# Homework Help: Need help with conduction and oscillation question.

1. Feb 2, 2004

### Skyblitz

Hi, these two questions have been boggling me for a week.. if anyone can I help I'd be very appreciative.

The first one is..

A cylindrical rod of length 1.5 m and radius 0.02 m is insulated to prevent heat loss through its curved surface. One end is attached to a thermal reservoir at 573 K and another at 303 K. What is the rate at which entropy increaes for the rod-reservoir system?

Now, when I saw rate I immediately thought dS/dt.. I've tried to solve it in numerous ways but I'm not sure what the correct way is.

I first took the equation dS = dQ/T, and for dQ/dt = kA (Th-Tc)/L where k = 400 since it's copper.

Anyway I got dQ = 90.48 dt. I then substituted this back into the dS equation and got dS = 90.48 dt/T, then I brought dt to make it dS/dt = 90.48/T.. but what do I plug in for T?

Another way that I did this was take the equation
delta S = Q/Tc - Q/Th

I took the derivative of it with respect to time .. and got

d(delta S)/dt = 1/Tc dQ/dt - q/Th dQ/dt

and I subbed in dQ/dt and solved for d(delta S)/dt.. and I'm assumign this is wrong since you're finding the rate of change, of the change of entropy with respect to time.

Other people I know just used S = dQ/T and then substituted S = dQ/Th + dQ/Tc and got an answer. however, this neither gives the rate of change..

And I just wanted to clarify that A is the cross sectional area under all circumstances, correct?

And on to my 2nd question:

Block 1 of mass 0.2kg is sliding to the right over a frictionless elevated surface at 8m/s. The block undergoes an elastic collision with stationary block 2. Assume that the spring does not affect the collision. After the collision, block 2 oscillates in Simple Harmonic Motion, with a period of 0.14 s, and block 1 slides off the opposite end of the surface landing at a distance d from the base of the surface after falling height 4.9 m. What is the value of d?

So basically I talked to a teaching assistant who said that I was supposed to use the equation m1v1 = m1v1 + m2v2, but this makes no sense since if it's in a collision, wouldn't it transfer some of its energy towards the 2nd block? I'm having a hard time solving it..

basically I can find M2 and M1 from omega and the equation for period, but I'm still confused.

2. Feb 3, 2004

### Staff: Mentor

Here's how to think of this problem. Heat is flowing at a certain rate between the high temp reservoir and the low temp reservoir. You can calculate the rate of heat flow. Now calculate the entropy changes (1) when heat is removed from the high temp reservoir, and (2) when heat is added to the low temp reservoir. What's the net rate of entropy change? Got the idea?
That equation looks like a misguided attempt to write the equation for conservation of momentum. Here's what you need to do. Apply what you know about elastic collisions. What's conserved? You'll get two equations. Also, apply what you know about simple harmonic motion: that will give you another equation. Are you given the spring constant? Your goal, of course, is to solve for the final velocity of the first block so you can calculate d.

3. Feb 3, 2004

### Skyblitz

Ah I see, thanks for your help!