1) A stationary block explodes into two pieces that slide along a frictionless floor and then into regions with friction, where they stop. The first piece, with a mass of 2.0 kg, encounters a coefficient of kinetic friction of 0.40 and slides to a stop in a distance 0.15 m. The second piece encounters a coefficient of kinetic friction of 0.50 and slides to a stop in a distance of 0.25 m. What was the mass of the block?
2) A block slides along a track from one level to a higher level after passing through an intermediate valley. The track is frictionless until the block reaches the higher level. There a frictional force stops the block in a distance d. The block's initial speed is 6.0 m/s, the height difference between the levels is 1.1 m, and the coefficient of kinetic friction is 0.60. Find d.
for first piece, by energy law:
0.5*m1*v1^2 = mu1*m1*g*s1
m1 = 2.0 kg (mass)
mu1 = 0.40 (coeff. of friction)
g = 9.8 m/s^2 (gravitational acceleration)
s1 = 0.15 m (displacement of 1st piece)
v1 = ? (velocity of 1st piece after explosion)
Hence, v1 = ...
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