Velocity of the center of mass in constrained motion

[Prabs3257]

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

 

[tnich]

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?

 

[Prabs3257]

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??

 

[haruspex]

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.

 

[Prabs3257]

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

 

[haruspex]

I don't know the direction can you please explain it to me

What is the locus of P?

 

[Prabs3257]

What is the locus of P?

I am guessing maybe its a straight line

 

[jbriggs444]

I am guessing maybe its a straight line

Try googling "trammel of archimedes" and watch how the center of mass moves.

 

[haruspex]

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?