PHY11-Problem-Set

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1. You push your physics book 1.50 m along a horizontal tabletop with ahorizontal force of 2.40 N. The opposing force of friction is 0.600 N. a)How much work does your 2.40-N force do on the book? b) What is thework done on the book by the friction force? C) What is the total workdone on the book?

2. You throw a 20-N rock vertically into the air from ground level. Youobserve that when it is 15.0 m above the ground, it is travelling at 25.0m/s upward. Use the work-energy theorem to find a) its speed just as itleft the ground; b) its maximum height.

3. A spring of negligible mass has a force constant k=1600N/m. a) Howfar must the spring be compressed for 3.20 J of potential energy to bestored in it? b) You place the spring vertically with one end of the floor.You then drop a 1.20 kg book onto it from a height of 0.80 m above thetop of the spring. Find the maximum distance the spring will be

compressed.

4. You and your friends are doing physics experiments on a frozen pondthat serves as a frictionless, horizontal surface. Sam, with a mass 80.0 kg,is given a push and slides eastward. Abigail, with mass 50.0 kg, is sentsliding northward. They collide and. After the collision, Sam is moving at

north of east with a speed of 6.00 m/s and Abigail is moving atsouth of east with a speed of 9.00 m/s. a) What was the speed of eachperson before the collision? b) by how much did the total kinetic energy ofthe two people decrease during the collision?

5. A 10.0 g marble slides to the left with a velocity of magnitude 0.4010m/s on the frictionless, horizontal surface of an icy, New York sidewalkand has a head-on elastic collision with a larger 30.0 g marble sliding tothe right with a velocity of magnitude 0.200 m/s (Fig. 8.35). a) Find thevelocity of each marble (magnitude and direction) after the collision.(Since the collision is head-on, all the motion is along a line.) b) Calculatethe change in momentum (that is, the momentum after the collisionminus the momentum before the collision) for each marble. Compare thevalues you get for each marble. c) Calculate the change in kinetic energy(that is, the kinetic energy after the collision minus the kinetic energybefore the collision) for each marble. Compare the values you get for each

marble.


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ROTATIONAL MOTION

1. A circular disk rotating at 1800 rpm is applied upon by a constant breaking force until itsspeed becomes 60 rpm, 10 seconds after the application of the force. (a) What is its angularacceleration? (b) In how many seconds will it come to rest? (c) How many revolutions does itmake in 10 seconds?

2. A tennis ball is a hollow sphere with a thin wall. It is set rollingwithout slipping at 4.03 m/s on a horizontal section of a track, as shownin Figure P10.56. It rolls around the inside of a vertical circular loop90.0 cm in diameter, and finally leaves the track at a point 20.0 cmbelow the horizontal section. (a) Find the speed of the ball at the top ofthe loop. Demonstrate that it will not fall from the track. (b) Find itsspeed as it leaves the track.


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3. The combination of an applied force and a friction force produces a constant total torque of

36.0 N-m on a wheel rotating about a fixed axis. The applied force acts for 6.00 s. During thistime the angular speed of the wheel increases from 0 to 10.0 rad/s. The applied force is thenremoved, and the wheel comes to rest in 60.0 s. Find (a) the moment of inertia of the wheel, (b)the total number of revolutions of the wheel.

4. A hungry bear weighing 700 N walks out on a beam in an attempt to

retrieve a basket of food hanging at the end of the beam. The beam is uniform,weighs 200 N, and is 6.00 m long; the basket weighs 80.0 N. (a) When the bearis at x = 1.00 m, find the tension in the wire and the components of the forceexerted by the wall on the left end of the beam. (b) If the wire can withstand amaximum tension of 900 N, what is the maximum distance the bear can walkbefore the wire breaks?


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5. A water molecule consists of an oxygen atom with two hydrogen atoms bound to it. The angle

between the two bonds is 106. If the bonds are 0.100 nm long, where is the center of mass ofthe molecule?

HOMEWORK NO.2 (ROTARY MOTION, SECOND CONDITION OF

EQUILIBRIUM, CENTER OF GRAVITY)

INSTRUCTIONS:

1. COPY AND ANSWER THE PROBLEMS.

2. USE ONE BOND PAPER PER PROBLEM.

3. SHOW COMPLETE AND DETAILED SOLUTIONS.

4. SUMMARIZE THE FINAL ANSWERS.

5. DUE FOR SUBMISSION ON NOVEMBER 22, 2012 DURING THE

SCHEDULED QUIZ. LATE HOMEWORKS WILL NOT BE ACCEPTED.


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FOR STRICT COMPLIANCE.

1. An electric motor rotating a grinding wheel at 100 rev/minis switched off. With constant negative angular acceleration ofmagnitude 2.00 rad/s2, (a) how long does it take the wheel to

stop? (b) Through how many radians does it turn while it isslowing down?

2. A car accelerates uniformly from rest and reaches a speedof 22.0 m/s in 9.00 s. If the diameter of a tire is 58.0 cm, find (a)the number of revolutions the tire makes during this motion,assuming that no slipping occurs. (b) What is the final angularspeed of a tire in revolutions per second?

