Two objects undergo a perfectly inelastic collision. Using conservation of momen

Question

Two objects undergo a perfectly inelastic collision. Using conservation of momentum, derive an expression for the velocity after collision, in terms of masses and initial velocities (assume that, except collision forces, all other interactions are negligible Using expression from part (a), calculate the final velocity, if the masses and initial velocities are follows: m_1 - 3.2 kg, m_2 - 2.5 kg; v_1 = 1.1 m/s, v_2 = - 0.85 m/s. Recalculate the final velocity, if v_2 - 0, i.e. the second object is motionless before collision.

Explanation / Answer

Hi,

(a) We have two objects of masses m1 and m2 and each one has a certain speed (v1 and v2, respectively). When they collide in a perfectly inelastic way, the kinetic energy of one of them is reduced to zero and both of them move together at a common speed (u). To represent this, we can evaluate the momentum of this system (the one formed by the two masses) just before and just after the collision. As the other forces that can affect this system are considered negligable, then the system can be considered as insulated and the momentum is conserved.

po = pf ::::::::::   m1v1 + m2v2 = u(m1 + m2) ; so the value of said common speed is:

u = (m1v1 + m2v2)/(m1 + m2)

(b) If m1 = 3.2 kg, m2 = 2.5 kg, v1 = 1.1 m/s and v2 = -0.85 m/s, then we have the following:

u = [(3.2 kg)(1.1 m/s) + (2.5 kg)(-0.85 m/s)]/(3.2 kg + 2.5 kg) = 0.25 m/s

(c) If we maintain all the previous data except for v2 which new value is zero (the second mass is at rest), we have the following:

u = [(3.2 kg)(1.1 m/s)]/(3.2 kg + 2.5 kg) = 0.62 m/s

I hope it helps.

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