# Solve HW Question: Find Maximum Distance Frame Moves Down from Initial Position

• lala56
In summary, the problem involves a suspended frame with a mass of 0.150 kg and a lump of putty with a mass of 0.2 kg being dropped onto it from a height of 30.0 cm. The maximum distance the frame moves downward from its initial position needs to be found. Using the initial position as the reference point for calculating gravitational potential energy and using the stretched position of the spring as the reference point for calculating spring potential energy, the equation .5(.2+.15)(1.39)^2 + .5(29.4)(.05)^2 + mgh = .5(29.4)x^2 + mgx can be used to solve for the maximum distance, with x being
lala56
HW question, help, momentum

"A 0.150 kg frame, when suspended from a coil spring, stretches the spring 0.05 m. A 0.2 kg lump of putty is dropped from rest onto the frame from a height of 30.0 cm (Fig. 8.38). Find the maximum distance the frame moves downward from its initial position."

This problem has been posted before, but I have been unable to use it to solve my question

so, here is what I tried:
the k for the spring = 29.4 using F=kx

then
i found the velocity of the putty as soon as it touched the frame
mgh=.5mv^2
v=2.42
now, find the velocity of the system (putty and the frame)

Mp=mass of putty
Vp=velocity of putty
Mf=mass of frame
MpVp=(Mp+Mf)V2
plug the v found above into Vp, and then V2=1.39

so, now use this:
K1+U1+Ue1=K2+U2+Ue2

K1=kinetic energy
U1= potential energy (gravity)Ue1 = potential energy (spring)

i get:
.5(.2+.15)(1.39)^2 + .5(29.4)(.05)^2 + mgh = .5(29.4)x^2 + mgx

this is how I believe it should be done, except I don't know what to put in place of the "mgh". What is the original potential energy before the spring stretches.

I basically need to find the "x".

thanks, any help is greatly appreciated

Last edited:
I recommend that you use the unstretched position as your zero point for calculating gravitational PE as well as spring PE. Using that, what would the initial height be?

hm, but there is no "unstretched" postition cause when the frame is hanging on it, it is stretched .05m, so it is streteched form the beginning, before the putty is dropped

Sure there's an unstretched position: that's what you are measuring spring PE with respect to. I see three positions: unstretched (h=0), "initial" (h= -0.05m), and lowest point (h = x).

yes, I said that initial height is h=.05, and plugged that into the
.5(.2+.15)(1.39)^2 + .5(29.4)(.05)^2 + mgh = .5(29.4)x^2 + mgx

but I plugged it into the potential energy for spring part of the above equation: 5(29.4)(.05)^2

is everything up there correct thus far? (i mean the reasoning)

Maybe I am not quite understanding what you are trying to say, is it that the initial height of the spring ALSO applies to the gravitational potential energy, so the "mgh" above would be mg(.05)?

i tried that, and the answer is incorrect

(or maybe I didnt quite get what you were trying to say)

lala56 said:
yes, I said that initial height is h=.05, and plugged that into the
.5(.2+.15)(1.39)^2 + .5(29.4)(.05)^2 + mgh = .5(29.4)x^2 + mgx

but I plugged it into the potential energy for spring part of the above equation: 5(29.4)(.05)^2

is everything up there correct thus far? (i mean the reasoning)
Note that your final gravitational PE is mgx, using the same "x" used in calculating the spring PE. To me, that means you've chosen the unstretched position as your zero point for calculating gravitational PE. Did you mean to do that?

Maybe I am not quite understanding what you are trying to say, is it that the initial height of the spring ALSO applies to the gravitational potential energy, so the "mgh" above would be mg(.05)?

i tried that, and the answer is incorrect
Note that the initial height is 0.05 m below the unstretched position.

You can pick any point you want as your reference level for measuring gravitational PE, since all that matters is the change in PE. Just be consistent.

OOOOOOHHHHHHHH

YESSSSSS
ic what you'rse saying
i messed up
it should really be (x+.05)
and then I solve for x

what is the initial gravitational potential here?
.5(.2+.15)(1.39)^2 + .5(29.4)(.05)^2 + mgh = .5(29.4)(X+.05)^2 + mg(X+.05)

it will probably be mg(.05) because .05 is the initial stretch and this even applies to the gravitaitonal force

edit:
it wouldn't really matter though if i made it (x+.05) cause when its is just x, i can subtract .05 from the final answer I get for x

Last edited:
lala56 said:
what is the initial gravitational potential here?
.5(.2+.15)(1.39)^2 + .5(29.4)(.05)^2 + mgh = .5(29.4)(X+.05)^2 + mg(X+.05)
First tell me what the final gravitational PE is? You have now changed the meaning of X to be "the additional amount of stretch beyond the initial 0.05 stretch". What are you using as your reference height for gravitational PE? Pick any point, but pick!
it will probably be mg(.05) because .05 is the initial stretch and this even applies to the gravitaitonal force
Not sure what you are doing here. If GPE is mg(.05), then you are saying that the initial position is 0.05 m above some point?

Try this: Measure GPE from the lowest point that the system reaches, which is the position of maximum stretch. Set GPE = 0 for that point. Given that, what's the initial GPE? Hint: What's the initial height measured from the lowest point?

## 1. What is the purpose of solving this homework question?

The purpose of solving this homework question is to understand the concept of maximum distance frame moves down from initial position and how to calculate it using mathematical equations.

## 2. What is the meaning of "maximum distance frame moves down from initial position"?

Maximum distance frame moves down from initial position refers to the furthest distance that a frame can move downwards from its starting point without hitting any obstacles or reaching the end of its range.

## 3. How do you calculate the maximum distance frame moves down from initial position?

To calculate the maximum distance frame moves down from initial position, you need to know the initial position of the frame, the height of the obstacles, and the range of the frame's movement. Then, you can use the equation d = h - (r - p), where d is the maximum distance, h is the height of the obstacles, r is the range of the frame's movement, and p is the initial position of the frame.

## 4. What factors can affect the maximum distance frame moves down from initial position?

The maximum distance frame moves down from initial position can be affected by the initial position of the frame, the height of the obstacles, and the range of the frame's movement. Other factors that can affect it include the weight and size of the frame, the surface it is moving on, and any external forces acting on the frame.

## 5. How can solving this homework question be useful in scientific research?

Solving this homework question can be useful in scientific research as it involves understanding and applying mathematical concepts and equations. It can also be used to analyze and predict the movement of objects in different scenarios, which can be helpful in fields such as physics, engineering, and robotics.

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