Saitama
4,243
93

Homework Statement


The velocity of end 'A' of rigid rod placed between two smooth vertical walls moves with velocity 'u' along vertical direction. Find out the velocity of end 'B' of that rod, rod always remains in contact with the vertical walls.
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Homework Equations





The Attempt at a Solution


I have no idea where to start from.
Should i take the component of 'u' along the rod? But if so, then why should i do it?
 
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  • #2
At any instant, if x and y are the distances of B and A from the bottom of the wall, and L is the length of the rod AB, then what is the relation between x , y and L?
 
  • #3
rl.bhat said:
At any instant, if x and y are the distances of B and A from the bottom of the wall, and L is the length of the rod AB, then what is the relation between x , y and L?

Thanks for the reply rl.bhat!

[tex]L=\sqrt{x^2+y^2}[/tex]
But how this relation would help me solve the problem? :smile:
 
Last edited:
  • #4
Rl.Bhat has suggested a really good method.

Another method is that the relative velocity of the two ends along the rod should be 0.
This is because if there was relative velocity along the rod between the ends , then the rod would compress/elongate.
But we know the rod is rigid.So rel velocity should be 0.
 
  • #5
Using rl. Bhats method as u said L^2 = x^2+ y^2

Differentiate the equation.
What is dl/dt, dx/dt and dy/dt
 
  • #6
emailanmol said:
Using rl. Bhats method as u said L^2 = x^2+ y^2

Differentiate the equation.
What is dl/dt, dx/dt and dy/dt

If i differentiate the equation.
dl/dt is zero because there is no change in the length of rod as the time passes.
dx/dt is the horizontal velocity of point B.
dy/dt is 'u'.

Thanks for the help, i have understood how to solve this problem. :smile:
 

1. What are Newton's Laws of Motion?

Newton's Laws of Motion are a set of three physical laws that describe the relationship between the forces acting on an object and its motion. They were developed by Sir Isaac Newton in the 17th century and are considered to be the foundation of classical mechanics.

2. What is the first law of motion?

The first law of motion, also known as the law of inertia, states that an object at rest will remain at rest and an object in motion will continue in motion with a constant velocity unless acted upon by an external force. In simpler terms, objects will not change their state of motion unless a force is applied to them.

3. What is the second law of motion?

The second law of motion states that the acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to its mass. This means that the greater the force applied to an object, the greater its acceleration will be. Similarly, the more massive an object is, the less it will accelerate for a given amount of force.

4. What is the third law of motion?

The third law of motion, also known as the law of action and reaction, states that for every action, there is an equal and opposite reaction. This means that when one object exerts a force on another object, the second object will exert an equal and opposite force back on the first object.

5. How do Newton's Laws of Motion apply to everyday life?

Newton's Laws of Motion can be seen in everyday life, such as when a car accelerates forward, a person jumps off the ground, or a ball rolls down a hill. These laws also have practical applications in various fields, including engineering, physics, and sports. Understanding these laws can help us predict and explain the behavior of objects in motion.

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