Question

Blake stands in a canoe in the middle of a lake. The canoe is stationary. Blake holds an anchor with mass 15 kg, then throws it west with a speed of 8 m/s. Blake and the canoe have a combined mass of 135 kg.

a. The system is defined as Blake, the canoe, and the anchor. What is the total momentum of the system before he throws the anchor?

b. What is the total momentum of the system after he throws the anchor?

c. What is the velocity of the canoe after he throws the anchor?

Answer 1

A.
p=mv
p=135*8
p=1080 kg m/s

Answer 2

Actually this would be B

Answer 3

a) before he throws the anchor nothing is moving so momentum = ?

Answer 4

A would be 0

Answer 5

good

since momentum is conserved, momentum before = momentum after, so B is 0 as well

Answer 6

i would do vf-vi

Answer 7

for c right

Answer 8

for c) set the total momentum equal to 0 and solve for the velocity of the canoe

(mass of blake + mass of canoe)(velocity of blake + canoe) = (mass of anchor)(velocity of anchor)

solve for the blake + canoe system velocity

Answer 9

(mass of blake + mass of canoe)(velocity of blake + canoe)
(135)(8)

Answer 10

8 is the speed of the anchor not the canoe

Answer 11

135*8=8

Answer 12

(135)(velocity of canoe + blake) = 15*8

Answer 13

oh okay so i would eliminate that

Answer 14

8/9

Answer 15

good, we would probably want to write this as a decimal instead

0.88889 m/s east (since the anchor was thrown west, the canoe goes in the opposite direction east)

Answer 16

Lincoln goes bungee jumping. He has a mass of 102 kg.

a. The bungee cord will stretch 8 m when 500 N of force is applied to it. What is the spring constant of the bungee cord?



b. After his jump, Lincoln hangs from the cord motionless. How stretched is the bungee cord past its natural length?

c. The maximum force the bungee cord can handle without breaking is 20,000 N. How far would you have to stretch it to get it to break?

Answer 17

F=-kx

Answer 18

500=(-k)(8)

Answer 19

k=-125/2

Answer 20

good (for force constant we will use the positive value so 125/2 or 62.5 N/m

Answer 21

for b) you will set F = mg and solve for x, using the k value already obtained

Answer 22

102*9.8=62.5(x)
x=16

Answer 23

good 16 m

Answer 24

then for c) just substitute F = 20,000N and solve for x

Answer 25

20000=62.5(x)

Answer 26

x=320m

Answer 27

good

Answer 28

Dwight uses a spring (k = 40 N/m) on a horizontal surface to make a launcher for model cars. The spring is attached to a holder that has a mass of 0.5 kg. If he compresses the spring and releases it, the launcher will move back and forth in periodic motion.

a. If he compresses the spring by 0.2 m, what is the acceleration of the launcher as the spring reaches its natural length?

b. What is the maximum kinetic energy of the launcher?

c. What is the maximum speed of the launcher?

Answer 29

A is 0

Answer 30

good

good

for b) max KE is same as initial potential energy, so U = (1/2)kx^2 where x = 0.2 (initial displacement)

Answer 31

U = (1/2)k(0.2)^2

Answer 32

I solve for U right

Answer 33

yes (you are also given k)

Answer 34

U = (1/2)(40)(0.2)^2
U=0.8

Answer 35

good (0.8J)

then, since it's asking for KE not U, we say KE = 0.8J

for c) set KE equal to (1/2)mv^2 and solve for v

Answer 36

0.8=(1/2)(0.5)v^2
=1.79

Answer 37

good, 1.79 m/s

Answer 38

When Heather swings on a swing set, she moves in periodic motion like a pendulum. She has a mass of 62 kg. If Heather has a maximum height of 1.2 m, what is her maximum velocity?

Answer 39

max U = mgh = (1/2)mv^2 solve for v

Answer 40

(62)(9.8)(1.2)=(1/2)(62)v^2
4.85

Answer 41

m/s

Answer 42

good

Answer 43

Mars has a mass of 6.4 × 1023 kg. It has a moon named Phobos with a mass of 1.07 × 1016 kg.

a. If their centers are 9400 km apart, what is the force of gravity acting on Phobos?

b. A scientific satellite of mass 1300 kg orbits Mars 200 km above its surface. If Mars has a radius of 3396 km, what is the force of gravity acting on the scientific satellite?

c. The satellite is in a circular orbit around Mars. How does the gravitational potential energy of the satellite change as it orbits Mars?

d. How does the acceleration of the satellite change as it orbits Mars?

Answer 44

fg=mg

Answer 45

a) F = Gm1m2/r^2 where G is the gravitational constant 6.674×10−11

Answer 46

F = (6.674×10−11)m1m2/r^2

Answer 47

F = (6.674×10−11)(6.4 × 1023 )( 1.07 × 1016 )/r^2

Answer 48

good, r is the distance between the two planets (9400 km) convert this to meters first

Answer 49

F = (6.674×10−11)(6.4 × 1023 )( 1.07 × 1016 )/9400000^2

Answer 50

good, then just chuck that into a calculator

Answer 51

F = 4.48998×10^-6

Answer 52

there needs to be an exponent sign between 10 and the exponents

Answer 53

(6.674×10^(−11))(6.4 × 10^23 )( 1.07 × 10^16 )/9400000^2 = ?

Answer 54

8.836 × 10^13

Answer 55

I got something a little different, 5.172 e 15 N

http://www.wolframalpha.com/input/?i=(6.674%C3%9710%5E(%E2%88%9211))(6.4+%C3%97+10%5E23+)(+1.07+%C3%97+10%5E16+)%2F9400000%5E2

Answer 56

for b)

the total distance between the satellite and the planet is (3396 + 200) km, use this value for r, then calculate F using the two masses given, and r

Answer 57

that's weird, it's interpreting your input as 9400000^2 only

Answer 58

do you have a scientific calculator you could use instead

Answer 59

F=3596(1300)

Answer 60

Yeah i used another calculator and it got what you got

Answer 61

3596 is the distance not the mass

Answer 62

Wait is the formula
f=ma

Answer 63

What formula are we using

Answer 64

I think that is what is confusing me

Answer 65

we are seeking the gravitational force between two objects

F = Gm1m2/r^2

Answer 66

F = G(6.4 × 1023 )(1.07 × 1016)/3596^2

Answer 67

big G = 6.674×10^(−11) as usual

Answer 68

mass of satellite is 1300 kg

Answer 69

F = ((6.4 × 1023 ))(1.07 × 1016)/3596^2

Answer 70

the two masses are the mass of mars and the mass of the satellite

((6.4 × 10^23 )) and 1300

Answer 71

also you need to convert 3596km to m

Answer 72

F = (6.4 × 1023 )(1300)/3596000^2

Answer 73

good, then just evaluate this (make sure to include the exponent sign betweeen 10 and 23)

Answer 74

*** hold on you forgot G

Answer 75

F = (6.67*10^-11)(6.4 × 1023 )(1300)/3596000^2

Answer 76

there needs to be an exponent between 10 and 23, it's interpreting it as 1023 not 10^23

Answer 77

yup good

Answer 78

so the answer would be F = 4291.51

Answer 79

yes

Answer 80

c. The satellite is in a circular orbit around Mars. How does the gravitational potential energy of the satellite change as it orbits Mars?

as the distance between mars and the satellite increases potential energy decreases

d. I'm not 100% sure on this but I believe acceleration decreases too

Answer 81

THank you so much !

Answer 82

yeah I have to get going now, take care

Answer 83

You as well