1.A ceramic dish falls directly downward onto the floor and breaks cleanly into

Question

1.A ceramic dish falls directly downward onto the floor and breaks cleanly into two pieces. The first piece has a mass of 193 g and moved at 5.0 m/s in the -x direction. The other piece had an initial speed of 3.92 m/s. The xy plane is the horizontal floor.

A. In what direction did the piece move? Explain why you know.

B. Find the mass of the original, unbroken dish.

2.Suppose a person tries to reduce his effort in cleaning a flat wooden floor. At one wall, he pushes the dust mop (mass 395 g) toward the other wall 4.50 m away. If the coefficient of kinetic friction between the floor and the mop is 0.15, find how fast he has to push the mop for it to get to the other wall without banging against it.

3.Suppose you twirl a 0.250 kg yo-yo around your head on the end of a string 95 cm long. If it spins one time around your head every second, find the speed of the yo-yo.

B. Find the magnitudes of the centripetal acceleration and centripetal force on the yo-yo.

Explanation / Answer

a)The piece moved in the +x direction since the momentum should be conserved and initially there was no horizontal momentum, so finally there should be no horizontal momentum as well. Similarly for y momentum,

b)Let the mass of the unbroken dish be M.

Conserving momentum in x direction,

0=0.193*-5+(M-0.193)*3.92

M=0.439kg=439g

2)deceleration due to friction=ug=0.15*9.81=1.4715m/s^2

Using third equation of motion,

u^2=-2as

u=sqrt(-2*-1.4715*4.5)

u=3.64m/s

3)a)v=2pir/t=2pi*0.95/1=5.97m/s

b)a=v^2/r=5.97^2/0.95=37.52m/s^2

F=ma=0.25*37.52=9.38N

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