Newton Laws of motion question

In summary, the conversation discusses a physics problem involving a rod AB fixed on the ground, a moving block, and the velocity of end B when the rod is at a 60° angle. The problem is solved by differentiating the equation with respect to time, but there was an error in the solving process which was corrected. The final correct answer is (dy/dt)=-1, which represents the vertical component of the velocity of end B.
  • #1
Saitama
4,243
93

Homework Statement


A rod AB is shown in figure. End A of the rod is fixed on the ground. Block is moving with velocity √3 m/s towards right. The velocity of end B when rod makes an angle of 60o with the ground.
90yf4g.jpg




Homework Equations





The Attempt at a Solution


I assumed that at any instant the distance of A from block is x and distance of B from ground is y. The length of rod is l.
l^2=x^2+y^2
Differentiating with respect to time.
0=2x(dx/dt)+2y(dy/dt)
y=xtan(60o)
dx/dt=√3 m/s
Solving, i get

(dy/dt)=-3 m/s
But that's not correct, the answer says its 2 m/s. I don't seem to get where i am wrong.
Any help is appreciated. :smile:

Thanks!
 
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  • #2
Hi Pranav! :smile:

Pranav-Arora said:
y=xtan(60o)
dx/dt=√3 m/s
Solving, i get

(dy/dt)=-3 m/s

Are you sure about that step?

Recheck your solving,

[tex]0 = 2x\sqrt{3} + 2\sqrt{3} x \frac{dy}{dt}[/tex]
 
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  • #3
Infinitum said:
Hi Pranav! :smile:

Are you sure about that step?

Recheck your solving,

[tex]0 = 2x\sqrt{3} + 2\sqrt 3 x \frac{dy}{dt}[/tex]

Oh yes, sorry, my mistake, i wrote tan60=1/√3. :tongue:

But now i get (dy/dt)=-1.
 
  • #4
Pranav-Arora said:
Oh yes, sorry, my mistake, i wrote tan60=1/√3. :tongue:

But now i get (dy/dt)=-1.

Yes. That's correct. So, what's the velocity of the end B of the rod now?
 
  • #5
Infinitum said:
Yes. That's correct. So, what's the velocity of the end B of the rod now?

Isn't (dy/dt) the velocity of the end B?
 
  • #6
Pranav-Arora said:
Isn't (dy/dt) the velocity of the end B?

That is the vertical component of B's velocity :wink:
 
  • #7
Infinitum said:
That is the vertical component of B's velocity :wink:

Ah i get it, thanks for the help Infinitum!
I shouldn't be studying Physics at midnight.
 
  • #8
Pranav-Arora said:
Ah i get it, thanks for the help Infinitum!
:smile:
I shouldn't be studying Physics at midnight.

Good night, then :wink:
 
  • #9
Good night, then :wink:
Hehe, no, i am posting one more question and then i will go to sleep. :D
 

1. What are Newton's three laws of motion?

Newton's three laws of motion are:
1. An object at rest will remain at rest, and an object in motion will remain in motion at a constant velocity, unless acted upon by an external force.
2. The force acting on an object is equal to its mass multiplied by its acceleration (F=ma).
3. For every action, there is an equal and opposite reaction.

2. How do these laws apply to everyday life?

These laws can be seen in everyday life in many ways. For example, the first law can be observed when a book on a table remains at rest until someone picks it up or an external force, such as wind, knocks it off. The second law can be seen when a car accelerates when pressing down on the gas pedal. The third law is evident when jumping off a diving board and feeling the force of the water pushing back up.

3. What is the significance of these laws in the field of science?

Newton's laws of motion are fundamental principles in the field of physics and have greatly contributed to our understanding of how objects move and interact with each other. They are used in various scientific fields, such as engineering, astronomy, and biomechanics, to explain and predict the behavior of objects and systems.

4. Can these laws be broken or disproven?

No, Newton's laws of motion have been extensively tested and have been found to accurately describe the behavior of objects in motion. However, they are not applicable in extreme situations, such as at the atomic or subatomic level, or in situations involving very high speeds or massive objects, where the laws of quantum mechanics and relativity must be used instead.

5. Who was Sir Isaac Newton and how did he discover these laws?

Sir Isaac Newton was an English physicist and mathematician who lived from 1642 to 1727. He is widely known for his contributions to the fields of mathematics, physics, and astronomy, including the development of the laws of motion. Newton discovered these laws through his experiments and observations of the motion of objects and published them in his book "Philosophiæ Naturalis Principia Mathematica" in 1687.

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