PHY 1351

Fall 2001

**Fourth Hour Exam**

5 December 2001

**1. **A uniform ladder of length L and weight w = 50 N rests against a
smooth, frictionless, vertical wall. If the coefficient of static friction between
ladder and ground is µ_{s} = 0.40, find the minimum angle theta(_{min})
such that the ladder does not slip. (This is Example 12.4 from Serway, page
344).

Don'teven begin without a goodforce diagram!Diagrams reallyareimportant.When we calculate the torques, I have chosen our origin as the foot of the ladder:

It seemed to be very easy to interchange sine and cosine.

Alwaysstart from the diagram and remember thattorque = (dist) x (force) x sin(theta)

where (theta) is the angle

betweenthe distance and the force.

**2.** A 0.50 kg mass connected to a light spring of force constant 20.0
N/m oscillates on a horizontal, frictionless track.

(a) Calculate the total energy of the system if the amplitude of the motion
is 3.0 cm ( 0.03 m).

(b) Calculate the maximum speed of the mass if the amplitude of the motion is
3.0 cm ( 0.03 m).

(c) What is the speed of the mass when the displacement is 2.0 cm (0.02 m)?

(d) What are the kinetic and potential energies of the system when the displacement
is 2.0 cm (0.02 m)?

(d_{1}) What is the kinetic energy of the system when the displacement
is 2.0 cm (0.02 m)?

(d_{2}) What is the potential energy of the system when the displacement
is 2.0 cm (0.02 m)?

(This is Example 13.5 from Serway, p 369)

A geosynchronous satellite has a **period** of 24 hours.

Show all your work and calculate the **orbital radius** of a geosynchronous
satellite.

(This was done in class).

This turned out to be a poor problem.

What I

intendedwas that you would start by setting the centripetal force equal to the gravitational force and,from that,deriving Kepler's Third Law,

However,I forgot that I had already included this last equation on the front equation sheet. So all the real Physics work was alreadydonefor you. Now, it is just an arithmetic evaluation problem.Be sure to convert the period from

hoursintoseconds;This question

beganby stating that r = 42,200 km. However,manysolutions then evaluated r and found adrastically differentvalue for r.I do not understand that!

1 cm^{3} = 1 mL = 0.001 L

1 L = 10^{3} cm^{3}

(This is Example 15.12 from Serway, p 433).

This is barely a

Physics problemat all. It's more a question of simple geometry or ordinary reasoning. It is aPhysics problemonly in that we use these ideas -- like the equation of continuity -- in fluid flow. I will try to have a more "robust" problem from fluids on the final!

Conceptual Questions:Describe qualitatively the motion of a mass-spring system when the mass of the spring is not neglected.

1.

When we made measurements in the lab we could not neglect the mass of the spring. There, we included the mass of the spring by adding one-third of the spring's mass to the "ordinary mass" that we had used in theory or in lecture. That meant that the "real mass" or the "effective mass" was greater than we had used in the lecture. This gave alonger period.

2.What happens to the period of a simple pendulum if the mass of the bob is doubled?

For a pendulum, the period isindependentof the mass so there isno changein the period.[Note, of course, that this is

quite differentfor a "spring-and-mass" simple harmonic oscillator.]

3. Does the escape speed of a rocket depend on its mass?

No, when we derived an expression for the escape speed, it didnotinclude the mass of the rocket.

4.Why don't we put a geosynchronous weather satellite in orbit around the 45th parallel? Wouldn't this be more useful to the United States than such a satellite in orbit around the equator?

The force of gravity due to Earth is exertedtoward the centerof Earth. That means the plane of any orbit around Earth mustincludethecenterof the Earth.

5.Does a ship ride higher in the water of an inland lake or in the ocean?To float, a ship must

displacea volume of water that has as much weight as the weight of the ship. Sea water has a greaterdensitythan fresh water so less sea water must be displaced. This means the ship will ridehigherin theocean.