Connected Particles

[Bucky]

Homework Statement

Two bodies A and B of equal mass m, connected by a light inextensible string, are placed on a smooth horizontal table with the string just taut. A is projected with velocity U at 45 degrees to the direction AB. Determine the impuslive tension in the string when it becomes taut.

Homework Equations

The Attempt at a Solution

Well, following from previous examples i tried to find the momentum in direction AB and perpendicular to AB.

Momentum in direction AB

mu + mu = U cos45
2mu = Ucos45
u = (Ucos45) / 2m

Momentum perpendicular to AB
mv = U sin45
v = (Usin45)/m

Impulsive Energy at A
T = mu
= (Ucos45)/2
= (U * 1/root2)/2


I think I've gotten it wrong. answer should be 1/4 m U root 2. can anyone help me out? I don't know if it's an algebra problem or (most likley) a method problem.

 

[denverdoc]

try expressing the cos 45 as sqrt(2)/2, subbing that= u*sqrt(2)/4

 

[Bucky]

annoyingly I've lost an 'm' somewhere, but otherwise the answer checks out :)

i didn't know cos 45 could be expressed as root(2)/2 ? or have you done some mathmatical jiggery-pokery that i have missed?

 

[denverdoc]

no real trickery, just dividing or multiplying both top and bottom by sqrt(2).