a mass m is moving horizontally in the +x Direction with a velocity Vsub0 and st

Question

a mass m is moving horizontally in the +x Direction with a velocity Vsub0 and strikes a pendulum of mass m. assume that the Collision is perfectly inelastic the first time and that the masses stick together find the maximum height reached by the pendulum and strikes a pendulum of mass m first assume that the Collision is perfectly inelastic the first time and that the masses stick together find the maximum height reached by the pendulum next assume that the Collision is perfectly elastic Now find the maximum height of the pendulum

Explanation / Answer

a)

when the collision is perfectly inelastic

m = mass of pendulum and mass

Vo = initial speed of mass

V = final speed of mass and pendulum combination

Using conservation of momentum

m Vo + 0 = (m + m) V

V = m Vo /(2m)

V = Vo/2

Using conservation of energy

PE at maimum height = kE at the bottom

(2m) gh = (0.5) (2m) V2

h = V2/2g = (Vo/2)2 /2g = Vo2/(4g)

b)

V1 = speed of mass after collision

V2 = speed of pendulum after collision

for perfectly elastic collision

e = 1 = (V2 - V1) /Vo

V2 - V1 = Vo               eq-1

using conservation of momentum

m Vo = m V1 + m V2

V1 + V2 = Vo                eq-2

additing eq-1 and eq-2

V2 = Vo

Using conservation of energy

PE at maximum height = kE at the bottom

(m) gh = (0.5) (m) V22

h = V22/2g = (Vo)2 /2g = Vo2/(2g)

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