Question

A 2.41 kg wood block is launched up a wooden ramp that is inclined at a 32° angle. The block's initial speed is 9.67 m/s. What vertical height does the block reach above its starting point?

Answer 1

Do you know of the conservation of energy? We can use this to solve this kind of problem.. Let me know what you know so I can best help you understand... How would you go about solving this?

Answer 2

conservation of energy = ki+ui=Kf+uf+w

Answer 3

Good.

Answer 4

so 9.67 m/s = ui?

Answer 5

idk what does ki, kf, ui, uf and w stand for?

Answer 6

ki, kf = initial/final kinetic energy
ui, uf = initial/final gravitational potential energy
w = work done by external forces

Do you know how to apply the conservation of energy equationi to this situation? Yes/No? If not I can show you how. It's very straight forward.

Answer 7

no i dont know

Answer 8

Ok... but you have seen the equation before. Allow me to explain how it works. There are 2 kinds of energy you have identified for me, kinetic energy and gravitational potential energy. If something has kinetic energy, what does that mean? If something has gravitational energy what does that mean?

By the way, I apologize for any delay as I am between you and one other student whom I hope to finish up with here in a few minutes. Just FYI..

Answer 9

its okay. well is kinetic energy is energy exerted when an object is in motion and gravitational energy is energy exerted on an object through gravity (ex. as an object falls)?

Answer 10

yep. If it moves it has KE. If its elevated (up or down) it has graviational energy (Ue).
So do you know how to calculate the kinetic energy of the block at the bottom of the ramp?

Answer 11

k= (mv^2)/2
.......... so

Answer 12

Yep. So what is the ke at the bottom. You're right on.

Answer 13

v =9.67
so would 2.41 be m or k?

Answer 14

Ah... it would be m for mass. Mass has units of kg.

Answer 15

ok so

k=((2.41)(9.67)^2)/2

Answer 16

Excellent. What number does that yield?

Answer 17

i got 112.678

Answer 18

as the yield

Answer 19

Yep. So your KE = 113 J (J stands for Joules. That is the unit of kinetic energy). Looks good so far. Any questions yet? All we have doen is determined the kinetic energy of the block. So far so good?

Answer 20

yes so far so good

Answer 21

Ok. So if this block were to slide up a ramp, do you suppose it would slide forever or would gravity eventually make it stop sliding at some high point before pulling it back down?

Answer 22

it would stop at some time then fall back down

Answer 23

Good. At the point where it stops before sliding back down, is the block moving or is it stopped?

Answer 24

it stops

Answer 25

Very good. So if it stops on a ramp, does it have kinetic energy or gravitational potential energy?

Answer 26

it has a grav. pot. energy

Answer 27

You are correct. It has GPE because the block slides up the ramp to its highest point and stops for a split second. This is where we are at now.

The law of conservation of energy says that energy isnot created or destroyed, only converted from one form to another. Do you understand that our block had kinetic energy initially and then through its motion up the ramp was eventually transformed into gravitational potential energy? Yes/No

Answer 28

yes i understand

Answer 29

Ok so then with this logic in mind, because our kinetic energy = our gravitational potential energy,

Ke = Ue
113 = mgh

Make sense? If so, are there any more numbers that we can plug in for this problem?

Answer 30

yes it makes sense so far.

Answer 31

So what is the number we can plug in for m? Also, what number does your instructor prefer you to use for g?

Answer 32

i think m would be 2.41 and would g equal 9.81 (for gravity)

Answer 33

yep.
\[113 = (2.41)*(9.81)*h\]
Do you know how to solve for h?

Answer 34

yes give me a sec....

Answer 35

Take your time... I'm still bouncing around.

Answer 36

i got 4.77 m

Answer 37

That is the best answer ever.

What are your thoughts now? Anything I may clear up?

Answer 38

so 4.77 m would be the answer? I plugged that in and they said its wrong.

Answer 39

Does your program consider significant figures?

Answer 40

im not sure about that but if it does would it be 4.8 because the lowest sig fig is 2 from the 32 degrees?

Answer 41

hmm.... When I did this real fast I ended up with 4.78 m, not 4.77. Let me do a real fast calculation just to verify the answer doing things the more difficult way....

