Further compression in the spring (after the collision) is found to be k α m 3 v 0 . Find the value of α where α is the least integer.

Physics - Center of Mass Question with Solution | TestHub

PhysicsCenter of MassCollisionMedium2 minQB

PhysicsMediuminteger

Passage / Comprehension

A particle of mass m collides elastically with the pan of mass M = 2m of a spring balance. The pan is in equilibrium before collision. The spring constant is k and the particle speed before collision is $v_{0}$ . The figure shows the collision geometry. Answer the question using this common setup.

Source diagram for Phase II Advanced shared passage group 2

Further compression in the spring (after the collision) is found to be $\frac{α m}{k} \frac{v _{0}}{3}$ . Find the value of $α$ where $α$ is the least integer.

Answer:

Solution:

Take the vertical component of the incident velocity at 60° to the vertical.

$u_{y} = v_{0} cos 6 0^{\circ} = \frac{v _{0}}{2}$

For an elastic collision of m with the stationary pan of mass 2m, the pan gains vertical speed

$V = \frac{2 m}{m + 2 m} u_{y} = \frac{v _{0}}{3}$

Measured from its initial equilibrium, the spring-pan oscillation amplitude is

$x = V \frac{2 m}{k} = \frac{v _{0}}{3} \frac{2 m}{k}$

$α = 2$

Stream:JEESubject:PhysicsTopic:Center of MassSubtopic:Collision

⏱ 2mℹ️ Source: QB

Doubts & Discussion

Loading discussions...