Test Wednesday, March 15th 7pm,

Bring your calculator and #2 pencil with a

good eraser!

20 Multiple choice questions from:Chapter 4

• Newton’s Three Laws, Free Body Diagrams, Friction

Chapter 5 (except 5.4)

• Work, Kinetic Energy, Gravitational Potential

Energy, Energy Conservation

Chapter 6 (except 6.5) plus 9.2

• Momentum, Impulse, Pressure, Elastic and Inelastic

Collisions

Main Ideas in Class Today

You should be able to:

• Distinguish between Elastic and

Inelastic Collisions

• Solve Collisions in 1 & 2 Dimensions

Practice: 6.31, 6.33, 6.39, 6.41, 6.43, 6.45,

6.47, 6.49, 6.51, 6.53, 6.55, 6.63, 6.73

Elastic and Inelastic Collisions

• Inelastic collisions: mechanical energy (KE+PE)

is not conserved

– Initial mechanical energy

mechanical energy after collision

– Energy lost in the form of heat (dissipative forces)

• Special case: Perfectly inelastic, objects stick

• Elastic collisions: mechanical energy is conserved

• In all real cases, some energy is lost to heat. In

many cases (eg billiard balls), however, this amount

is so small that it makes more sense to ignore this

loss.

Elastic and Inelastic CollisionsFor both elastic and inelastic

collisions linear momentum is

conserved (unlike energy)

• Only for elastic collisions,

mechanical energy (KE+PE) of

the system is also conserved.

Initial (i)

Final (f’)

fvm 11

fvm 22

ffii vmvmvmvm 22112211

Elastic Collisions• Only for elastic collisions, mechanical energy

(KE+PE) of the system is also conserved.

• y=0, then PEi = PEf and 1 2 1 2i i f fKE KE KE KE

1 2 1 2( ) ( )initial finalv v v v

2 2 2 2

1 1 2 2 1 1 2 1

1 1 1 1

2 2 2 2i i f fm v m v m v m v 2 2 2 2

1 1 1 2 1 2i f f im v v m v v

1 1 1 1 1 2 2 2 2 2i f i f f i f im v v v v m v v v v

1 1 2 2 1 1 2 2i i f fm v m v m v m v 1 1 1 2 2 2i f f im v v m v v Conservation of Momentum

1 1 2 2i f f iv v v v

Conservation of Energy for Elastic Collision

Perfectly Inelastic Collisions• In an inelastic collision, mechanical

energy is not conserved, but momentum

is.

• In a perfectly inelastic collision, the

objects stick together after the collision

1 1 2 2 1 1 2 2i i f fm v m v m v m v Conservation of Momentum

1 1 2 2 1 2i i fm v m v m m v

A compact car and a large truck collide

head on. Which vehicle undergoes the

larger magnitude of acceleration during

the collision?

A. car

B. truck

C. Both experience the same acceleration.

D. Can’t tell without knowing the initial

and final velocities. Q7

Suppose that a 2000.0-kg car, initially at rest,

is struck head on by a 36,000.0-kg semitruck

moving at 20.0 m/s. Determine the velocity

of each of the vehicles after the collision,

assuming that the collision is perfectly

inelastic.

Collisions in Two Dimensions

• Linear momentum of an isolated system is

always conserved

• In two dimensions, components of vectors

are conserved

Before After

1p

2p

1p

2p

xxoxox pppp 2121

yyoyoy pppp 2121

systemfsystemi pp ,,

means

If collision is elastic, then

we also have

2121 EKEKKEKE ooy not in vertical direction to

conserve PE

Car Accident ExampleAn eastward car strikes a northward car traveling

at an intersection, and the two move together as a

unit. A property owner on the southeast corner of

the intersection claims that his fence was torn

down in the collision. Should he be awarded

damages by the insurance company?

Let the eastward car have a mass of 1250 kg and a

speed of 16 m/s and the northward car a mass of

1100 kg and a speed of 21 m/s. Find the velocity

after the perfectly inelastic collision.

Block A has mass 1.00 kg and block B has

mass 3.00 kg. The blocks collide and stick

together on a level, frictionless surface.

After the collision, the kinetic energy

(KE) of block A is

A. 1/9 the KE of block B.

B. 1/3 the KE of block B.

C. 3 times the KE of block B.

D. 9 times the KE of block B.

E. the same as the KE of block B. Q8

A B

Think fast! You’ve just driven around a curve in a

narrow, one-way street when you notice a car

identical to yours coming straight toward you at

the same speed. You have only 2 options: hitting

the other car head on or swerving into a massive

concrete wall, also head on. What should you

decide to do in order to minimize your injury due

to stopping?

(Assume car doesn’t crumple)

A. hit the other car.

B. hit the wall.

C. hit either one—it makes no difference to you.Q9

A billard ball moving at 5.00 m/s strikes a

stationary ball of the same mass. After the

collision, the first ball moves at 4.33 m/s at

an angle of 30° with respect to the original

line of motion.

Find the velocity (magnitude and direction)

of the second ball after the collision.

Was the collision elastic or inelastic?

Chapter/Section: Clicker #=Answer

Ch.6C: 7=A, 8=B, 9=C