PHYSICS 231 MIDTERM II Form B November 4, 2002
Name: PID Sec.
Useful constants:
rwater=1000 kg/m3, g=9.8 m/s2, 1 hp = 746 W, Rearth = 6.38x106 m,
G=6.67x1011 Nm2/kg2, g=9.81 m/s2, kB=1.38x10-23 J/degK,
Absolute Zero = -273.15 degC.
For each problem, choose the most nearly correct answer.
Answer Key at End
1. A new planet “Horatio” has been discovered which is four times as far from the sun as Earth. What is the period of Horatio’s orbit?
a) 8 years
b) 4 years
c) 2 years
d) 1 year
e) 6 months
2. A hollow cylinder starts from rest at the top of an inclined plan and rolls down. The height of the inclined plane is h=5 m and it makes an angle of 30° with respect to the horizontal. What is the translational velocity of the cylinder when it reaches the bottom? The moment of inertia of a hollow cylinder is I = MR2.
a) 10.0 m/s
b) 8.4 m/s
c) 7.0 m/s
d) 4.2 m/s
e) 2.1 m/s
3. A copper wire of length 4 meters, cross sectional area 7.1 ´ 106 m2 and Young’s modulus 11 ´ 1010 N/m2 has a 300 kg load hung on it. Its increase in length DL is 5.0 mm. Now, the wire is cut to a quarter of its original length to 1m, and the load is increased to 600 kg. What is the increase in length DL?
a) 1.25 mm
b) 2.5 mm
c) 1.0 cm
d) 5.0 mm
e) 0.625 mm
4. A block is dropped from a height h=8000 km above Earth's surface. Neglecting Earth's rotation and neglecting air resistance, which expression(s) gives the velocity of the block when it strikes the surface? R refers to Earth’s radius.
a)
b)
c)
d) All the above expressions work
e) None of the expressions work, because the answer depends on the mass of the block.
5. An object of mass m moves with a velocity of v. It collides head-on with an object of mass 3m moving with speed 2v/3 in the opposite direction. If the two objects stick together, what is the velocity (magnitude and direction) of the combined object after the collision?
a) 0
b) v/2
c) v/4
d) –v/2
e) –v/4
6. In a ballistic pendulum experiment, two processes occur in succession: (1) A bullet at high initial velocity v0 is stopped in a wooden block (which is suspended from the ceiling by a string), and the combined system acquires a velocity of V; and (2) the system executes a pendulum motion in which the velocity decreases as the pendulum rises until it reaches a maximum height and turns back. Linear momentum (along the direction of motion) is conserved in
a. process (2) but not (1);
b. process (1) but not (2);
c. both (1) and (2);
d. neither (1) nor (2);
e. none of the above.
7. Each of the three cylinders pictured in the accompanying figure has the same mass, and each cylinder’s mass is uniformly distributed throughout the colored regions. Order the cylinders according to their moment of inertia with the largest moment of inertia being first. Assume that the reference axis passes through the center of each cylinder and points out of the page.
a) large solid cylinder, large hollow cylinder, small cylinder
b) large hollow cylinder, large solid cylinder, small cylinder
c) small cylinder, large hollow cylinder, large solid cylinder
d) large solid cylinder, small cylinder, large hollow cylinder
e) large hollow cylinder, small cylinder, large solid cylinder
8. Consider a light beam hung by two cables as shown above. A weight,
Mg = 8000 N is hung as shown. What is the tension TR in the right-side cable?
a) 10400 N
b) 6333 N
c) 5600 N
d) 4000 N
e) 3200 N
9. A helicopter suspends a 2000-N probe into Lake Michigan by a cable. After the weight is submerged, the tension in the cable is 800 N. What is the average density of the probe?
a) 2800 kg/m3
b) 3000 kg/ m3
c) 2500 kg/ m3
d) 1667 kg/ m3
e) 2111 kg/ m3
10. An incompressible fluid moves through a pipe that has a radius of 30 cm at point ‘A’ and then narrows to a radius of 20 cm at point ‘B’. Which of the following is true? (Assume non-viscous laminar flow).
a) The amount of mass that passes ‘A’ in one second equals the amount of mass that passes ‘B’ in the same time.
b) The velocity of the fluid at ‘A’ equals the velocity of the fluid at ‘B’.
c) The pressure of the fluid at ‘A’ equals the pressure at point ‘B’.
d) The kinetic energy density at ‘A’ equals the kinetic energy density at ‘B’.
e) The pressure is larger at point ‘B’ than at ‘A’.
11. A leak-proof cylinder with a movable piston is filled with helium gas and compressed at a constant pressure of 2 atm. The initial temperature is 0 °C and the initial volume is 20 L. The final volume is 10 L. Find the temperature of the gas after the compression.
a) 0 °C
b) 546.3 °C
c) 32 °C
d) -40 °C
e) -136.6 °C
f)
12. The r.m.s. velocity of molecules in an ideal gas is measured to be 8000 m/s when the temperature is 50 °C. The gas is then compressed to half its original volume while keeping the temperature fixed at 50 °C. What is the r.m.s. velocity of the molecules in the compressed gas.
a) 8000 m/s
b) 1.60x104 m/s
c) 4000 m/s
d) 1.13x104 m/s
e) 5657 m/s
Answers:
1. a
2. c
3. b
4. a
5. e
6. b
7. b
8. c
9. d
10. a
11. e
12. a