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Physics 151 Roster No.: October 22, 2010 Score:
Midterm Exam #2, Part A
Exam time limit: 50 minutes. You may use a calculator and both sides of ONE sheet of notes, handwritten only****. Closed book; no collaboration. Ignore friction and air resistance in all problems, unless told otherwise. Part A: For each question, fill in the letter of the one best answer on your bubble answer sheet. Physical constants: g = 9.80 m/s^2 G = 6.67 × 10 –^11 N·m^2 /kg^2 Useful conversions: 1 year = 3.156 × 107 s Sun, Earth, & Moon data: masses physical radii orbital distances orbital periods M Sun = 2.00 × 1030 kg R Sun = 6.95 × 108 m M Earth = 5.97 × 1024 kg R Earth = 6.37 × 106 m d Earth-Sun = 1.50 × 1011 m T Earth = 1 year (exact) M Moon = 7.35 × 1022 kg R Moon = 1.74 × 106 m d Earth-Moon = 3.84 × 108 m T Moon = 27.3 days (2 pts. each) Convert the following quantities into the given units:
1. 99 kW = mW ( Note: “W” = watt, the MKS unit for power) A. 9.9 × 10 –^10 mW D. 9.9 × 104 mW B. 9.9 × 10 –^7 mW E. 9.9 × 107 mW C. 9.9 × 10 –^4 mW 2. 3.3 × 1011 m^3 = km^3 A. 330 km^3 D. 3.3 × 105 km^3 B. 3.3 × 103 km^3 E. 3.3 × 106 km^3 C. 3.3 × 104 km^3 3. 25 cm/s = km/h ( Note: “h” = hour) A. 9.0 × 10 –^3 km/h D. 9.0 km/h B. 9.0 × 10 –^2 km/h E. 90. km/h C. 0.90 km/h Questions #4–5: A child’s toy airplane flies in uniform circular motion at the end of a massless tether (cord). The plane of the circle is exactly horizontal (parallel to the ground). ( Neglect gravity and air resistance. ) 4. (1 pt.) The acceleration of the airplane is always… A. tangent to the circle, in the direction of the airplane’s velocity B. exactly toward the center of the circle C. exactly away from the center of the circle D. zero 5. (2 pts.) The tether will break if its tension exceeds 95 N. If the length of the tether is 1.5 m, and the airplane has a mass of 0.20 kg, what is the toy airplane’s maximum linear speed? A. 11 m/s D. 27 m/s B. 16 m/s E. 34 m/s C. 22 m/s
Questions #6–8: A block of mass m initially sits at rest on a horizontal surface. The coefficients of friction between the block and the surface are μk and μs. A person pushes on the block with a horizontal force Fp in an attempt to dislodge it.
6. (2 pts.) What is the minimum magnitude of Fp needed for the block to start sliding? A. μk mg C. ! mg μ k
E.
mg μ k
7. (2 pts.) Later, suppose the block is sliding to the right. If the block has a rightward acceleration a , what is the magnitude of Fp? A. ma C. m ( a + μk g ) E. ! ma μ k B. μk ma D. m ( a – μk g ) 8. (1 pt.) In the previous question, the person exerts a rightward force of F p on the crate, and the crate accelerates to the right. At the same time , the crate exerts a leftward force on the person that is… A. zero B. weaker than F p C. equal to F p D. stronger than F p Questions #9–11: Consider two spherical masses, A and B , as shown, released from rest at an initial separation r 0. Mass A is larger than mass B. ( Assume that NO other masses exist in the universe.) 9. (1 pt.) As the two masses fall toward each other, the gravitational force acting on mass A is ____________ the gravitational force acting on mass B , at all times. A. stronger than B. equal strength as C. weaker than D. None of the above answers is true at all times. 10. (1 pt.) The two masses will finally collide at a location … A. closer to the starting position of mass A B. closer to the starting position of mass B C. exactly halfway between their original positions 11. (1 pt.) Just before the two masses collide, the speed of mass A will be ____________ the speed of mass B. A. faster than B. equal to C. slower than μk and μs m Fp A B r 0
Physics 151 Roster No.: October 22, 2010 Score:
Midterm Exam #2, Part B
Part B: Show your work on all free-response questions. Be sure to use proper units and significant figures in your final answers. For any multiple-choice questions, circle the letter of the one best answer (unless more than one answer is asked for).
1. A large, heavy crate ( m = 250.0 kg) is suspended on cable A from a crane. At all times , a worker pulls downward on cable B with a constant 380. N of force, to help guide and steady the crate. Both cables are exactly vertical. Assume that both cables are massless and inelastic. a. (2 pts.) Using the crate shown at right, create a free-body diagram of m , showing ALL forces acting on it. LABEL ALL force vectors with names. (You do NOT need to calculate their magnitudes for this diagram.) b. (2 pts.) If the crate is at rest , the magnitude of the tension in cable A is: ___________________ You do NOT need to show your work for part (b). c. (5 pts.) Later, while the crate is moving, the tension in cable A is measured to be 2750. N. (The worker is still applying 380. N of downward force on cable B .) Find the magnitude and direction of the crate’s acceleration. Show your work completely. m cable A cable B m
2. In the not-too-distant future, astronauts may use Mars’s larger moon, Phobos, as a location for a lunar base and way-station to Mars. Throughout this question, assume that Phobos is a uniform-density, perfectly smooth sphere with radius 1.11 × 104 m and mass 1.07 × 1016 kg. ( Ignore the presence of Mars or any other astronomical bodies.) Two astronauts, Adam and Beverly, are having a friendly argument: Adam bets Bev that he can throw a 145 - gram baseball horizontally (tangent to the ground) fast enough to put it into a circular orbit just barely above the surface of Phobos. Bev is skeptical, so she does a quick calculation… a. (5 pts.) Find the linear speed necessary for the baseball. Show your work. ( Thought question: Could a human indeed throw a baseball this fast? Recall: 1 m/s ≈ 2.24 miles/hour.) To prove his point, Adam does it: he throws the baseball at just the right speed, and away it goes in a circular orbit. While Adam stands grinning at Bev, the baseball circles Phobos completely and smacks him right in the helmet. Bev decides that it was worth the extremely long wait. b. (5 pts.) How much time is needed for the baseball to complete one full orbit of Phobos? Convert your final answer to hours. Show your work. ( Hint: Your final answer will be between 1 and 3 hours.) continued on next page…
