An air-track cart with mass m = 0.20 kg and speed v_0 = 1.0 m/s approaches two o

Question

An air-track cart with mass m = 0.20 kg and speed v_0 = 1.0 m/s approaches two other carts that are at rest and have masses 2m and 3m, as indicated in (Figure 1). The carts have bumpers that make all the collisions elastic. Find the final speed of cart 1, assuming the air track extends indefinitely in either direction. Express your answer to two significant figures and include appropriate units. Find the final speed of cart2, assuming the air track extends indefinitely in either direction. Express your answer to two significant figures and include appropriate units. Find the final speed of cart 3, assuming the air track extends indefinitely in either direction. Express your answer to two significant figures and include appropriate units.

Explanation / Answer

given

m = 0.2 kg , vo = 1 m/sec

and 2m and 3 m masses

V1 - V2 = - ( Vif - V2f )

Vo = V2 - V1

Vo = V2 - Vo + 2 V2

so V2 = 2/3 X Vo

then V2 = 2/3 X 1

V2 = 0.666 m/sec

then V1 = - Vo / 3

V1 = - 1 / 3

V1 = - 0.33 m/sec

now same way using conservation of momentum

2 m ( 2/3 Vo ) = 2 m V2 + 3 m V3

2/3 Vo = - ( V2 - V3 )

so

V3 = 2/3 Vo + V2

V3 = 2/3 X 1 + 0.666

V3 = 0.666 + 0.666

V3 = 1.332 m/sec

a ) V1 = - 0.33 m/sec

b ) V2 = 0.666 m/sec

c ) V3 = 1.332 m/sec

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