- #1

quicksilver123

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## Homework Statement

Football player 1 with a mass of 110kg is moving at 8.0m/s

A) What is their velocity after the collision?

B) What is the net force (affecting each player) during the collision?

## Homework Equations

p = momentum

v' = velocity after collision

p=mv

Δp=mv

_{2}-mv

_{1}

Net Force = Δp / Δt

Conservation of momentum:

m

_{1}v

_{1}+ m

_{2}v

_{2}= m(v')

## The Attempt at a Solution

m

_{1}= 110kg

v

_{1}= -8m/s

m

_{2}= 105kg

v

_{2}= 12m/s

Let [N] be positive.

A)

m

_{1}v

_{1}+ m

_{2}v

_{2}= m(v')

110kg(-8m/s) + 105kg(12m/s) = (110kg+105kg)v'

-880kg(m/s) + 1260kg(m/s) = 215kg v'

380kg(m/s) / 215kg = v'

v' = 1.76744186 m/s [N]

I've verified this answer with the course's book. I'm including it because the answer for part B depends on the answer from part A.

B)

Net Force = Δp / Δt

Net Force = (m

_{1}v' - m

_{1}v

_{1}) / (0.3 seconds)

Net Force = [(110kg(1.76744186m/s)) - (110kg)(-8m/s))] / (0.3 seconds)

Net Force = [ 194.4186046kg(m/s) + 880kg(m/s) ] / (0.3 seconds)

Net Force = (1074.4418605kg(m/s)) / (0.3 seconds)

Net Force = 3581.395349kg(m/s

^{2})

Net Force on Player 1 = 3581.395 Newtons

Net Force on Player 2 (from Newton's 3rd LoM) = -3581.395 Newtons

I think this should be correct, but I think I'm doing something wrong. The book's answer work uses the formula :

Net Force = (m

_{1}v

_{1}- m

_{1}v' / (0.3 seconds)

for net force, which doesn't make sense to me... seeing as how a change in momentum should be found by subtracting the final value from the initial.

By the way, the book's answer for player 1 is :

-2280 N

... Which makes sense if you use their formula (the calculations are correct)... but its the formula itself that I don't understand.

Any thoughts?