# A block of mass m is dropped onto the top of a vertical spring....

• Ammar2211
In summary, a block of mass m is dropped onto the top of a vertical spring whose force constant is k. If the block is released from a height h above the top of the spring, the maximum energy of the block is the sum of the potential energy of the mass at the top of the spring and the kinetic energy of the block.
Ammar2211
Summary:: A block of mass m is dropped onto the top of a vertical spring whose force constant is k. If the block is released from a height h above the top of the spring,
a) what is the maximum energy of the block?
b) What is the maximum compression of the spring?
c) At what compression is the block's kinetic energy half its maximum value?

A block of mass m is dropped onto the top of a vertical spring whose force constant is k. If the block is released from a height h above the top of the spring,
a) what is the maximum energy of the block?
b) What is the maximum compression of the spring?
c) At what compression is the block's kinetic energy half its maximum value?Anybody who can solve these 3 parts of the question, although I have a solution but I am confused whether its right or wrong so need your directions...

For part a) either max. energy would be mgh or mg(h+x)
For part b) either expression would be mgh=(1/2)kx^2 or mg(h+x)=(1/2)kx^2
For part c) I am stucked how to solve this part, kindly help me out to solve...

[Moderator's note: Moved from a technical forum and thus no template.]

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Hello Ammar, !

Ammar2211 said:
I am confused whether its right or wrong
Well, if you give two different answers for both part a) and part b), then there are definitely wrong answers present !
And if you don't say what ##x## is, everyone is in the dark ! But: let me guess: it is the compression distance of the spring, with 0 = no compression and x> 0 yes compression. So ##h## and ##x## have different orientations ?

A picture would be very welcome !

Re energy: what kind of energy ? let me guess: mechanical energy -- and I suspect we may assume it is conserved in this scenario. Meaning there is no max enregy, just the (constant) energy ? I don't want to appear too harsh: which of the b) answers do you think is more likely when the spring is compressed ?

Ammar2211
I assumed the compression of spring due to the mass block would me x
Obviously mass block is present at a certain height so P.E & K.E are associated with it

You need to decide what is your system - just the mass ##m##, or the mass ##m## and the spring. Try deriving the following:
##mgh = \frac{1}{2}mV^2## where ##V## is the velocity of ##m## at the moment of impact with the spring.
##mgh + mgx = \frac{1}{2}kx^2##
Use the principle of conservation of mechanical energy.

Ammar2211
ok, forget about each and every point I provided you, just assume this is a problem then how you will solve it?

Q: A block of mass m is dropped onto the top of a vertical spring whose force constant is k. If the block is released from a height h above the top of the spring,
a) what is the maximum energy of the block?
b) What is the maximum compression of the spring?
c) At what compression is the block's kinetic energy half its maximum value?

a) if there is no energy loss, the energy is constant ##\Rightarrow## maximum energy = energy

Wrt the top end of the spring the potential energy is ##mgh## (as you mentioned).
Wrt the point of maximum compression the potential energy is ##mg(h+x)## (as you also mentioned).
Wrt the bottom end of the spring the potential energy is ##mg(h+L)## (if L is the length of the spring).

b) was given away (somewhat against PF guidelines) by @thinkingcap81 -- and it matches one of your answers for b) -- you still have to solve the quadratic equation, but I am sure you can do that.

c) is a matter of writing down a suitable equation -- make a start !

Ammar2211
I'm guessing there's a typo in your text of the question. Perhaps it should be,

a) what is the maximum KINETIC energy of the block?

If you put that word in there, it makes more sense. Is it correct?

After that, thinkingcap81 gave you more than enough hints.

DEvens said:
I'm guessing there's a typo in your text of the question. Perhaps it should be,

a) what is the maximum KINETIC energy of the block?

If you put that word in there, it makes more sense. Is it correct?

After that, thinkingcap81 gave you more than enough hints.
Maximum energy indicates all types of possible energies!

Ammar2211 said:
Maximum energy indicates all types of possible energies!

Note that total energy is dependent on your zero point for GPE. This suggests that it should be the maximum KE you are looking for. Otherwise, there is no definite answer to how much GPE the block has at any point.

## 1. What happens when a block of mass m is dropped onto the top of a vertical spring?

When the block is dropped onto the spring, it will compress the spring due to the force of gravity acting on the block. This compression creates potential energy in the spring.

## 2. How does the mass of the block affect the spring's compression?

The heavier the block, the greater the force of gravity acting on it, and therefore the greater the compression of the spring.

## 3. What happens to the potential energy of the spring when the block is dropped onto it?

When the block is dropped onto the spring, potential energy is stored in the spring due to its compression. This potential energy can be converted into kinetic energy when the spring is released.

## 4. What other factors can affect the compression of the spring?

The stiffness of the spring and the height from which the block is dropped can also affect the amount of compression in the spring.

## 5. How does the spring's compression affect the motion of the block?

The compressed spring exerts a force on the block, causing it to accelerate and move upwards. As the spring decompresses, the force decreases and the block will eventually come to a stop at the top of its motion.

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