Warm-up U7-#1 1/13/141) What is the force felt on a 3200kg truck

moving at 16 m/s which runs into a haystack bringing the truck to a stop in 25.6 seconds.

Ft = mvF (25.6s) = 3200kg (0-16m/s)

F(25.6s) = - 51200 kgm/s

F = - 2,000 N

B

m=3200kg

vi =16m/s

vf = 0m/s

t=25.6s

F=?

Law of Conservation of Momentum-

Momentum is neither gained nor lost in the absence of an external force

momentum before = momentum after pbefore = pafter

• BEFORE – object at rest momentum zero.

• AFTER – cannon and ball go in opposite directions. Momentums cancel total

momentum = zero.

pcannon before + pball before = 0

pcannon after + pcball after = 0

before after

Collision #1 – Object at rest or Explosions

• ex 1) A 2 kg rifle shots a 0.001kg bullet at 200 m/s. What will be the recoil velocity of the rifle?

G: mrifle = 2 kg

mbullet = 0.001kg

vbullet = 200m/s

pbefore = pafter

pbefore = 0

U: vrifle = ?

Eq: pafter = 0

pafter = (mv)bullet + (mv)rifle

Sub: 0=(0.001kg*200m/s)+(2kg*vrifle)

-2kg*vrifle = 0.2kgm/s

“”

Solve: vrifle = -0.1 m/s

“-”

Collision #2 - Elastic Collisions• Elastic collision- When objects collide without

being permanently deformed and without generating heat. Objects do not stick together!

• Kinetic Energy is conserved in elastic collisions.

(m1v1 + m2v2)Before = (m1v1 + m2v2)after

Ex. G: A 1000 kg car traveling at 20.0 m/s hits a 3000 kg truck atrest. If the truck is traveling 10 m/s forward after the elastic collision, what is the cars final velocity?

Before:

mcar=1000kg

mtruck=3000kg

vcar=20 m/s

vtruck=0

After:

vcar = ?

vtruck = 10m/s

(mcvc + mtvt)Before = (mcvc + mtvt)after

1000kg*20m/s+0=1000kg*vcar+3000kg*10m/s

20,000kgm/s - 30,000kgm/s = 1000kg * vcar

-10,000kgm/s = 1000kg * vcar

“”

vcar = -10 m/s

“-”

Collision #3 - Inelastic Collisions

• Inelastic collision- collision where the objects become distorted or generate heat.

• Objects stick together so the after the collision there is only one object.

(m1v1 + m2v2)before = (m1+m2)(vf)after

Example 3: Sam, who is 85kg, jumps into a 300 kg rowboat initially at rest. His initial velocity was 5 m/s forward. What is the velocity of Sam in the boat after he lands?Before:

msam=85kg

mrow=300kg

vsam=5m/s

vrow = 0

After:

vf = ?

(msvs + mrbvrb)before = (ms+mrb)(vf)

(85kg*5m/s + 0) = (300kg+85kg)vf

425kgm/s = 385kg * vf

vf = 1.1 m/s

“”

Warm-up 1/14/14Mike is traveling forward at 20.0 m/s in his 1000 kg car and hits Justice’s 1,500 kg car going slower at 8 m/s in the same direction. Justice’s car is traveling 15 m/s forward after the elastic collision, what is the final velocity of Mike’s car?

v1i = 20 m/s

GIVEN:m1 = 1000 kg

UNKNOWN:

EQUATION:m1v1i + m2v2i = m1v1f + m2v2f

SUBSTITUTE:

SOLVE:

v2i = 8 m/s

m2 = 1500 kg

v1f = ? m/s

(1000)(20) + (1500)(8) = (1000)(v1f) + (1500)(15)v2f = 15 m/s

v1f = 9.5 m/s

20,000 + 12,000 = (1000)(v1f) + 22,500

9500 = (1000)(v1f)

20,000 + 12,000 – 22,500 = (1000)(v1f)

9500/1000 = v1f

Problem 1A 40 kg child runs across a store at 4.0 m/s and jumps onto a 15 kg shopping cart initially at rest. At what speed will the shopping cart and the child move together across the store assuming negligible friction?

v1i = 4.0 m/s

GIVEN:m1 = 40 kg

UNKNOWN:

EQUATION:m1v1i + m2v2i = (m1 + m2)vf

SUBSTITUTE:

SOLVE:

Vf = 2.9 m/s

v2i = 0 m/s

m2 = 15 kg

vf = ? m/s

What type of collision is this?

(40)(4.0) + (15)(0) = (40 + 15)vf

160 + 0 = (55)vf

160 = (55)vf

160/55 = vf

Inelastic

Problem 2Tanner throws a 0.20 kg football and knocks over a 0.90 kg vase at rest. (bad Tanner!) After the collision the football bounces straight back with a speed of 3.9 m/s while the vase is moving at 2.6 m/s in the opposite direction. How fast did Tanner throw the football?

