Physics 111

Test #3 Formula Sheet

Physics 111 – Test 3

16 June 2015

Name______

Directions: This is a CLOSED BOOK test, and you may only use the calculator and cheat sheet provided. SHOW ALL OF YOUR REASONING! You can only get partial credit for an incorrect answer if you show your reasoning. You may have as much time as you like to finish this exam.

  1. (5 pts) An elevator is hoisted by cables up at a constant speed. Do the cables do any work on the elevator? Explain.
  1. Consider the 3 below situations. In each case, the mass starts at the top at rest and goes down from there. There is NO FRICTION anywhere.

a)(5 pts) In which situation(s) does the mass have the greatest speed at the bottom (or do they all have the same speed)? Explain.

b)(5 pts) In which situation(s) does gravity do the most work on the mass (or does it do the same work for all three)? Explain.

  1. A particle experiences a potential energy of

where , a constant. Note that the argument of the cosine function has units of radians. This potential energy function is plotted below.

A particle of mass m = 8.0 kg is released at x = 9.0 m from rest. It experiences no other forces other than the one represented by the PE above. EXPLAIN YOUR REASONING.

a)(5 pts) At what value of x does the particle stop and go back the other way (or does it just keep going)?

b)(5 pts) At what value of x does the particle experience the largest magnitude of force due to this PE? (If you think there is more than one x, you need only include one of them.)

c)(8 pts) Determine the maximum speed the particle has on its journey to its furthest value of x.

4. (20 pts) A45 kg rocket sled begins slipping from rest down a frictionless hill as shown. It then hits a 2 m long level rough patch where the coefficient of kinetic friction between it and the ground is 0.80. Just as it starts on this 6m-long very rough patch, it turns on a reverse thruster (force = 500 N), further slowing it down. The thruster turns off at the same moment it leaves the rough patch. It then slides along a frictionless level surface until it encounters a spring with spring constant k = 800 N/m. Determine how far the spring compresses before the sled comes to a stop.


5. A satellite is in a circular orbit 1.0 × 106 m above the Earth’s surface. It fires its thrusters until it is in a circular orbit 2.0 × 106 m above the Earth’s surface.

a) (10 pts) Determine the speed of the satellite in each orbit. (HINT: Unit 2 problem)

b) (15 pts) Determine how much work the thrusters did to move the satellite from one orbit to the next. (HINT: No, you do not need to know the distance over which the thrusters were on.)

6. 12.00 hp are required to drive an2000-kg automobile at 20.0 m/s on a level road.

a) (12 pts) What is the total retarding force on the car due to friction, air resistance, etc.?

b) (10 pts) Down what percent grade or slope would the car coast at 20 m/s?

BONUS BRAIN BUSTER!!! (+ 5 pts)

An airplane in flight is subject to an air resistance force proportional to the square of its speed, v. But there is an additional resistive force because the airplane has wings. Air flowing over the wings is pushed down and slightly forward, so from Newton’s third law the air exerts a force on the wings and the airplane that is up and slightly backwards. The upward force is the lift force that keeps the airplane aloft, and the backward force is called the induced drag. At flying speeds, induced drag is inversely proportional to v2, so that the total air resistance force can be expressed by

,

whereα and β are positive constants that depend on the shape and size of the airplane and the density of the air. For a Cessna 150, a small single-engine airplane, α = 0.30 N·s2/m2 and β = 3.5 × 105 N·m2/s2. In steady flight, the engine must provide a forward force that exactly balances the air resistance force. Determine the speed at which this airplane will have the maximum range (that is, travel the greatest distance) for a given quantity of fuel.

Credit will only be given for correct reasoning. If you are able to guess the correct answer but give no correct reasoning, you will receive no extra credit. However, if you give some correct reasoning that would (or does) lead to the correct answer, at least some credit will be given.

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By signing my name above, I affirm that this test represents my work only, without aid from outside sources. In all aspects of this course I perform with honor and integrity.