I managed to get C

can anyone elaborate on B pleaseeeee

Originally Posted by Scuderia

I managed to get C

can anyone elaborate on B pleaseeeee

B is calculate the change in gravitational potential energy, correct?


Plug & chug.

HINT: Don't think of Work as a rigid concept. It's not just "W = F dot d" that's simply one form of it. (Dot meaning Dot product*)

Remember that Work is defined as the change in energy of a system, when acted on by an external force (like gravity). With this in mind, your change in energy is precisely the change in potential energy, (which is vertical since gravity is an 'up and down' force).

Your initial potential energy is U1 = m*g*height1...your final potential energy is U2 = m*g*height2. This information has been given in the problem, and so you simply compute DeltaU = U2 - U1 (which also equals mgheight2 - mgheight1 = mg(height2 - height1) = mgDeltah).

So B is then a trick question (Why?).

And Part C, you simply have to assume height1 = 0, and height2 = -x, where x is the height of the cliff given in your problem. Then U = m*g*(-x). (This is also a trick question)

HINT: All three answers should look veeeery similar.


Hope that helps.

EDIT: I also want to emphasize that Work (change in energy) depends only on the start and end points...not how the object gets there! In physics jargon, the d in "F dot d" stands for displacement, and not distance.

If I lift a boulder up to the top of a cliff, I've done work on it and given it potential energy. It's the same amount of potential energy whether I walk around the block six times before doing so, or if I haul it to the top, back down (because I forgot my hat) and then back up. In particular, this is why you were getting an incorrect answer when adding that 'extra height' the washer travelled.

this isn't directly from any specific CAPA question, but i'd really appreciate it if someone would help clarify some things relating to work

1) the work done by a spring is given by W = - 1/2 kx^2
- is the negative sign always there? can it be positive?
- for ex. one of the capa questions involved a rocket on a spring, in this case, the force exerted by the spring and displacement of the rocket are in the same direction (i think), would the work then be W= + 1/2 kx^2?

2) work-kinetic energy theorem says W = ΔK
but apparently, the following is also true W = ΔE (sys) = ΔE(mech) + ΔE(th) = ΔK+ΔU+ΔE(th)
makes no sense to me whatsoever how both equations can be true

3) E(mech) = K + U
-does the U involve just (1) gravitational potential energy, or is it (2) gravitational + spring pot. engy? i'm thinking 2, but i'm not too sure about it

i would really appreciate it if someone's willing to help me out with some of this stuff! midterm on monday on work/energy/momentum and i'm ok with most of the stuff, except for pretty much these 3 things

1. It depends on whether or not the force is going the same direction as the force that the spring applies on the load. You`re right about number 2. (opposite direction (cos180) is negative, and same direction (cos0) is positive)

2. Only the second one is true. The first one is just an approximation we use in the course, assuming that the objects are point-particles, that is, to say that there is no internal energy (we neglect it).

3. It is 2. E(mech) = total kinetic energies + all potential energies (which includes both of what you mentioned)

so the work-kinetic energy theorem only holds true when thermal/potential energies are 0? so it's just a special case of the general W = ΔE (sys) right?

Originally Posted by waldo92

this isn't directly from any specific CAPA question, but i'd really appreciate it if someone would help clarify some things relating to work

1) the work done by a spring is given by W = - 1/2 kx^2
- is the negative sign always there? can it be positive?
- for ex. one of the capa questions involved a rocket on a spring, in this case, the force exerted by the spring and displacement of the rocket are in the same direction (i think), would the work then be W= + 1/2 kx^2?

The negative sign designates the direction of force. Since a spring always resists stretching, namely the applied force, it's always going to be negative, yes. The Spring Constant, K may differ from 1/2 however. In your rocket problem, the scenario is presumably that the rocket is trying to "get away from" the spring, and the spring is trying to oppose this motion...so again, should be negative.

2) work-kinetic energy theorem says W = ΔK
but apparently, the following is also true W = ΔE (sys) = ΔE(mech) + ΔE(th) = ΔK+ΔU+ΔE(th)
makes no sense to me whatsoever how both equations can be true

Work is defined as the total gain/loss of energy within a system due to external forces.

