Grade 11 Physics Problem About Work and Energy

AI Thread Summary
The discussion revolves around solving a physics problem involving a spring and an object with kinetic energy. The key equation for elastic potential energy is 1/2 kx^2, where k is the spring constant and x is the compression distance. Participants clarify that the initial kinetic energy of the object, calculated as 1/2 mv^2, is converted into the spring's potential energy upon maximum compression. The consensus is that the correct compression distance x is 8 meters, derived from equating the initial kinetic energy to the spring's potential energy. The conversation emphasizes the importance of understanding energy conservation in solving the problem effectively.
Felicity26
Messages
11
Reaction score
0
1. The energy from elastic potential is 1/2 kx^2. K is a spring constant and x is the displacement distance of the spring from its equilibrium position. How far will a spring of spring constant k=25 N/m compress if an obejct of mass 4 kg has an initial velocity of 20 m/s runs into the spring without slowing down or speeding up?



2. 1/2 kx^2,



3. Basically, all I could come up with was putting the variables into the equation. To be honest, I don't know where to start solving this question or what equations I should use other than the six kinematic equations. The best I can think of after this is converting the mass into Newtons. Actually, what I wanted to know was how do I start solving this question? Sorry:(
 
Last edited:
Physics news on Phys.org
Felicity26 said:
1. The energy from elastic potential is 1/2 kx^2. K is a spring constant and x is the displacement distance of the spring from its equilibrium position. How far will a spring of spring constant k=25 N/m compress if an obejct of mass 4 kg has an initial velocity of 20 m/s runs into the spring without slowing down or speeding up?



2. 1/2 kx^2,



3. Basically, all I could come up with was putting the variables into the equation. To be honest, I don't know where to start solving this question or what equations I should use other than the six kinematic equations. The best I can think of after this is converting the mass into Newtons. Actually, what I wanted to know was how do I start solving this question? Sorry:(

Conservation of energy. What is the initial energy?
 
I would take that 20m/s and find the KE(.5mv^2). then that is converted into "spring energy" solve from there.
 
pat666 said:
I would take that 20m/s and find the KE(.5mv^2). then that is converted into "spring energy" solve from there.

Right. Initially the only energy is the kinetic energy of the object. When it compresses the spring to the maximum distance its final speed will be v = 0 (no kinetic energy). So the only energy at the maximum distance compressed is the potential energy in the spring.
 
hey, just wondering is the answer 17.9m. also the question is not written well. when you say that it doesn't slow down i assumed that it meant that the final velocity is also 20m/s(y/n) if it doesn't slow down at all the spring will be destroyed and carried away with the projectile.
 
pat666 said:
hey, just wondering is the answer 17.9m. also the question is not written well. when you say that it doesn't slow down i assumed that it meant that the final velocity is also 20m/s(y/n) if it doesn't slow down at all the spring will be destroyed and carried away with the projectile.

It says the INITIAL VELOCITY = 20m/s and it doesn't speed up or slow down. All that means is that it stays at v = 20m/s until it hits the spring. No friction is slowing it down and no other force is speeding it up. Once it hits the spring it does start slowing down as the kinetic energy is converted into potential energy of the spring.
 
yep that's what i thought, do you have an answer for the question?
 
pat666 said:
yep that's what i thought, do you have an answer for the question?

That is not the answer I got. Show your work.
 
Sorry, I don't know if the answer is 17.9m; I wasn't given an answer key. I put the numbers in and got 800 J. I was wondering if the equation Eg=mgh would be any help to figuring out the distance?
 
  • #10
Felicity26 said:
Sorry, I don't know if the answer is 17.9m; I wasn't given an answer key. I put the numbers in and got 800 J. I was wondering if the equation Eg=mgh would be any help to figuring out the distance?

Your still not showing your work and thus I cannot help you. Why would gravitational potential energy have to do with this system when it is all on a flat table (presumably)? The height does not change in the problem.
 
  • #11
yeah mgh is static(no movement in the j direction)... 1/2mv^2=1/2kx^2 mv^2=kx^2
4*20^2=25x^2 x=8m not sure how i got 17 or 19 or whatever..
 
  • #12
pat666 said:
yeah mgh is static(no movement in the j direction)... 1/2mv^2=1/2kx^2 mv^2=kx^2
4*20^2=25x^2 x=8m not sure how i got 17 or 19 or whatever..

I got 8m as well.
 
  • #13
I thought there was some kind of relation between height and distance. Right now, all I have is Us=1/2 mv^2, which would be 1/2 (25)(x)^2. Since I'm trying to find x, I'd have to find Us first. But I also have a kinetic energy of 800 J. So I'm guessing I'll have to find an equation that would find Us that includes the kinetic energy? Am I on the right track?
 
  • #14
Felicity26 said:
I thought there was some kind of relation between height and distance. Right now, all I have is Us=1/2 mv^2, which would be 1/2 (25)(x)^2. Since I'm trying to find x, I'd have to find Us first. But I also have a kinetic energy of 800 J. So I'm guessing I'll have to find an equation that would find Us that includes the kinetic energy? Am I on the right track?

No 8m is the answer. Height and distance of what? Do you understand what is happening in this problem? All of the kinetic energy is transferred into elastic potential energy of the spring. At that point the spring is the most compressed and that compression distance is x = 8m. what is Us?
 
  • #15
Sorry, I didn't refresh the page when I submitted the reply. I think I get it now. But, I was wondering, if the equation is 1/2mv^2, why is the half missing? (Oh, I was trying to look up the notation for potential energy and I got U and s as the sub for the spring, but I'm guessing I looked up the wrong thing)
 
  • #16
When I say the missing 1/2, I mean when you put then numbers into solve.
 
  • #17
E_i = K_i + Ui = K_i + U_gravity + U_spring = (1/2)M(V_i)^2 + Mgh + 0
E_f = K_f + U_f = K_f + U_gravity + U_spring = (1/2)M(V_f)^2 + Mgh + (1/2)kx^2

E_i = E_fand V_f = 0

(1/2)M(V_i)^2 + Mgh = (1/2)kx^2 + Mgh

Mgh's cancel out. We could have ignored gravitational potential energy from the beginning since we know it did not change during the problem.

(1/2)M(V_i)^2 = (1/2)kx^2

Solve for x.
 
  • #18
do the math there is a half on both sides of the equation so you can cancel them, if you prefer leave them it will give you the same answer. hope i was helpful.
 
  • #19
Thank you!
 

Similar threads

A block dropping onto a spring system
2
Replies
58
Views
2K
Distribution of Energy when work is done on a system of 2 masses connected by a spring
Replies
17
Views
1K
Difficulty in deciding when to apply work energy theorem
Replies
2
Views
1K
Why doesn't this solution work? (Springs and Conservation of Energy)
Replies
2
Views
1K
Question about springs and rotational/translational energy
Replies
4
Views
1K
Spring with mass hangs from the ceiling
Replies
22
Views
1K
Find elastic energy in the compressed spring.
Replies
12
Views
3K
Irodov- 1.123- Simple conceptual question with two masses connected by a spring
Replies
20
Views
564
Spring Problem Involving Variables and Constants Only
Replies
3
Views
1K
Why can we move the spring with constant speed when we apply a force?
Replies
29
Views
2K

Hot Threads

Recent Insights

Back
Top