Question

A boat floats south on the Amazon River at a speed of 6 m/s. The boat and passengers have a combined mass of 540 kg.

a. What is the momentum of the boat? (Remember, momentum is a vector quantity.)

b. The passengers paddle backward, reducing the speed to 4 m/s. What was the impulse applied to the boat by the paddling?

Answer 1

a) p = mv as usual

Answer 2

P=540*6
p=3240 kg*m/s

Answer 3

good, since momentum is a vector we also need to specify the direction

so p=3240 kg*m/s south

Answer 4

for b) impulse = change in momentum = ?

Answer 5

2?

Answer 6

would it be 6-4

Answer 7

that's the change in velocity

what about the change in momentum?

Answer 8

p=540*4
p=2160
3240-2160=1080

Answer 9

1080 was the change in momentum

Answer 10

good, and since the impulse is in the opposite direction as the initial momentum we say the impulse was 1080 kg m/s north

Answer 11

At a race track, a car of mass 1150 kg crashes into a concrete wall at a speed of 85 m/s.

a. If the car comes to a stop when it hits the wall, what is the magnitude of the impulse applied to the car?

b. The car crashes into the wall, stopping in 0.1 seconds. What force is applied to the car?

Answer 12

a) impulse is change in momentum (magnitude means we can disregard direction for now)

Answer 13

p=1150*85
p=97750

Answer 14

good (units are kg m/s as usual)

for b) impulse = f * delta t, calculate f

Answer 15

97750=f*0.1

Answer 16

good, solve for f

Answer 17

977500N

Answer 18

good

Answer 19

Bill forgets to put his car in park, and it starts rolling forward. When it is moving at a speed of 2 m/s, it collides with Tanya's car, which is stationary. Bill's car bounces backward at a speed of 1.2 m/s. Bill's car has a mass of 1100 kg, and Tanya's car has a mass of 800 kg.

a. What is the total momentum of the system before the collision?

b. What is the total momentum of the system after the collision?


c. What is the velocity of Tanya's car after the collision?

Answer 20

a) total momentum = initial momentum of Billy's car + initial momentum of Tanya's car = ?

Answer 21

i combine the masses first right?

Answer 22

oh okay so do it separately

Answer 23

hint: initially, only bob's car is moving so it's just bob's car mass * velocity

Answer 24

Bob
p=mv
p=1100*2
p=2200 kg m/s

Answer 25

Tanya
p=mv
p=800*2
p=1600 kg m/s

Answer 26

good, and the direction is "forward" so 2200 kg m/s forward

b) momentum is conserved so final momentum = initial momentum

for part c) set bob's momentum equal to tanya's and solve for tanya's velocity

Answer 27

2200-1600=600

Answer 28

tanya's car is not moving at the beginning so you do not need to add tanya's momentum for parts a and b.

Answer 29

okay cool so just bob's momentum

Answer 30

okay now for b

Answer 31

i combine the two masses and then calculate momentum right

Answer 32

\(\color{#0cbb34}{\text{Originally Posted by}}\) @Vocaloid
good, and the direction is "forward" so 2200 kg m/s forward

b) momentum is conserved so final momentum = initial momentum

for part c) set bob's momentum equal to tanya's and solve for tanya's velocity
\(\color{#0cbb34}{\text{End of Quote}}\)

the answers for part a and part b should be the same because momentum is conserved.

Answer 33

so it would just be 2200 for B

Answer 34

yes

Answer 35

so b.) 2200 kg m/s forward
c.)2200=960

Answer 36

for part c) the statement you have given is not logical, 2200 is not equal to 960

set Bob's final velocity * Bob's car mass = Tanya's final velocity * Tanya's car mass and solve for tanya's velocity

Answer 37

1100=1.2*800

Answer 38

wait

Answer 39

1100=v(800)

Answer 40

1.4?

Answer 41

bob's final momentum = 1100 * 1.2 = tanya's final momentum = 800 * v

solve for v

Answer 42

1320=800*v
v=1.65

Answer 43

good, 1.65 m/s forward

Answer 44

thank you so much!