In the figure, a stationary block explodes into two pieces L and R that slide ac

Question

In the figure, a stationary block explodes into two pieces L and R that slide across a frictionless floor and then into regions with friction, where they stop. Piece L, with a mass of 2.4 kg, encounters a coefficient of kinetic friction mu_L = 0.40 slides to a stop in distance d_L = 0.15 m. Piece R encounters a coefficient of kinetic friction 0.45 and slides to a stop in distance d_R = 0.38 m. what was the mass of the block? Split the problem into two parts: explosion and then slowing. The explosion involves internal forces and cannot change the momentum. Did you write an equation for the conservation of momentum, using symbols where you don't have a value? To get the speeds of the two pieces, you need to recall how kinetic friction can slow an object until it slides to a stop. Using the sliding distances should give you the speeds. A 6.0 kg mess kit sliding on a frictionless surface explodes into two 3.0 kg parts: 1.4 m/s, due north, and 5.3 m/s, 30 degree north of east. What was the original speed of the mess kit? m/s

Explanation / Answer

FOr L:

aL = - uk g = - 0.40 x 9.8 = - 3.92 m/s^2

Applying vf^2 - vi^2 = 2 a d

0^2 - vL^2 = 2 x -3.92 x 0.15

vL = 1.084 m/s

For R:

aR = - 0.45 x 9.8 = 4.41 m/s^2

0^2 - vR^2 = 2 x - 4.41 x 0.38

vR = 1.83 m/s

now applying momentumn conservation,

initial = final momentum

0 = (2.4 x - 1.084) + (mR x 1.83)

mR = 1.42 kg

m = mL + mR = 2.4 + 1.42

= 3.82 kg ..........Ans

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