Answer 42

ok

Answer 43

ok. So I did this the hard way. We are correct. The answer I receive is 4.76 m. This tells me we just need to get our stuff together and figure out what the correct answer is due to sig figs. I just quickly read a math website called ask Dr. Math. He talks about this issue here:

http://mathforum.org/library/drmath/view/54139.html

The correct answer may be 4.8 m if that is the case. Otherwise we are just so very close to it.

Answer 44

i tried 4.8 and they said its wrong.

Answer 45

How about our other possibilities? Our answer is not incorrect. I'm certain of that. It's just working out the sig figs at this point. Have you tried 4.76?

Answer 46

ok that works. one more question how would i attempt to solve this? What speed does it have when it slides back down to its starting point?

Answer 47

Sure.... We talked about energy conservation in this whole process correct? And that means that the energy we start with is the energy we finish with just in a different form (converting from kinetic energy to gravitational potential energy). So what do you intuitively think the speed will be at its starting point?

Answer 48

0 m/s?

Answer 49

I guess this was a poorly worded question on my part. If we mean top of ramp starting point you would be correct as this is what the initial velocity would be as the block begins to slide back down. How fast do you think the block is moving at its original starting point, meaning at the bottom of the ramp as it approaches the bottom of the ramp?

Answer 50

If youre not sure just say so. This is fine as well and I'll explain.

Answer 51

But you are encouraged to take an educated guess.

Answer 52

9.67 m/s

Answer 53

idk

Answer 54

You are so very close... it would actually be -9.67 m/s if we are talking about its velocity. If we are talking about its speed then you would be correct in only saying 9.67 m/s. Velocity is a vector quantity that requires + or - signs to indicate the direction of motion. So if it is velocity it would be -9.67 m/s. Does that guess and explanation make sense to you?

Answer 55

yes

Answer 56

see what it says when you enter the data. The nice thing about physics is that if you can see the symmetry in a problem, you will only have to do one half of it saving you time.

Answer 57

what is the difference between velocity and speed?

Answer 58

speed is like 55 km/h
velocity is like 55 km/h south.

you just put a direction or a +/- sign with your number depending on how the math works out and that makes it a velocity.

Answer 59

i typed it in and they said its wrong.

Answer 60

so velocity has a direction to it and speed doesnt bascically

Answer 61

yes that is correct.

Answer 62

did you enter -9.67 or just 9.67?

Answer 63

-9.67

Answer 64

then i typed in 9.67 and they said thats wrong

Answer 65

what is your question again?

Answer 66

What speed does it have as it attempts to slide back down to its starting point???... Well its initial velocity would be zero as you had said for the reasons we have discussed. But I cannot see why the final velocity of the object at its starting point would not be the opposite of what its original value was. That just does not make any sense to be otherwise.

Answer 67

What speed does it have when it slides back down to its starting point?

Answer 68

It is not a constant speed because it is accelerated down the ramp due to gravity. Its starting velocity/speed would be 0 m/s.

Answer 69

i know that is why i was confused. i plugged in 0 m/s. do you think it could be that fact that we didnt use the angle given to us in the problem (32 degrees)?

Answer 70

Perhaps its -9.66 m/s. I just plugged in the number we used for the max height (4.76m) and I end up with -9.66 m/s. We did use the 32 degrees in a very indirect manner. Actually, we were able to ignore it because there was another method employed in solving the problem but when I did things the hard way, we used it. let me do things the hard way again and see what number i come up with now.

Answer 71

ok

Answer 72

Well I end up with -9.67 doing things with the angle. Because they are asking for speed, we need not worry about the - signs. Can you try 9.66 m/s without fear of penalty? We have the right answer. Its just convincing the machine on how to accept it.

Answer 73

they said 9.66 is wrong

Answer 74

hello are you still there?

Answer 75

I'm really at a loss on this one. I do not understand why it is not accepting our answer. In working backwards I arrive at either the answer 9.66 m/s or 9.67 m/s depending on how you go about solving the problem. Again, this is only true of they're talking about speed. If they want velocity then we need to say -9.66 m/s or -9.67 m/s but I honestly do not know why it is not working. It should be the exact opposite of what we've done. Is there any additional information you may be missing? Just out of curiosity?

Answer 76

Any luck?