Spring and block of mass problem

In summary, the plot shows that the kinetic energy increases as x gets closer to the position where the spring is stretched (the equilibrium position). The kinetic energy at this point is 8.0 J.
  • #1
tigerlili
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0

Homework Statement

a block of mass m lies on a horizontal frictionless surface and is attached to one end of a horizontal spring (spring constant k) whose other end is fixed. The block is initially at rest at the position where the spring is unstretched (x = 0) when a constant horizontal force in the positive direction of the x-axis is applied to it. A plot of the resulting kinetic energy of the block versus its position x is shown in Fig. 7-38.

http://edugen.wiley.com/edugen/courses/crs1650/art/qb/qu/c07/pict_7_38.gif

Homework Equations



f= -kx
k= 1/2 mv^2
ui + ki = uf + kf

The Attempt at a Solution



i'm really confused about how to start this one :/
 
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  • #2
What are you supposed to find? I see no question there.
 
  • #3
oh, woops! i forgot to paste the rest :X

The scale of the figure's vertical axis is set by Ks= 8.0 J. (a) What is the magnitude of ? (b) What is the value of k?

sorry about that!
 
  • #4
Your part (a) question still isn't complete.
For (b), k is the maximum kinetic energy which the graph says is at distance 1 m.

I don't think you can use your k = 1/2*m*v^2 directly. You'll have to think about the work being done by that force and the spring energy (have to look up the formula for the energy of a stretched spring). Give us a start on that and someone will help you if you need help.
 
  • #5
haha wow.. sorry about that
the vector notation didn't actually paste properly

and i really don't remember even learning the equation for a stretched spring, I'm just so lost
it no longer really matters, because the homework was already due
i just want to understand what's going on in the problem
thanks for your help, though
 
  • #6
Take a look here: http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html
E = .5*k*x^2 where x is the distance the spring is stretched.
The idea is that the work done goes into a combination of kinetic and spring energy:
Fd = .5*k*x^2 + .5*m*v^2
Might be worth doing even though too late to hand in. Problems like this will come back to haunt you on exams.
 
  • #7
i know you're right, I've just been so overwhelmed by this class lately
i think i understand it now, thanks for your help :)
 

1. What is a "spring and block of mass problem"?

A "spring and block of mass problem" is a common physics problem that involves a block of mass attached to a spring and experiencing simple harmonic motion. The problem typically requires solving for the displacement, velocity, and acceleration of the block as it oscillates back and forth on a horizontal surface.

2. What are the key equations used in solving a spring and block of mass problem?

The key equations used in solving a spring and block of mass problem include Hooke's Law (F = -kx), the equation for simple harmonic motion (x = A*cos(ωt + φ)), and the equations for displacement, velocity, and acceleration in SHM (x = A*sin(ωt), v = -ω*A*sin(ωt), a = -ω^2*A*cos(ωt)).

3. How do you determine the period and frequency of a spring and block of mass system?

The period (T) and frequency (f) of a spring and block of mass system can be determined using the equation T = 2π/ω and f = 1/T, where ω is the angular frequency (ω = 2π*f). The angular frequency can be calculated by taking the square root of the spring constant divided by the mass (ω = √(k/m)).

4. Is there a difference between a vertically suspended spring and a horizontally placed spring in a spring and block of mass problem?

Yes, there is a difference between a vertically suspended spring and a horizontally placed spring in a spring and block of mass problem. The main difference is in the direction of the force exerted by the spring. In a vertically suspended spring, the force is always acting downwards, while in a horizontally placed spring, the force alternates between pulling and pushing the block in opposite directions.

5. How does the amplitude affect the motion of the block in a spring and block of mass problem?

The amplitude (A) of a spring and block of mass system affects the maximum displacement of the block from its equilibrium position. A larger amplitude will result in a greater maximum displacement and a longer period of oscillation. However, the amplitude does not affect the frequency or the period of the system.

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