Spring compressed, find velocity.

AI Thread Summary
A block with a mass of 0.3 kg and a spring constant of 24 N/m is set into motion from a compression of 3.5 cm on a frictionless surface. The maximum velocity can be determined using the conservation of energy principle, equating the initial spring energy to kinetic energy at maximum speed. The energy stored in the spring is calculated as Es = ½kx², which leads to the equation (1/2)mv² + (1/2)kx² = constant. The discussion highlights confusion around applying these formulas correctly, particularly in setting the right constants for energy conservation. The key takeaway is to correctly use energy equations to find both maximum velocity and spring compression at a given speed.
demonslayer42
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Homework Statement


A block of mass 0.3 kg and spring constant 24 N/m is on a frictionless surface. If the block is set into motion when compressed 3.5 cm, what is the maximum velocity of the block? How much is the spring compressed when the block has a velocity of 0.19 m/s?


Homework Equations


F = -kx


The Attempt at a Solution


m = 0.3 kg
k = 24 N/m
3.5cm = 0.035m is what? amplitude or distance I'm not sure.

F = 24*0.035 = 0.84 N?

I'm stuck, any help would be greatly appreciated :)
 
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hi demonslayer42! :smile:

use conservation of energy (∆PE + ∆KE = constant) :wink:
 
In F = -kx, x is the compression or stretch of the spring, so at first the force on the mass is F = k*0.035 = 0.84 N as you found. You could get the initial acceleration with F = ma. However, as the mass moves and the spring is less compressed, the force and acceleration decrease. Calculus integration would be necessary to deal with the diminishing acceleration.

This problem is easier to deal with using energy formulas.
The energy stored in a spring is Es = ½kx². You can answer the first question by starting with
Initial Es = kinetic energy at maximum speed
 
I'm sorry, but I don't understand what you are saying.
Es = ½kx²
(1/2)(24)(0.035)^2 = 0.0147 ? So if this is Es what am I suppose to do with this?
 
(1/2)mv^2 + (1/2)kx^2 = k

(1/2)(0.3)(v^2) + 0.0147 = 24

(1/2)(0.3)(v^2) = 23.9853

v^2 = 23.9853/0.15
=12.645 ?
That doesn't look right.
 
hi demonslayer42! :smile:

(try using the X2 icon just above the Reply box :wink:)
demonslayer42 said:
(1/2)mv^2 + (1/2)kx^2 = k

no, wrong constant

your equation is KE + PE = constant,

but that shouldn't be the spring constant, it should be the constant that fulfils the initial conditions …

so set the constant at the value of KE + PE at time zero :smile:
 
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