3. An electric motor turns a flywheel through a drive belt thatjoins a pulley on the motor and a pulley that is rigidly attached tothe flywheel, refer to the figure below. The flywheel is a soliddisk with a mass of 80.0 kg and a diameter of 1.25 m. It turns ona frictionless axle. Its pulley has much smaller mass and a radiusof 0.230 m. If the tension in the upper (taut) segment of the beltis 135 N and the flywheel has a clockwise angular acceleration of1.67 rad/s2, find the tension in the lower (slack) segment of the


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belt.

4. A tennis ball is a hollow sphere with a thin wall. It is setrolling without slipping at 4.03 m/s on a horizontal section of atrack, as shown in the figure below. It rolls around the inside of avertical circular loop 90.0 cm in diameter, and finally leaves thetrack at a point 20.0 cm below the horizontal section. (a) Findthe speed of the ball at the top of the loop (b) Find its speed as itleaves the track. (c) Suppose that static friction between ball

and track were negligible, so that the ball slid instead of rolling.Would its speed then be higher, lower, or the same at the top ofthe loop? Explain.


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5. The reel shown in the figure below has radius R andmoment of inertia I. One end of the block of mass m is connectedto a spring of force constant k, and the other end is fastened to acord wrapped around the reel. The reel axle and the incline arefrictionless. The reel is wound counterclockwise so that the

spring stretches a distance d from its unstretched position and isthen released from rest. (a) Find the angular speed of the reelwhen the spring is again unstretched. (b) Evaluate the angularspeed numerically at this point if I = 1.00 kgm2, R = 0.300 m,k = 50.0 N/m, m = 0.500 kg, d = 0.200 m, and = 37.0.


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6. A playground merry-go-round of radius R = 2.00 m has amoment of inertia I = 250 kgm2 and is rotating at 10.0 rev/minabout a frictionless vertical axle. Facing the axle, a 25.0-kg childhops onto the merry-go-round and manages to sit down on theedge. What is the new angular speed of the merry-go-round?


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7. A mobile is constructed of light rods, light strings, andbeach souvenirs, as shown below. Determine the masses of theobjects (a) m1, (b) m2, and (c) m3.


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8. A uniform plank of length 6.00 m and mass 30.0 kg rests

horizontally across two horizontal bars of a scaffold. The barsare 4.50 m apart, and 1.50 m of the plank hangs over one side ofthe scaffold. Draw a free-body diagram of the plank. How far cana painter of mass 70.0 kg walk on the overhanging part of theplank before it tips?

9. The figure below shows three uniform objects: a rod, a

right triangle, and a square. Their masses and their coordinatesin meters are given. Determine the center of gravity for thethree-object system.


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10. A vertical post with a square cross section is 10.0 m tall.Its bottom end is encased in a base 1.50 m tall, which isprecisely square but slightly loose. A force 5.50 N to the rightacts on the top of the post. The base maintains the post inequilibrium. Find the force that the top of the right side wall ofthe base exerts on the post. Find the force that the bottom ofthe left side wall of the base exerts on the post.

PHY11 SW No. 3


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6. A child slides across a floor in a pair of rubber-soled shoes. The friction force actingon each foot is 20.0 N. The footprint area of each shoe sole is 14.0 cm2, and thethickness of each sole is 5.00 mm. Find the horizontal distance by which the upper andlower surfaces of each sole are offset. The shear modulus of the rubber is 3.00 MN/m2.Mega Newton (MN).

7. A 0.500-kg object attached to a spring with a force constant of 8.00 N/m vibrates insimple harmonic motion with amplitude of 10.0 cm. Calculate (a) the maximum value ofits speed and acceleration, (b) the speed and acceleration when the object is 6.00 cm

from the equilibrium position, and (c) the time interval required for the object to movefromx= 0 tox= 8.00 cm.


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8. A 50.0-g object connected to a spring with a force constant of35.0 N/m oscillates on a horizontal, frictionless surface with amplitudeof 4.00 cm. Find (a) the total energy of the system and (b) the speedof the object when the position is 1.00 cm. Find (c) the kinetic energyand (d) the potential energy when the position is 3.00 cm.

9. A U-tube of uniform cross-sectional area, open to the atmosphere, is partially filledwith mercury. Water is then poured into both arms. If the equilibrium configuration ofthe tube is as shown, with h2 = 1.00 cm, determine the value ofh1.


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10. A frog in a hemispherical pod just floats without sinking into a sea of blue-green ooze with density 1.35 g/cm3. If the pod has radius 6.00 cm andnegligible mass, what is the mass of the frog?

11. A village maintains a large tank with an open top, containing water for emergencies.The water can drain from the tank through a hose of diameter 6.60 cm. The hose endswith a nozzle of diameter 2.20 cm. A rubber stopper is inserted into the nozzle. Thewater level in the tank is kept 7.50 m above the nozzle. (a) Calculate the friction forceexerted on the stopper by the nozzle. (b) The stopper is removed. What mass of waterflows from the nozzle in 2.00 h? (c) Calculate the gauge pressure of the flowing water inthe hose just behind the nozzle.


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INSTRUCTIONS:

1. COPY AND ANSWER THE PROBLEMS.

2. USE ONE BOND PAPER PER PROBLEM.

3. SHOW COMPLETE AND DETAILED SOLUTIONS.

4. SUMMARIZE THE FINAL ANSWERS.


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Note: Y = 10 X 1010

Pa

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PHY11-Problem-Set