A 0.430 kg bead slides on a curved wire, starting from rest at point A as seen i

Question

A 0.430 kg bead slides on a curved wire, starting from rest at point A as seen in the Figure below.

Assume h1 = 5.16 m and h2 = 1.46 m. If the wire is frictionless, find the speed of the bead at B.

Also, If the wire is frictionless, find the speed of the bead at C.

A 0.430 kg bead slides on a curved wire, starting from rest at point A as seen in the Figure below. Assume h1 = 5.16 m and h2 = 1.46 m. If the wire is frictionless, find the speed of the bead at B. Also. If the wire is frictionless, find the speed of the bead at C.

Explanation / Answer

energy is conserved

so potntial energy at A is converted to kinetic energy at B

difference between potential energies at A and B = m*g*(h1)

let velocity at B = X

mgh = (1/2)*m*(X^2)

X = sqrt(2gh) = sqrt(2*9.8*h1) = sqrt(2*9.8*5.16) = 10.0566396 m/s

 

speed at B =  10.0566396 m/s

b) Now let velocity at C = Y

so potntial energy at A is converted to kinetic energy at C

difference between potential energies at A and C = m*g*(h1-h2)


mg(h1-h2) = (1/2)*m*(Y^2)

Y = sqrt(2g(h1-h2)) = sqrt(2*9.8*(h1-h2)) = sqrt(2*9.8*(5.16-1.46)) = 8.51586754m/s

speed at C = 8.51586754 m/s

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