What is the spring constant in this scenario?

In summary: So the sum of the initial kinetic energies equals the final spring potential energy. In summary, Using conservation of momentum, and conservation of energy, the spring constant is calculated to be 959.58 g.
  • #1
vincisonfire
4
0

Homework Statement


A mass of 50 kg falls 50 cm onto the platform of a spring scale and sticks. The platform comes to rest 10 cm below its initial position. The mass of the platform is 2 kg. Find the spring constant.


Homework Equations





The Attempt at a Solution


I thought of the following solution using conservation of energy:
m*g*h = (k*A^2)/2
leads to k = 1000g
But I also thought of the solution using conservation of momentum:
v0^2=2*a*(ds)=g
m*v0=M*v1 (M is the total mass)
m*v0/M=v1=5*g/6
(m*v1)^2/2=(k*A^2)/2
k = 5000*g^2/3
Could it also simply be that the spring comes to rest when forces are at equilibrium
M*g=k*x
That yields
k=100*g
 
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  • #2
Using conservation of energy is the correct approach, but you are missing a couple of terms. The initial energy is associated with the potential energy (relative to some reference point) of both masses. And don't forget to consider the distance that the 50 kg mass falls includes both it's initial height and the spring displacement. You can't use conservation of momentum, because it is not conserved after the initial collision.
 
  • #3
Why isn't the momentum conserved? I mean, immediately after collision, m1*v0 should equal (m1+m2)*v1 ??
About energy I think this is :
m1*g*h=(k*A^2)/2
with A = 0.1 + (m2*g)/k
because you have kx0=m2*g
and we should get k = 959.58 g
 
Last edited:
  • #4
vincisonfire said:
Why isn't the momentum conserved? I mean, immediately after collision, m1*v0 should equal (m1+m2)*v1 ??
About energy I think this is :
m1*g*h=(k*A^2)/2
with A = 0.1 + (m2*g)/k
because you have kx0=m2*g
and we should get k = 959.58 g
Let me clarify my response, because I didn't state it correctly.
1. Momentum is conserved only when there is no external force acting on the system.
2. Mechanical energy is conserved only when conservative forces act (like spring or gravity forces) and when no energy is lost due to heat or sound. etc.
3. In this problem, the platform comes momentarily to a rest when the spring is extended 10 cm below it's intial position. When mg=kx, it is not at rest; it has no acceleration at that point, but it is still moving.
To solve this problem, you need to apply conservation of momentum during the collision, and conservation of mechanical energy before and after the collision. Thus, one calculates the speed of the falling block at the instant before it hits the other block, using the kinematic equation of motion or conservation of energy equation, which I believe is what you have designated as Vo. Then during the collision, you use conservation of momentum, (which you can get away with doing even though the external gravity force is still acting, because it acts for such a short distance during the deformation of the 2 objects that you can ignore it), and you can solve for the speed of the combined masses per your correct equation for V1, using conservation of momentum. Finally, you must apply conservation of energy to get the value of the spring constant k, noting that initially after the collision, the combined blocks have both kinetic an potential energies, and at the max compression (10cm) of the spring, there is spring potential energy only.
 

What is the "spring constant"?

The spring constant, also known as the force constant, is a measure of the stiffness of a spring. It represents the amount of force required to stretch or compress a spring by a certain distance.

How do you find the spring constant?

The spring constant can be found by dividing the force applied to the spring by the distance the spring is stretched or compressed. This is known as Hooke's Law, which states that the force exerted by a spring is directly proportional to the distance it is stretched or compressed.

What unit is the spring constant measured in?

The spring constant is typically measured in units of newtons per meter (N/m) or pounds per inch (lb/in).

What factors can affect the spring constant?

The spring constant can be affected by the material and shape of the spring, as well as the temperature and any external forces acting on the spring.

Why is the spring constant important?

The spring constant is an important factor in understanding the behavior of springs and other elastic objects. It is used in various fields such as engineering, physics, and biology to calculate the amount of force needed to move or manipulate objects that involve springs.

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