Simple harmonic motion, spring, block on block, static friction help

In summary: So it didn't matter if I knew it or not.In summary, the conversation was about finding the coefficient of static friction between two blocks in a simple harmonic motion system. The person working on the problem had found negative mass as a solution, and was unsure if the mass of the top block was needed. Through further discussion, it was determined that the mass of the top block was not needed and the coefficient of static friction was found to be 0.72.
  • #1
scholio
160
0
been working on this for a long time, haven't got far, keep getting a negative mass!


Homework Statement



A 440 g block on a frictionless surface is attached to a rather limp spring of constant k = 8.7 N/m. A second block rests on the first, and the whole system executes simple harmonic motion with a period of 1.4 s. When the amplitude of the motion is increased to 35 cm, the upper block just begins to slip. what is the coefficient of static friction between the blocks?
*mass of block on top is not given

Homework Equations



see below

The Attempt at a Solution



this is what I've done thus far

m1 = 440g = 0.44kg
m2 = ?
k = 8.7n/m
T(period) = 1.4s
A(amplitude) = 35cm = 0.35m
omega = angular velocity

using T = 2pi/omega --> gives omega = 4.48 m/s
using omega = sqrt(k/m) ---> where m = m1 + m2 = 0.44kg + m2 ---> solve for m2 = -0.0065 kg

that is impossible, negative mass? what am i doing wrong? one i get m2 i'll be able to figure mu static by comparing static friction force to force = ma

thanks
 
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  • #2
EDIT - another quick question, since the mass of the block on top was not given in the problem, does that imply that that mass is not needed? i think you do need it to find the normal force to find the force of static friction
 
  • #3
Newton's 2nd Law on top block:

[tex]m_1 a = f[/tex]

[tex]m_1 a =\mu m_1 g[/tex]

[tex]a=\mu g[/tex]

SHO equation for both blocks (the same acceleration because no slipping-- they accelerate together)
[tex]a=\omega^2 A[/tex]

Put them together--
[tex]\mu=\frac{\omega^2 A}{g}[/tex]

[tex]\mu = \frac{(2\pi)^2 A}{T^2 g}[/tex]

So yeah it looks like you don't need to find the other mass.
 
  • #4
thanks so much, i'll have a closer look, the answer was correct mu static = 0.72, how did you determine that you didn't need to know the mass of the block on top?
 
  • #5
scholio said:
thanks so much, i'll have a closer look, the answer was correct mu static = 0.72, how did you determine that you didn't need to know the mass of the block on top?

Well I didn't know a priori, I just started typing and saw that the final formula is independent of mass.
 

1. What is simple harmonic motion?

Simple harmonic motion is a type of oscillating motion in which an object moves back and forth in a periodic manner. It is characterized by a restoring force that is proportional to the displacement of the object from its equilibrium position.

2. How does a spring affect simple harmonic motion?

A spring can act as the restoring force in a system of simple harmonic motion. When a spring is stretched or compressed, it exerts a force that is proportional to the amount of displacement from its equilibrium length. This force causes the object attached to the spring to oscillate back and forth.

3. What is a block on block system?

A block on block system refers to a setup in which one block is resting on top of another block. This system is often used in physics experiments to study friction and simple harmonic motion.

4. How does static friction affect a block on block system?

Static friction is the force that resists the motion between two surfaces that are in contact with each other. In a block on block system, static friction can affect the motion of the blocks by either helping to maintain their relative position or by preventing them from sliding against each other.

5. How can I calculate the frequency of a block on block system?

The frequency of a block on block system can be calculated using the equation f = 1/(2π)√(k/m), where f is the frequency, k is the spring constant, and m is the mass of the block. This equation is derived from the relationship between the period of oscillation and the mass and spring constant of the system.

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