GIVEN:

m1 = 0.20 kg

UNKNOWN:

EQUATION:m1v1i + m2v2i = m1v1f + m2v2f

SUBSTITUTE:

SOLVE:

v2i = 0 m/s

m2 = 0.90 kg

v1i = ? m/s

(0.20)(v1i) + (0.90)(0) = (0.20)(-3.9) + (0.90)(2.6)v1f = -3.9 m/s

v2f = 2.6 m/s(0.20)(v1i) + 0 = (-0.78) + (2.34)

(0.20)(v1i) = 1.56

v1i = 1.56/0.20

v1i = 7.8 m/s

Problem 3After missing an easy lay up, Whitney tosses a 0.75 kg basketball at a 1.2 kg water jug initially at rest on the sidelines. The ball is thrown to the right at 8.5 m/s and continues to move to the right at 3.0 m/s after the collision. What is the velocity of the jug after the collision?

v1i = 8.5 m/s

GIVEN:

m1 = 0.75 kg

UNKNOWN:

EQUATION:m1v1i + m2v2i = m1v1f + m2v2f

SUBSTITUTE:

SOLVE:

v2i = 0 m/s

m2 = 1.2 kg

v2f = ? m/s

(0.75)(8.5) + (1.2)(0) = (0.75)(3.0) + (1.2)(v2f)v1f = 3.0 m/s

v2f = 3.4 m/s

6.375 + 0 = 2.25 + (1.2)(v2f)

6.375 – 2.25 = (1.2)(v2f)

4.125 = (1.2)(v2f)

4.125/1.2 = v2f

Problem 4

What is the final velocity of a 85 kg halfback rushing to the right at 10 m/s that hits a 130 kg linebacker running to the left at 8 m/s. After the elastic collision, the linebacker has slowed to 2 m/s.

v1i = 4.0 m/s

GIVEN:m1 = 85 kg

UNKNOWN:

EQUATION:m1v1i + m2v2i = (m1 + m2)vf

SUBSTITUTE:

SOLVE:

Vf = 2.9 m/s

v2i = 0 m/s

m2 = 15 kg

vf = ? m/s

(40)(4.0) + (15)(0) = (40 + 15)vf

1) In an experiment, a toy wooden car with a mass of 300g, initially at rest, is struck in the rear by a 30g dart traveling at 15 m/s as shown. With what speed does the car with the dart stuck in it move after the collision?

1) A 50 kg astronaut traveling at 8 m/s to the left catches a 10 kg meteor traveling at 20 m/s to the left. What is the final velocity of the astronaut holding the meteor?

2) In an experiment, a toy wooden car with a mass of 300g, initially at rest, is struck in the rear by a 30g dart traveling at 15 m/s as shown. With what speed does the car with the dart stuck in it move after the collision?

30g 300g 30g 300g

V= 0 m/sV= 15 m/s

V= ?

3) A 50 kg astronaut traveling at 8 m/s to the left catches a 10 kg meteor traveling at 20 m/s to the left. What is the final velocity of the astronaut holding the meteor?

Warm-up 1/14/14Megan is traveling forward at 20.0 m/s in her 1000 kg car and hits Samantha’s 1,500 kg car going slower at 8 m/s in the same direction. Sam’s car is traveling 15 m/s forward after the elastic collision, what is the final velocity of Megan’s car?

v1i = 20 m/s

GIVEN:m1 = 1000 kg

UNKNOWN:

EQUATION:m1v1i + m2v2i = m1v1f + m2v2f

SUBSTITUTE:

SOLVE:

v2i = 8 m/s

m2 = 1500 kg

v1f = ? m/s

(1000)(20) + (1500)(8) = (1000)(v1f) + (1500)(15)v2f = 15 m/s

v1f = 9.5 m/s

20,000 + 12,000 = (1000)(v1f) + 22,500

9500 = (1000)(v1f)

20,000 + 12,000 – 22,500 = (1000)(v1f)

9500/1000 = v1f

Warm-up 1/14/14Mike is traveling forward at 20.0 m/s in his 1000 kg car and hits Joseph’s 1,500 kg car going slower at 8 m/s in the same direction. Joseph’s car is traveling 15 m/s forward after the elastic collision, what is the final velocity of Mike’s car?

v1i = 20 m/s

GIVEN:m1 = 1000 kg

UNKNOWN:

EQUATION:m1v1i + m2v2i = m1v1f + m2v2f

SUBSTITUTE:

SOLVE:

v2i = 8 m/s

m2 = 1500 kg

v1f = ? m/s

(1000)(20) + (1500)(8) = (1000)(v1f) + (1500)(15)v2f = 15 m/s

v1f = 9.5 m/s

20,000 + 12,000 = (1000)(v1f) + 22,500

9500 = (1000)(v1f)

20,000 + 12,000 – 22,500 = (1000)(v1f)

9500/1000 = v1f