How to Calculate Spring Compression and Body's Launch Height from Falling Mass?

In summary, at the point of greatest impact, the body's weight causes the spring to be compressed by .5*kx2, resulting in a displacement of 7.54*10-4m. The body launches with a velocity of 9.8m/s.
  • #1
DEckrich7
4
0

Homework Statement


A falling body has a mass of 15 kg over a height of 135 m onto a spring. The spring has a spring constant of 1.95*105N/m.
a) How far is the spring compressed?
b) At the point where the body's impact on the spring scale the greatest, what is the reading?
c) Assuming all of the elastic potential energy in the compressed spring scale is converted into kinetic energy, what is the body's initial velocity?
d) How high will the body launch?

Homework Equations


F=ma, F=-kx, Ue= .5*k*x2, K=.5*m*v2, Weight=mg, UG=mgy

The Attempt at a Solution


Since we're in the metric system, I'm using the gravitational constant of 9.8 m/s2. So, with F=ma, I'll do F=15kg*9.8m/s2 to give me a force of the body on the scale of 147 N. I'll substitute that value into F=-kx along with the spring constant and solve for x. 147 N/1.95*105N/m yields a displacement of about 7.54*10-4m. This seems really small however... For letter b, I'm assuming I'll multiply 15kg and 9.8m/s2 to find the body's weight in Newtons. For c) and d), I'm just stuck.
Thank you all for your time :).
 
Physics news on Phys.org
  • #2
Welcome to PF!

Hi DEckrich7! Welcome to PF! :wink:

DEckrich7 said:
A falling body has a mass of 15 kg over a height of 135 m onto a spring. The spring has a spring constant of 1.95*105N/m.
a) How far is the spring compressed?
b) At the point where the body's impact on the spring scale the greatest, what is the reading?
c) Assuming all of the elastic potential energy in the compressed spring scale is converted into kinetic energy, what is the body's initial velocity?
d) How high will the body launch?
…
So, with F=ma, I'll do F=15kg*9.8m/s2 to give me a force of the body on the scale of 147 N. I'll substitute that value into F=-kx along with the spring constant and solve for x.…

Nooo, that won't work at all :redface:

Start again, using conservation of energy …

what do you get? :smile:​
 
  • #3


tiny-tim said:
Hi DEckrich7! Welcome to PF! :wink:



Nooo, that won't work at all :redface:

Start again, using conservation of energy …

what do you get? :smile:​

Thank you very much, I am so happy to join the community!
We haven't learned much about the conversation of energy in my class; a similar question to this one was my physics quiz, so we should know how to do this one however (so I should have enough knowledge to solve it!). What I do know however, is that initial Kinetic and potential energy, are equal to the final kinetic and potential energy. I also know that Etotal= K+PE+Q. Would that mean the body his bouncing off of the spring with the same velocity it is hitting it with?
Thank you very much, tiny-tim :)
 
  • #4
Hi DEckrich7! :wink:
DEckrich7 said:
What I do know however, is that initial Kinetic and potential energy, are equal to the final kinetic and potential energy. I also know that Etotal= K+PE+Q. Would that mean the body his bouncing off of the spring with the same velocity it is hitting it with?

That's right, KE + PE = constant.

In this case, the PE is both gravitational PE (=mgh) and spring PE (= 1/2 kx2)

(btw, what's Q? :confused: if it's heat, ignore it in problems like this)

So, for a), KEinitial and KEfinal are both 0, so that should give you an equation in x …

what do you get? :smile:​
 
  • #5
Thank you very much for your help tiny-tim, I'll work on the problem, and yes, Q is heat loss.
 

FAQ: How to Calculate Spring Compression and Body's Launch Height from Falling Mass?

1. How does a spring store energy?

A spring stores energy by deforming or stretching when a force is applied to it. The potential energy stored in a spring is directly proportional to the amount of deformation or displacement from its equilibrium position.

2. What is the relationship between the force applied to a spring and the resulting displacement?

According to Hooke's law, the force applied to a spring is directly proportional to the displacement or stretch of the spring. This means that the more force applied to the spring, the more it will stretch or compress.

3. How does the spring constant affect the energy stored in a spring?

The spring constant, also known as the stiffness constant, determines how much force is needed to stretch or compress a spring by a certain distance. The higher the spring constant, the more force is required to stretch the spring, resulting in more potential energy stored.

4. Can a spring have both potential and kinetic energy?

Yes, a spring can have both potential and kinetic energy. When a spring is compressed or stretched, it has potential energy. When it is released, it converts that potential energy into kinetic energy as it returns to its equilibrium position.

5. How does the mass of an object affect its potential energy in a spring system?

The mass of an object does not affect the potential energy stored in a spring. The potential energy is solely dependent on the displacement of the spring. However, the mass of the object will affect the kinetic energy of the system, as a heavier object will have more energy when moving at the same speed as a lighter object.

Similar threads

Distribution of Energy when work is done on a system of 2 masses connected by a spring
Replies
17
Views
488
Spring Problem Involving Variables and Constants Only
Replies
3
Views
858
Compression of a spring by an object in free fall
Replies
8
Views
2K
Calculating Initial Height of a Falling Safe on a Spring
Replies
5
Views
2K
A block of mass m is dropped onto the top of a vertical spring....
Replies
8
Views
5K
Height of falling object vs. compression of spring
Replies
1
Views
1K
Calculating spring constant of a spring loaded cannon
Replies
7
Views
3K
Spring Question -- A mass falls onto a spring compressing it....
Replies
3
Views
2K
Force and Energy of a block on a spring as it compresses.
Replies
3
Views
1K
Mass sliding on frictionless inclined plane compresses a spring
Replies
7
Views
3K

Hot Threads

Recent Insights

Back
Top