# Homework Help: Amplitude and coefficient of friction problem

1. Nov 15, 2008

### grog

1. The problem statement, all variables and given/known data
A large block with mass 30 kg executes horizontal simple harmonic motion as it slides across a frictionless surface with a frequency of .75 Hz. A smaller block with mass 10 kg rests on it, as shown in the figure, and the coefficient of static friction between the two is mu_s=.6

What maximum amplitude of oscillation can the system have if the top block is not to slip? the acceleration of gravity is 9.8m/s^2. Answer in units cm

In the picture, there is a block on a frictionless surface attached to a wall by a horizontal spring. the block on the surface has another block on top of it, and the coefficient of static friction between the two is given.

2. Relevant equations

freq = omega/2pi
vmax=omega*Amplitude
friction_s_max=mu*mg
a_x=friction_s_max/m=mu*g

3. The attempt at a solution

I've taken the frequency times 2pi to find omega. using the above equation for a_x, I used mass*a_x to find the velocity, vmax.
Then I plugged in values for vmax and omega to solve for Amplitude. Unfortunately that gave me the wrong answer. Where is my approach wrong?

2. Nov 15, 2008

### LowlyPion

Isn't the crucial question what the maximum acceleration of the blocks can be before dislodging the upper block?

You know the coefficient of friction and isn't that going to give you your maximum tolerable acceleration?

Acc_max = u*g

Where then is the point of maximum acceleration?

If A*cos(ω t) is the form of your equation of position then isn't the acceleration function given by

A*ω2Cos(ω t)

So Acc_max = A*ω2 = u*g

3. Nov 15, 2008

### grog

That seems to make sense, but if I plug values in and solve for amplitude, (mu*g)/omega^2, I'm told I have an incorrect answer for the Amplitude. What am I missing? or did I completely miss your point?

I'm computing omega by taking the frequency and multiplying it by 2pi.

4. Nov 15, 2008

### LowlyPion

Check your units. g is m/s2

They want to know cm.

5. Nov 15, 2008

### grog

bah. units, my old nemesis.

That worked perfectly. thanks for the insight