10 m/s ??? m/s
Following the collision, an angered Tiger Woods is traveling -10m/s. What
velocity does the tree have?
I hatecollisions
Masscar = 1000kg Masstree = 500kgPcar, initially = mcarvcar,i Ptree = mtreevtree,i
= (1,000kg) * 25m/s = 500kg * 0m/s= 25,000 (kg*m)/s = 0 (kg*m)/s
Ptotal,i = Pcar,i + Ptree,i
= 25,000 (kg*m)/s + 0(kg*m)/s= 25,000 (kg*m)/s
Initial Momentum
25 m/s
Remember: you can solve momentum by using the equationm1v1,i + m2v2,i = m1v1,f + m2v2,f
10 m/s
Pcar,f = mcarvcar,f
= (1,000kg)(-10m/s)= -10,000(kg*m)/s
Ptotal,f = Pcar,f + Ptree,f
Ptree,f = Ptotal,f - Pcar,f
= 25,000(kg*m)/s – (-10,000(kg*m)/s))= 35,000(kg*m)/s
Ptree,f = mtree * vtree,f
vtree,f = ptree,f / mtree
vtree = [35,000(kg*m)/s] / 500kgvtree =70 m/s
70 m/s
Solving for velocity
It is physically impossible for the car’s final velocity in this problem to be the
result of an elastic collision
The momentum of Tiger Woods’ car is much, much larger than that of the tree. In an elastic collision, one would expect
the car to continue in the positive x-direction, not the negative x-
direction, following the collision.
If momentum is conserved, and Tiger Woods’ car travels at a velocity of -10m/s
following the collision, kinetic energy cannot be conserved.
But, it could be an inelastic collision.
Inelastic collisions result in a change in total kinetic energy.
Initial Kinetic Energy
KEinitial, car = 1/2mv2
= 1/2(1000kg)(25m/s)2
= 312,500 Joules
KEtotal = 312,500 Joules
KEinitial, tree = 1/2mv2
=1/2(500kg)(0m/s)= 0 Joules
25 m/s
Final Kinetic EnergyKecar = 1/2mv2
= 1/2(1000kg)(-10m/s)2
= 50,000 Joules
KEtotal = 1,275,000 Joules
ΔKE = KEfinal – KEinitial
= 1,275,000 Joules - 312,500 Joules= 962,500 Joules
KEtree = 1/2mv2
=1/2(500kg)(70m/s)2
= 1,225,000 Joules
10 m/s
70 m/s
In an inelastic collision, if another form of energy is converted to kinetic
energy, than the final kinetic energy may increase.
There may have been some external energy wandering around in Florida
that evening
Is this the way to the fireworks show?
??? m/s
Immediately following the collision, the tree is stuck in the front
grill, and the tree and an angered Tiger Woods have formed a hybrid. What velocity does the tree/angered Tiger
Woods hybrid have?
I hate it when I completely inelasticallycollide with
things
Masscar = 1000kg Masstree = 500kg
Pcar, I = mcarvcar,i Ptree,I = mtreevtree,i
= (1,000kg) * 25m/s = 500kg * 0m/s= 25,000 (kg*m)/s = 0 (kg*m)/s
Ptotal = Pcar + Ptree
= 25,000 (kg*m)/s + 0(kg*m)/s= 25,000 (kg*m)/s
Initial Momentum
25 m/s
Pinitial = Pfinal
mcarvcar,i = (mcar + mtree )vhybrid
vhybrid = mcarvcar / (mcar+ mtree )
vhybrid = [25,000(kg*m)/s] / 1,500kgvhybrid = 16.67 m/s
Solving for velocity
16.67 m/s
It’s science!
Initial Kinetic Energy
KEinitial, car = 1/2mv2
= 1/2(1,000kg)(25m/s)2
= 312,500 Joules
KEtotal = 312,500 Joules
KEinitial, tree = 1/2mv2
=1/2(500kg)(0m/s)= 0 Joules
25 m/s
Final Kinetic Energy
Kehybrid = 1/2mv2
= 1/2(1,500kg)(16.67m/s)2
= 208,416.675 Joules
The change in energy quantifies the energy that was transformed into heat, sound, light and/or reshaping of the car and the tree
ΔKE = KEfinal – KEinitial
= 208,416.675 Joules - 312,500 Joules= -104,083.325 Joules or 1.04x105 Joules
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