Let’s take a look at the problem I set up off the top of my head in class

25 m/s

Tiger Woods is driving his 1000kg car along the road at a velocity of 25m/s

The 1000kg car then collides with a 500kg tree, which is stationary

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?

70 m/s

Oh, physics, you’re a harsh

mistress

10 m/s

Let’s do a problem that is more believable for the MCAT…

25 m/s

Tiger Woods is driving his 1000kg car along the road at a velocity of 25m/s

The 1000kg car then collides with a 500kg tree, which is stationary

??? 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