Physics 213 Final 15 Points Each December 15, 1999

Instructor: K. W. Nicholson

1. The graph below shows the position vs. clock readings of the motion of two trains running on parallel tracks.

Circle all of the following that are true:

a. at time t_B both trains have the same velocity

b. both trains speed up all the time

c. both trains have the same velocity at some

time before t_B

d. somewhere on the graph, both trains have

the same acceleration

2. Describe very carefully the motion required to create the distance vs time graph .

3. Gi-Gi, the famous Daredevil Gazelle has decided to try for a new gazelle distance record by being shot from a cannon. The cannon is fired from a platform that is 100 m off the ground. The cannon is supposed to be aimed at an angle of 30E above the horizontal. But the guy hired to man the cannon doesn't really know how to operate it very well, and has no common sense. He sets the dial on the declination axis to -30Ethinking the minus sign is just a dash, and doesn't even notice that the cannon is pointed down 30E below the horizontal instead of instead of up 30Eabove the horizontal. So, how far from the base of the tower does Gi-Gi land? By the way, is her velocity at impact greater, less than or the same as the velocity would have been if she'd been aimed up 30E above the horizontal as intended?

4. A 20 kg block slides down the plane. If it is pulled by a 50 N force as indicated in the diagram below, its acceleration is 6 m/s², what is the kinetic coefficient of friction? (You must draw a FBD to receive any credit.)

5. A 5 kg block is set into motion up an inclined plane with an initial speed of 20 m/s. The block comes to rest after traveling 12 m up the incline, which is inclined at an angle of 37E with the horizontal.

Find the coefficient of kinetic friction between the block and the surface in the figure.

6. A 1000-kg space craft (including missiles), coasts east at a speed of 400.0 m/s relative to the ground. A 200 kg torpedo is fired east at an initial speed of 600 m/s relative to the space craft. Find the final velocity of the spacecraft.

7. A woman whose mass is 100 kg stands at the rim of a horizontal turntable that has a moment of inertia of 500 kg m² and a radius of 2m. Beside her is her faithful but very obese dog Fido, who's mass is 200 kg. The system is initially at rest, and the turntable is free to rotate about a frictionless, vertical axle through its center. The woman then starts walking around the rim in a clockwise direction (looking downward) at a constant speed of 1.5 m/s relative to the earth. How fast in which direction would Fido have to walk (at a distance of 1 m from the center) in order to keep the turntable from rotating ?

a) What principle is involved in solving the problem?

b) Draw a picture of the situation

c) Solve the problem
8a. Identical constant forces continuously push identical blocks A and B from the start line to the finish line. Block A is initially at rest whereas block B is initially moving right.

Which block has the larger change in momentum?

(Circle the correct response.)

i. A

ii. B

iii. They have the same momenta change.

iv. Too little information to answer.

8b. The reason for your answer to the question above is:

(Circle the correct response.)

(i) The same force acts on identical blocks for the same distance

(ii) Block B already has some momentum, so its change isn't as great.

(iii) The impulse on block B is less since the force acts for a shorter time interval.

(iv) Block B is moving faster at the finish line, so its change is greater.

(v) The initial and final velocities are not given.

9. Answer the following question about the stationary "Elevated Lecture Beam" system shown at the right. The vertical rope is secured to a harness about the professor's waist. The professor, (whose weight is 600 N) is supported by the harness and by sitting on the beam at its center of mass, (beam has a weight of 80 N). The pulley above is frictionless.

a) Draw a FBD for the beam.

b) Find the tension T in the cable and the force the professor imposes on the beam.

10. Define:

a. Temperature

b. Heat

c. Internal (mechanical) energy

d. specific heat

11. Assuming we could ignore air resistance, and that all the potential energy is turned in to internal energy on impact, from what height would one have to drop a chunk of ice at 0°C so that the impact with the earth would cause all of it to turn into steam at 100°C ?

12. In lab you heated 30 grams of 0° ice mixed with 80 grams of 0^o water until all the ice melted and the water finally boiled. Given that the actual value of latent heat of fusion and vaporization for water respectively are 3.33x10⁵J/kg and 2.26x10⁶ J/kg, the ice melted at time t = 120 s, the voltage and current are respectively 9V and 10 A, the temperature was 40^o C at time t = 370 s:

a) Find the experimental value L_{f exp} of the latent heat of fusion for water.

b) Find the percent error in L_{f exp} .

c) Find the experimental value c_{w exp} , of the specific heat of water.

d) Find the percent error in c_{w exp} .

e) Do you consider this experiment to be a success? Explain.

13. Sketch a PV diagram and find the work done by the gas during the following stages. (a) A gas is expanded from a volume of 1.0 L to 3.0 L at a constant pressure of 3.0 atm. (b) The gas is then cooled at constant volume until the pressure falls to 2.0 atm. (c) The gas is then compressed at a constant pressure of 2.0 atm from a volume of 3.0 L to 1.0 L. (Note: Be careful of signs.) (d) The gas is heated until its pressure increases from 2.0 atm to 3.0 atm at a constant volume. (e) Find the net work done during the complete cycle.

a)610 J, b) 0, c) -410 J, d) 0, e) 200 J

10 points Bonus!

An ideal gas undergoes the cyclic process shown in Figure P20.36 from A to B to C and back to A. Sketch a PV diagram for this cycle.