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We know from Pascal's Law that

Problem 1Saturday, June 09, 2012

5:07 PM

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The measurement for atmospheric pressure can be found using our

drinking straw approach.

Here, we have two configurations...

Putting these two expressions together...

Problem 2Sunday, November 04, 2012

8:39 PM

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This is just a unit conversion problem.

Problem 3Saturday, June 09, 2012

5:07 PM

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The weight of the water (formerly) displaced is the number of fighters n

times their laden mass.

Solving for the area...

Problem 4Saturday, June 09, 2012

5:07 PM

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Buoyant force is the weight of the fluid (in this case air) displaced.

To find the net force, we also need to find the weight of the balloon.

Net force is the difference between these two weights.

This is basically asking what mass needs to be added to make the net

force equal to zero.

Problem 5Sunday, November 04, 2012

8:41 PM

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Using the Bernoulli Eqsn...

For this we can use the continuity equation. More explicitly, the fact

that the continuity equation tells us what the flow rate is...

Be sure to convert the flow rate to m3/s rather than the stated value

of m3/min.

Problem 6Thursday, June 14, 2012

4:56 PM

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We first find the pressure at this particular depth. Because he alreadyhas atmospheric pressure helping him on his side, he needs to know

the gauge pressure.

To find the force, we have to integrate pressure over the area of the

hole.

Once again we are using the Bernoulli Eq to find the velocity that the

water leaves the hole...

And the continuity equation to tell us something about flow rate...

The expression for time is then...

Problem 7Thursday, June 14, 2012

4:56 PM

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This looks like a standard Bernoulli problem. This time, though, the

pressure that we apply is what makes the velocity at the end.

We don't know the velocity of the plunger, so we have to use the

continuity equation.

Using this expression in the Bernoulli Eq...

Solving for v2.

Problem 8Thursday, June 14, 2012

4:56 PM

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This is another instance of using the Bernoulli Eq. Here we are lookingfor a gauge pressure (P1 - P0) though...

Problem 9Thursday, June 14, 2012

4:56 PM

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Here we know position as a function of time. We just put in the time t=

0.

Because we know position as a function of time, that means we also

know velocity as a function of time.

The velocity at time t= 0 is...

We can also get the acceleration as a function of time...

Problem 10Thursday, June 14, 2012

4:56 PM

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The acceleration at time t= 0 is...

Amplitude is given to us by the expression.

The period can be found from our angular variables.

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We are given either the cycles per second or seconds per cycle in thisproblem. The period is the seconds per cycle.

Frequency is 1 over the period.

The angular frequency is also pretty straight forward...

Problem 11Thursday, June 14, 2012

4:56 PM

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For this part, it is just conservation of energy.

Because we know the period and the mass, we can find the spring

constant.

Because we know the spring constant, we can once again use

conservation of energy to find the maximum displacement.

Problem 12Thursday, June 14, 2012

4:56 PM

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The period is found from data given in the problem.

Now we can use what we know about the pendulum to find the length.

Problem 13Thursday, June 14, 2012

4:56 PM

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The frequency of damped oscillation is given by...

The amount of time needed for each cycle is the period T. In eachperiod, the amplitude will be exp(-bT/2m) times the amplitude it

previously was.

Energy at time t= 0 is given by...

The energy as a function of time is...

Problem 14Thursday, June 14, 2012

4:56 PM

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The natural resonance of this mass on a spring is...

We are not driving at the resonant frequency. The system is going to

move with this frequency we give it, even though this is not the

resonant frequency. In other words, we pick of the system by whatwe drive at.

Knowing these frequencies, we can find our amplitude by using the

expression...

Problem 15Thursday, June 14, 2012

4:56 PM

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