physics 8, fall 2017, homework #9

Physics 8, Fall 2017, Homework #9.Due at start of class on Friday, November 10, 2017

Problems marked with (*) must include your own drawing or graph representing the problemand at least one complete sentence describing your reasoning.

(Static-equilibrium problems.)

1*. Find the tension in the two cords shown in the figure below (left). Neglect the mass ofthe cords, and assume that the angle θ is 35◦ and the mass m is 105 kg.

2. Find the tension in the two wires supporting the traffic light shown in the figure above(right).

3. Using the equations for static equilibrium, find the “reaction” forces exerted by thesupports on the beam in the left figure below. (There are three forces: two vertical and onehorizontal. You may find that one force equals zero.)

4*. Find the “reaction” forces exerted by the supports A and B on the beam in the rightfigure above. (There are three forces to find: two vertical and one horizontal.)

phys008/hw09.tex page 1 of 5 2017-11-02 18:50

(Chapter 12 problems)

5. Archimedes’ screw, one of the first mechanical devices for lifting water, consists of a verylarge screw surrounded by a hollow, tight-fitting shaft (shown below). The bottom end ofthe device is placed in a pool of water. As the screw is turned, water is carried up along itsridges and comes out the top of the shaft and into a storage tank. As the handle is turned,work done by the torque exerted on the handle is converted to gravitational potential energyof the water-Earth system. Let’s say you want to take a shower using this device. You figureyour shower will consume 52 liters of water, and so you have to raise this amount to thestorage tank 2.5 m above the pool, so it can fall down on you. When you turn the handle,you apply a torque of 12 N · m. How many times must you turn the handle? (Hint: workdone by a torque τ is W = τ∆θ, with ∆θ measured in radians.)

6*. A 37 kg child stands on the edge of a 410 kg playground merry-go-round that is turningat the rate of 1 revolution every 2.3 s. She then walks to the center of the platform. Ifradius of the platform is 1.6 m, what is the platform’s rotational speed once the child arrivesat the center? (Treat the merry-go-round as a solid cylinder. Think carefully about whichconservation law to use. Also, be careful how you turn the given information into an initialvalue for rotational speed ω.)

(Chapter “G9” problems)

7. An elevator of mass (including passengers, at full capacity) 1400 kg hangs on a steel cable(of circular cross-section). Suppose that the building code requires a safety factor of 10 forsuch a cable. (The weakest point of the cable should not break when loaded with 10 timesthe maximum specified load.) (a) What should be the smallest diameter of the requiredcable? The weight of the cable itself can be neglected. (b) What should be the smallestdiameter of the cable if the elevator accelerates upward at 2.0 m/s2 ? Use 8 × 108 N/m2 asthe tensile strength of steel. Remember not to mix up radius, diameter, and cross-sectionalarea! The “safety factor of 10” in this problem means that the largest allowed stress in thecable is 1/10 of the quoted tensile strength.


8*. A person wants to push a lamp (mass 8.1 kg) across the floor. The coefficient of frictionbetween the lamp and the floor is µk = 0.20. Calculate the maximum height x above thefloor at which the person can push the lamp so that the lamp slides rather than tips. Thebase of the lamp is a circle of radius 0.12 m. The lamp’s center of gravity is directly abovethe center of the circular base. (You need to make sure that the lamp will not pivot clockwise

about the front of the base.)

9*. When a mass of 25 kg is suspended from the middle of a fixed straight aluminum wire(which is initially horizontal), the wire sags to make an angle of 12◦ with the horizontal, asshown below. (a) What is the tension in each of two diagonal wire segments? (b) If theoriginal length of each wire segment was 1.000 m when it was horizontal (before the 25 kgmass was attached), what is its length when it is diagonal? (c) What is the strain in thewire? (d) If Young’s modulus for aluminum is 7.0 × 1010 N/m2, what is the stress in thediagonal wire segments? (e) If the wire has a circular cross-section, what is the wire radius?(You know the tension (force) and you know the tensile stress, so you can calculate the area,and hence the radius.)


(Onouye/Kane Chapter 3 problems.)

10*. Solve for the support reactions at A and B (i.e. the forces exerted by the supports at Aand B on the beam) in the figure below. To do this, you will need to convert the distributedload into an equivalent concentrated load.

11*. Using the method of joints, find the force in each member of the truss shown below(left). Summarize the results on a diagram that indicates both the magnitude of each forceand whether each member is in tension or compression.

12*. Using the method of sections, solve for the forces in members BC, CH, and FH in thetruss shown above (right). Indicate both the magnitudes of these forces and whether themember is in tension or compression.

Remember online response at positron.hep.upenn.edu/wja/jitt/?date=2017-11-10


XC1*. Optional/extra-credit. A large steel bar of length ` = 1.0 m is hinged at one endto a wall. A mechanic holds the far end so that the bar is parallel to the ground and placesa penny on the bar right at the end she is holding. (a) What is the rotational acceleration ofthe bar at the instant after she lets go? (b) What is the magnitude of the downward linearacceleration of the far end of the bar at the instant after she lets go? (c) Does the pennyremain in contact with the bar after the far end of the bar is released?

XC2*. Optional/extra-credit. Using the method of sections, solve for the forces inmembers AB, BH, and HG in the truss shown below. Indicate whether each of thesemembers is in tension or in compression. Use only one section cut through the truss.


Physics 008 2017 homework #9 score sheet

Problem 1: ______ /4 Problem 8: ______ /4

Problem 2: ______ /4 Problem 9: ______ /4

Problem 3: ______ /4 Problem 10: ______ /4

Problem 4: ______ /4 Problem 11: ______ /4

Problem 5: ______ /4 Problem 12: ______ /4

Problem 6: ______ /4 Problem 13: ______ /4

Problem 7: ______ /4

The following 4 points reflect your maintaining good habits for all of the above problems:

Reasonable number of significant digits reported in answers: _____ /2

Sufficient level of explanation for reasoning behind answers: _____ /2(You can earn 3 out of 2 for consistently clear presentation/explanation of your answers.)

Total (out of 52): __________

+ Extra credit (if any): ______

scoring guideline (for each problem):4 = complete and correct solution3 = good but minor error or minor omission2 = serious error or omission but shows decent effort1 = we can't make sense of what is written down0 = no serious attempt to solve problem

Please write your name only on the bottom edge of this sheet (not on your own solutions), and staple the sheet to your own solutions, so that we don’t know whose paper we are grading until after we have finished grading it.

Name: ______________________________

physics 8, fall 2017, homework #9

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