W = ΔK only if there's no change in potential energy (or thermal energy, etc.). For instance, if you have a block sliding to a stop, on a horizontal surface with only friction acting on it, then indeed, W = ΔK, which is precisely the amount of energy lost due to friction.

So in other words, if there are lots and lots of factors at play, Work is then the net effect on energy after all those factors are accounted for. W = ΔK is in an "ideal" approximate scenario, in which Kinetic energy is the only thing that changes.

3) E(mech) = K + U
-does the U involve just (1) gravitational potential energy, or is it (2) gravitational + spring pot. engy? i'm thinking 2, but i'm not too sure about it

Mechanical energy is defined as Kinetic plus Potential energy, and "U" stands for potential energy. This means all potential energy that play a role in your problem.

Technically you are including terms like atomic potential (bond) energy, but we don't write them in the equation for mechanical energy if they don't change. So if you have for example, a rocket on a spring, the bond energy of the rocket before and after won't change:

ΔE_mech = ΔK + ΔU_gravity + ΔU_spring + Δ(Bond energy)

But Δ(Bond energy) = 0, because you're assuming the mass doesn't change, and so forth.

Does that help?

Originally Posted by waldo92

so the work-kinetic energy theorem only holds true when thermal/potential energies are 0?

Thermal energy of anything with mass is never 0...The work-kinetic energy theorem only holds when the change in thermal/potential (etc.) energy is 0. Or in other words, when only Kinetic energy changes.

Not to be nitpicky here, but that's a crucial point to understand.

also...a lot of the questions that are on CAPA are from textbook, just the numbers are changed
there is a website: www.cramster.ca ... make a free account, type in the name of the physics textbook, and u will get answers to most of the questions that are in the textbook. u will get free answers for odd numbered questions, and for even numbered questions, u have to buy some form of a membership thing...but its not worth it (the odd numbered are usually good enough to give u an idea of how to complete most questions)

thanks everyone, that helps a lot, and that cramster.com website is a gold mine lol

For capa, just take out the numbers and google it. 90% of the time, someone has posted it to yahoo answers or a similar site and it becomes quite easy to solve.

Hey guys, there's 2 questions I'm struggling with again and if anyone can help me out, that'd be great!

1. A spring is suspended from a ceiling and has a block attached to its lower end. The block is held a distance y1 from the ceiling (at this point the spring is at its rest length) and released. The block oscillates up and down with its lowest point being 0.119 m below y1. Find the frequency of the motion. Calculate the speed of the block when it is 0.074 m below the release point at y1.

Now I solved for the frequency to be 2.04 Hz and that is correct.
To calculate the speed, I thought it's just v = wA = 2*pi*2.04*0.074 but that's not giving me the correct answer..

2. A brick is resting atop a piston that is moving vertically with simple harmonic motion of period 1.17 s. At what amplitude will the brick separate from the piston? If the piston's amplitude is 4.56 cm, find the maximum frequency at which it can move without dislodging the brick.

Now for this question, I used the formula a = -w^2cos(wt) and solved for the amplitude to be 0.34 m (which is correct) but I'm unable to solve the second part of this question.

If anyone could kind me guide me as to how I should approach these questions, I'd be thankful!

for the second question, how'd you get that amplitude?

Originally Posted by waldo92

for the second question, how'd you get that amplitude?

To find amplitude:

mg - n = m A ω2
mg - m A ω2 = n
if the block and piston are to be seperated; normal force must be zero
so we get
mg = m A ω2
g = A ω2
A = g / ω2
as g = 9.8 m / s2
ω = 2 π / T

find amplitude A.

Originally Posted by ShesTheMan

2. A brick is resting atop a piston that is moving vertically with simple harmonic motion of period 1.17 s. At what amplitude will the brick separate from the piston? If the piston's amplitude is 4.56 cm, find the maximum frequency at which it can move without dislodging the brick.

Now for this question, I used the formula a = -w^2cos(wt) and solved for the amplitude to be 0.34 m (which is correct) but I'm unable to solve the second part of this question.

If anyone could kind me guide me as to how I should approach these questions, I'd be thankful!

xD and to find the frequency

A = g / ω2
A = .0## m
solve for ω

thn

ω = 2 π f
find frequency f



xD not taking cred for this answer since i found it on cramster *sigh*

^ Thank you so much!
Do you have any idea how to find the speed for the first question I posted (the last q in the capa assignment)