Silly Suzy Spider (mass .06 g ) is sitting on an icy (that is, frictionless) hil

Question

Silly Suzy Spider (mass .06 g) is sitting on an icy (that is, frictionless) hill of height 5.6cm. She slides from rest down the hill and into the arms (all of them) of her sweetheart Samuel Spider (mass .09 g), who is waiting patiently while hanging motionless from the end of a strand of web of length 9.0 cm which is attached to an overhead branch. The two love-spiders collide, Samuel embraces Suzy in his arms, and they swing together in an upwards arc while hanging from Samuel's web. (a) How fast is Suzy moving just before she slides into her loving Samuel's arms? (b) How fast is the lovely couple moving just after they lovingly collide? (c) How high above the ground level do the love-spiders swing before starting to swing back down again?

Explanation / Answer

m1 = 0.06*10^-3 kg

m2 = 0.09*10^-3 kg

(a)

from energy conservation

initial potential energy = final kinetic eenrgy

m1*g*h1 = (1/2)*m1*u1^2

0.06*10^-3*9.8*5.6*10^-2 = (1/2)*0.06*10^-3*v1^2

v1 = 1.05 m/s

(b)

momentum before collision = momentum after collision

m1*v1 = (m1+m2)*Vf

0.06*10^-3*1.05 = ((0.06*10^-3)+(0.09*10^-3))*Vf

vf = 0.42 m/s

(c)

kE at bottom = PE at top

(1/2)*(m1+m2)*vf^2 = (m1+m2)*g*h2

(1/2)*0.42^2 = 9.8*h2

h2 = 0.009 m = 0.9 cm <<<<----------answer

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