A 0.5 kg bead slides on a curved frictionless wire, starting from rest at point

Question

A 0.5 kg bead slides on a curved frictionless wire, starting from rest at point A, where d=1.5 m. At point B the bead collides elastically with a 0.8 kg ball at rest.

i A) Find the speed of the bead at point B just before it collides with the ball.
B) Find the speed of the ball just after the collision.
C) Find the maximum height of the ball rises at it moves up the wire. A 0.5 kg bead slides on a curved frictionless wire, starting from rest at point A, where d=1.5 m. At point B the bead collides elastically with a 0.8 kg ball at rest. Find the speed of the bead at point B just before it collides with the ball. Find the speed of the ball just after the collision. Find the maximum height of the ball rises at it moves up the wire.

Explanation / Answer

A) initial energy = final energy

mgd = 0.5*mv^2

so 9.8*1.5 = 0.5v^2

so v = 5.42 m/s

Speed of bead at point B just before it collides = 5.42 m/s

B) Elastic collision

So conserve momentum and kinetic energy

m1u1 + m2u2 = m1v1+m2v2

m1u1^2/2 + m2u2^2/2 = m1v1^2/2+m2v2^2/2

solving we get v2 = u2(m2-m1) + 2m1u1 /(m1+m2)

so v2 = 0+2*0.5*5.42 /1.3 = 4.16 m/s

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