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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=mv2-mv1
Net Force = Δp / Δt
Conservation of momentum:
m1v1 + m2v2 = m(v')
The Attempt at a Solution
m1 = 110kg
v1 = -8m/s
m2 = 105kg
v2 = 12m/s
Let [N] be positive.
A)
m1v1 + m2v2 = 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 = (m1v' - m1v1) / (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/s2)
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 = (m1v1 - m1v' / (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?