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physics
mechanics

Questions and Answers of Mechanics

A diving board 3.00 m long is supported at a point 1.00 m from the end, and a diver weighing 500 N stands at the free end (Fig. 11.24). The diving board is of uniform cross section and weighs 280 N.
A uniform aluminum beam 9.00 m long, weighing 300 N, rests symmetrically on two supports 5.00 m apart (Fig. 1I.25). A boy weighing 600 N starts at point A and walks toward the right.(a) In the same
Find the tension T in each cable and the magnitude and direction of the force exerted on the strut by the pivot in each of the arrangements in Fig. 11.26. In each case let w be the weight of the
The horizontal beam in Fig. 11.27 weighs ISO N, and its center of gravity is at its center. Find (a) The tension in the cable and (b) The horizontal and vertical components of the force exerted on
A door 1.00 m wide and 200 m high weighs 280 N and is supported by two hinges, one 0.50 m from the top and the other 0.50 m from the bottom. Each hinge supports half the total weight of the door.
Suppose that you can lift no more than 650 N (around 150lb) unaided. (a) How much can you lift using a 1.4-m-long wheelbarrow that weighs 80.0 N and whose center of gravity is 0.50 m from the center
You take your dog clear to the vet, and the doctor decides he must locate the little beast's center of gravity. It would be awkward to hang the pooch from the ceiling, so the vet must devise another
A 15,000-N crane pivots around a friction-free axle at its base and is supported by a cable making a 25° angle with the crane (Fig. 11.29). The crane is 16 m long and is not uniform, its center
A 3.00-m-long, 240-N, uniform rod at the zoo is held in a horizontal position by two ropes at its ends (Fig. 11.30). The left rope makes an angle of 150° with the rod and the right rope makes an
A non-uniform beam 4.50 m long and weighing 1.00 kN makes an angle of 25.0° below the horizontal. It is held in position by a frictionless pivot at its upper right end and by a cable 3.00 m
A Couple two forces equal in magnitude and opposite in direction, acting on an object at two different points, form what is called a couple. Two ant parallel forces with equal magnitudes F, = F2 =
Biceps Muscle A relaxed biceps muscle requires a force of 25.0 N for an elongation of 3.0 cm; the same muscle under maximum tension requires a force of 500 N for the same elongation. Find Young's
A circular steel wire 2.00 m long must stretch no more than 0.25 cm when a tensile force of 400 N is applied to each end of the wire. What minimum diameter is required for the wire?
Two circular rods, one steel and the other copper, are joined end to end. Each rod is 0.750 m long and 1.50 cm in diameter. The combination is subjected to a tensile force with magnitude 4000 N. For
A metal rod that is 4.00 m long and 050 cm2 in cross-sectional area is found to stretch 0.20 cm under a tension of 5000 N. What is Young's modulus for this metal?
Stress 011 a Mountaineer's Rope A nylon rope used by mountaineers e100gales 1.10 m under the weight of a 65.O-kg climber. If the rope is 45.0 m in length and 7.0 m in diameter, what is Young's
In constructing a large mobile, an artist hangs an aluminum sphere of mass 6.0 kg from a vertical steel wire 0.50 m long and 2.5 X 10 cm in cross ... sectional area. On the bottom of the sphere he
A vertical, solid steel post 25 cm in diameter and 2.50 m long is required to support a load of 8000 kg. You can ignore the weight of the post. What are? (a) The stress in the post; (b) The strain in
Outside a bouse 1.0 Ion from ground zero of a l00-kiloton nuclear bomb explosion, the pressure will rapidly rise to as high as 28 atm while the pressure inside the house remains 1.0 atm. If the front
A solid gold bar is pulled up from the hold of the sunken RMS Titanic. (a) What happens to its volume as it goes from the pressure at the ship to the lower pressure at the ocean's surface?(b) The
A petite young woman distributes her 500 N weights equally over the heels of her high-heeled shoes. Each heel has an area of 0.750 cm. (a) What pressure is exerted on the floor by each heel?(b) With
In the Challenger Deep of the Marianas Trench, the depth of seawater is 10.9 Ion and the pressure is 1.16 X 10" Pa (about 1.15 X 10 atm). (a) If a cubic meter of waters taken from the surface to this
A specimen of oil having an initial volume of 600 cm is subjected to a pressure increase of 3.6 X 10" Pa, and the volume is found to decrease by 0.45 cm. What is the bill: modulus of the material the
A square steel plate is 10.0 cm on a side and 0.500 cm thick. (a) Find the sbear strain that results if a force of magnitude 9.0 X 10" N is applied to each of the four sides, parallel to the side.
