Velocity of the center of mass in constrained motion

In summary: Consider the triangle APO (where O is the point at the bottom right corner). What shape would you call it? What does that tell you about the distance OP?The triangle is right-angled. The distance OP is half the length of the hypotenuse.
  • #1
Prabs3257
65
4
Homework Statement
In the figure shown A and B are two blocks of mass 5 kg each they are restraint to move in horizontal and vertical direction respectively as shown in the figure they are connected by a rigid massless rod as shown in the figure P is the midpoint of the rod when the velocity of B E is 4 upwards then the speed of of p at this instant is
Relevant Equations
Vcom = m1v1+m2v2/m1+m2
I tried getting the velocity of a which by using constraint came out to be 3 and by using the eqn for vcom i got the ans as 3.5 i just want to confirm is this the correct answer
 

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  • #2
I don't think you have the right answer. Write an equation for the position of A as a function of the position of B. Then find the velocity of A as a function of the velocity of B. How is the horizontal velocity component of P related to the velocity of A? How is the vertical velocity component of P related to the velocity of B?
 
  • #3
tnich said:
I don't think you have the right answer. Write an equation for the position of A as a function of the position of B. Then find the velocity of A as a function of the velocity of B. How is the horizontal velocity component of P related to the velocity of A? How is the vertical velocity component of P related to the velocity of B?
is the ans 2.5 coz i think i got the vcom wrong but now if we like resolve the component of vcom in x and y and calculate vcomx and vcomy seperately and just take the resultant i think then it should be correct??
 
  • #4
Prabs3257 said:
is the ans 2.5 coz i think i got the vcom wrong but now if we like resolve the component of vcom in x and y and calculate vcomx and vcomy seperately and just take the resultant i think then it should be correct??
Yes, 2.5 m/s. But the question should not describe this as a velocity - it is a speed. For velocity a direction should also be specified. Can you see what the direction would be? Hint: consider the distance from P to the origin.
 
  • #5
haruspex said:
Yes, 2.5 m/s. But the question should not describe this as a velocity - it is a speed. For velocity a direction should also be specified. Can you see what the direction would be? Hint: consider the distance from P to the origin.
I don't know the direction can you please explain it to me
 
  • #6
Prabs3257 said:
I don't know the direction can you please explain it to me
What is the locus of P?
 
  • #7
haruspex said:
What is the locus of P?
I am guessing maybe its a straight line
 
  • #8
Prabs3257 said:
I am guessing maybe its a straight line
Try googling "trammel of archimedes" and watch how the center of mass moves.
 
  • #9
Prabs3257 said:
I am guessing maybe its a straight line
Consider the triangle APO (where O is the point at the bottom right corner). What shape would you call it? What does that tell you about the distance OP?
 

FAQ: Velocity of the center of mass in constrained motion

1. What is the center of mass?

The center of mass is a point in a system of objects or particles where the total mass of the system is considered to be concentrated. It is also the point at which the system can be balanced on a pivot without any external forces acting on it.

2. What is constrained motion?

Constrained motion refers to the movement of an object or system that is restricted or limited in some way. This can be due to physical barriers, forces, or other factors that prevent the object or system from moving freely in all directions.

3. How is the velocity of the center of mass calculated?

The velocity of the center of mass in constrained motion can be calculated using the principle of conservation of momentum. This states that the total momentum of a system remains constant unless acted upon by an external force. The velocity of the center of mass can be found by dividing the total momentum of the system by its total mass.

4. Why is the velocity of the center of mass important in constrained motion?

The velocity of the center of mass is important in constrained motion because it can help us understand the overall movement and behavior of a system. It allows us to analyze how external forces and constraints affect the motion of the system as a whole, rather than individual components.

5. How does the velocity of the center of mass change in different types of constrained motion?

The velocity of the center of mass can change in different ways depending on the type of constrained motion. In some cases, it may remain constant, while in others it may vary or oscillate. The specific changes in velocity will depend on the constraints and forces acting on the system.

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