Deriving the Equation for Spring Deflection of a Dropped Mass

  • Thread starter Thread starter rotin089
  • Start date Start date
  • Tags Tags
    Mass Shm
AI Thread Summary
The discussion focuses on deriving the equation for spring deflection (x) when a mass (M) is dropped from a height (z) onto a spring with stiffness (k). It emphasizes the conservation of mechanical energy, where potential energy (PE) and kinetic energy (KE) are considered. Participants suggest setting up an energy balance equation that incorporates x, z, M, g (acceleration due to gravity), and k. The goal is to express x as a function of these parameters without solving the equation. Ultimately, the conclusion is that x depends on mass, gravitational acceleration, and spring stiffness.
rotin089
Messages
5
Reaction score
0
i have the following question and i have no idea how to answer it can any please help out...

consider a Mass M which is dropped a height z onto a spring of stiffness k N/m. when the mass hits the spring, the spring will deflect a distance x before the mass stops moving down. show that the distance x is a function of the mass M, acceleration due to gravity g and of stiffness of the spring k.

please help
 
Physics news on Phys.org
Hint: Is anything conserved?
 
energy both pe and ke
 
rotin089 said:
energy both pe and ke
The total mechanical energy is conserved. Use that to set up an energy equation to solve for X.
 
i do not need to solve the equation. i need to find the derivative of the equation. i need to conclude that x is a function of the mass M, acceleration due to gravity g and of stiffness of the spring k.
 
rotin089 said:
i do not need to solve the equation. i need to find the derivative of the equation. i need to conclude that x is a function of the mass M, acceleration due to gravity g and of stiffness of the spring k.
Set up the energy balance equation--which will involve x, z, M, g, and k--then you can rearrange to get x as a function of the other parameters. (That's what I mean by 'solving for x'.)
 

Thread 'Rolling without slipping on a curved surface'

Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
View full post »

Thread 'Struggling to understand the concept of this question (ice cube in water optics question)'

TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
View full post »
Thread 'A bead-mass oscillatory system problem'

Thread 'A bead-mass oscillatory system problem'

I can't figure out how to find the velocity of the particle at 37 degrees. Basically the bead moves with velocity towards right let's call it v1. The particle moves with some velocity v2. In frame of the bead, the particle is performing circular motion. So v of particle wrt bead would be perpendicular to the string. But how would I find the velocity of particle in ground frame? I tried using vectors to figure it out and the angle is coming out to be extremely long. One equation is by work...
View full post »

Similar threads

Distribution of Energy when work is done on a system of 2 masses connected by a spring
Replies
17
Views
2K
Question about springs and rotational/translational energy
Replies
4
Views
1K
What is the maximum spring displacement?
Replies
10
Views
2K
A block dropping onto a spring system
2
Replies
58
Views
2K
Force transmitted to a block in viscous fluid through a spring, cord, and pulley
Replies
6
Views
840
How to solve a differential equation for a mass-spring oscillator?
Replies
2
Views
2K
A block of mass m is dropped onto the top of a vertical spring....
Replies
8
Views
5K
Two spring-coupled masses in an electric field (one of the masses is charged)
Replies
1
Views
929
Why is my method for finding the spring constant incorrect?
Replies
17
Views
3K
Absolute motion analysis of pulley-spring system
Replies
10
Views
1K

Hot Threads

Recent Insights

Back
Top