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Some help with physics homework problem -- vectors?
Two pucks on an air-hockey table glide without friction across the surface of the table with velocities 1A and 1B, respectively. The pucks have double-sided tape stuck to their perimeters so that when the pucks collide, they stick together (in a perfectly inelastic collision). Puck B has a mass of 0.120 kg and puck A has twice this mass. Choosing coordinates in which the positive x-direction points to the right and the positive y-direction points up the page, we can say that 1A = (2.20 m/s) and 1B = (1.10 m/s).
What is the momentum of puck A just before the collision?
What is the momentum of puck B just before the collision?
What impulse was imparted to the system (consisting of the two pucks) between the initial and final conditions?
What impulse was imparted to puck A?
What impulse was imparted to puck B?
Should've put this before ... the answers are looking for the x and y components of each answer part.
Initial velocities are ua=2.20 m/s, ub = 1.10 m/s = ua/2
If both ua and ub are positive, then they are both traveling to the right, collide and travel to the right
>when the pucks collide, they stick together (in a perfectly inelastic collision) => momentum is conserved
Masses ma = 2mb=0.24 kg, mb = 0.12 kg
>What is the momentum of puck A just before the collision?
ma*ua =2ma*2ua = 0.24*2.2 = 0.528 = 4ma*ua
>What is the momentum of puck B just before the collision?
mb*ub = 0.12*1.1 = 0.132
>What impulse was imparted to the system (consisting of the two pucks) between the initial and final conditions?
Final mass = ma+mb = 0.36kg
Final velocity = v
ma*ua + mb*ub = (ma+mb)v
2mb*ua + mb*ua/2 = (2mb+mb)v
(5/2)*mb*ua = 3mb*v
(5/2)*ua = 3v
v = (5/6)*ua = 1.833 m/s
>What impulse was imparted to puck A?
I = Δp = p(new) - p(original) = mv - mu
= ma (v-u)
= 0.24(1.833-2.2)
= - 0.088 kg m/s
>What impulse was imparted to puck B?
I = Δp = mb (v-u)
= 0.12(1.833-1.1)
= +0.088 kg m/s (which you expect, since momentum was conserved in this case)
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