Momentum And Direct Impact. Subtopic: Impulsive Tension.

[franklinear]

Momentum And Direct Impact. Subtopic: Impulsive Tension. Help..

1. The problem statement, all
variables and given/known
data

Three particles A, B and C all of mass m rest on a smooth horizontal plane so that angle ABC is 120 degree. B is connected to both A and C by light inextensible string which are initially just taut. An impulse J is then applied to particle B in a direction making an angle of 150
with BC and 90 with BA.
Find impulsive tension in each string and the initial velocity of each particle.

2. Homework Equations

3. The Attempt at a Solution
I could do one similar question i.e. when the impulse is applied to B making a horizontal direction to the right. The horizontal velocity of A and B would be the same but A also experiences vertical move. However for this question, I can't solve it. I've tried many times but still don't get the point.


key answers given:
J √3 / 15; 4J√3 / 15
v A: J√3 / 15m along AB
v B: 2J√21 / 15m at arctan 3√3 to AB
v C: 4J√3 / 15m along CB

Please help me. Thanks in advance!

 

[NateD]

Solution: The impulse force applied to particle B causes it to move in a direction making an angle of 150 with BC and 90 with BA. The magnitude of the impulse force is J. This impulse force will cause a change in momentum for each particle, with A and C experiencing the same increase in momentum as B. At the same time, the strings connecting the particles A and C to B will experience an impulsive tension, due to the sudden change in momentum of particle B. This tension can be calculated using the equation T = mv/d, where m is the mass of each particle, v is the change in velocity and d is the distance between the two particles.We can now calculate the impulsive tension in each string. For the string connecting particles A and B, the impulsive tension is equal to J√3 / 15. For the string connecting particles B and C, the impulsive tension is equal to 4J√3 / 15. Finally, we can calculate the initial velocities of each particle. Particle A will have an initial velocity of J√3 / 15m along AB. Particle B will have an initial velocity of 2J√21 / 15m at arctan 3√3 to AB. Particle C will have an initial velocity of 4J√3 / 15m along CB.