Board A is placed on board B as shown. Both boards slide, without moving with respect to each other, along a frictionless horizontal surface at a speed 6 m/s. Board B hits a resulting board C "head-on". After the collision, boards B and C stick together and board A slides on top of board C and stops its motion relative to C in the position shown on the diagram. What is the length (in m) of each board? All three boards have the same mass, size and shape. The coefficient of kinetic friction between boards A and C and between boards A & B is 0.3.

Engineering

Physics

Static and Kinetic Friction

Collision

Relative Motion

Question

Board A is placed on board B as shown. Both boards slide, without moving with respect to each other, along a frictionless horizontal surface at a speed 6 m/s. Board B hits a resulting board C "head-on". After the collision, boards B and C stick together and board A slides on top of board C and stops its motion relative to C in the position shown on the diagram. What is the length (in m) of each board? All three boards have the same mass, size and shape. The coefficient of kinetic friction between boards A and C and between boards A & B is 0.3.

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v_f = v – 3t

$v_{f} = \frac{v}{2} + 1.5 t$

$0 = \frac{v}{2} - 4.5 t$

$t = \frac{6}{2 \times 4.5} = \frac{2}{3} \sec$

v_f = 6 – 2 = 4 m/sec

$0^{2} = \frac{v^{2}}{4}$ – 2 (+ 0.45) (L) for v = 6 m/sec

L = 1 m