Three trolley are free to move on a frictionless horizontal track. Trolley A has a mass of 2m and an initial speed 2v to the right; Trolley B has a mass of and an initial speed of v to the left; Trolley C has a mass of m and is originally at rest. All collisions are perfectly elastic.
The velocity of the center of mass of the system of the three trolleys after the last collision is
(1) 2v/3 (2) 3v/4 (3) 3v/2 (4) 3v/5 (5) v/3
Trolley B has a mass of ??
conserve momentum. It must start and end the same. So, that means
(2m)(2v)+(m)(-v)+(m)(0) = 4mv-mv = 3mv
since the final mass is 4m, that is 4m(3/4 v)
Looks Like #2.
Hey thank you very much:)
To find the velocity of the center of mass of the system of the three trolleys after the last collision, we need to consider the conservation of momentum. The center of mass velocity is the total momentum divided by the total mass.
Let's break down the problem step by step:
Step 1: Analyze the initial state of the system
Trolley A: mass = 2m, initial velocity = 2v to the right
Trolley B: mass = m, initial velocity = v to the left
Trolley C: mass = m, initially at rest (velocity = 0)
Step 2: Calculate the total momentum of the system before the collision
The total momentum of the system can be calculated by summing up the individual momenta of each trolley.
Momentum of Trolley A = (mass of A) * (velocity of A) = (2m) * (2v) = 4mv
Momentum of Trolley B = (mass of B) * (velocity of B) = (m) * (-v) = -mv
Momentum of Trolley C = (mass of C) * (velocity of C) = (m) * (0) = 0
Total momentum before the collision = Momentum of A + Momentum of B + Momentum of C
= 4mv + (-mv) + 0
= 3mv
Step 3: Analyze the final state after the collision
All collisions are perfectly elastic, meaning that the total kinetic energy is conserved.
Since there is no external force acting on the system, the center of mass will continue to have the same velocity before and after the collision.
So, the velocity of the center of mass of the system after the last collision is the same as the velocity before the collision, which is 3v.
Therefore, the correct answer is (3) 3v/2.