A copper cube measures 6.00 cm on each side. The bottom face is held in place by very strong glue to a flat horizontal surface, while a horizontal force F is applied to the upper face parallel to one
Shear forces are applied to a rectangular solid. The same forces are applied to another rectangular solid of the same material, but with three times each edge length. In each case the forces are
In a materials testing laboratory, a metal wire made from a new alloy is found to break when a tensile force of 90.8 N is applied perpendicular to each end. If the diameter of the wire is 1.84 cm,
A 4.0-m-long steel wire has a cross-sectional area of 0.050 cm Its proportional limit has a value of 0.0016 times its Young's modulus (see Table 11.1). Its breaking stress has a value of 0.0065 times
A steel cable with cross-sectional area 3.00 cm has an elastic limit of 2.40 X 108 Pa. Find the maximum upward acceleration that can be given a 1200-kg elevator supported by the cable if the stress
A brass wire is to withstand a tensile force of 350 N without breaking. What minimum diameter must the wire have?
Mountain Climbing Mountaineers often use a rope to lower themselves down the face of a cliff (this is called rappelling). They do this with their body nearly horizontal and their feet pushing against
Sir Lancelot rides slowly out of the castle at Camelot and onto the 12.0-m-long drawbridge that passes over the moat (Fig. 11.34). Unbeknownst to him, his enemies have partially severed the vertical
Three vertical forces act on an airplane when it is flying at a constant altitude and with a constant velocity. These are the weight of the airplane, an aerodynamic force on the wing of the airplane,
A pickup truck has a wheelbase of 3.00 In. ordinarily, 10,780 N rests on the front wheels and 8820 N on the rear wheels when the truck is parked on a level road. (a) A box weighing 3600 N is now
A uniform, 255-N rod that is 2.00 m long carries a 225-N weight at its right end and an unknown weight W toward the left end (Fig. 11.35) When W is placed 50.0 cm from the left end of the rod, the
A thin uniform metal rod is bent into three perpendicular segments, two of which have length L. You want to determine what the length of the third segment should be so that the unit will hang with
You open a restaurant and hope to entice customers by hanging out a sign (Fig. 11.37). The uniform horizontal beam supporting the sign is 1.50 m long, has a mass of 18.0 kg, and is hinged to the
A claw hammer is used to pull a nail out of a board (Fig. 11.38). The nail is at an angle of 60° to the board, and a force F, of magnitude 500 N applied to the nail is required to pull it from
End A of the bar AB in Fig. 11.39 rests on a frictionless horizontal surface, and end B is hinged. A horizontal force F of magnitude 120 N is exerted on end A. You can ignore the weight of the bar.
A museum of modem art is displaying an irregular 358-N sculpture by hanging it from two thin vertical wires, A and B, that are 1.25 m apart (Fig. 11.40). The center of gravity of this piece of art is
A Truck on a Drawbridge A loaded cement mixer drives onto an old drawbridge, where it stalls with its center of gravity three-quarters of the way across the span. The truck driver radios for help,
A non-uniform fire escape ladder is 6.0 m long when extended to the icy alley below. It is held at the top by a frictionless pivnt, and there is negligible frictional force from the icy surface at
A uniform strut of mass m makes an angle 6 with the horizontal. It is supported by a frictionless pivot located at one-third its length from its lower left end and a horizontal rope at its upper
You are asked to design the decorative mobile shown in Fig. 11.44. The strings and rods have negligible weight, and the rods are to hang horizontally.(a) Draw a free-body diagram for each rod.(b)
A uniform, 7.5-m-long beam weighing 9000 N is hinged to a wall and supported by a thin cable attached 1.5 m from the free end of the beam. The cable runs between the beam and the wall and makes a 400
A uniform drawbridge must be held at a 37° angle above the horizontal to allow ships to pass underneath. The drawbridge weighs 45,000 N and is 14.0 m long. A cable is connected 3.5 m from the hinge
A uniform, 250-kg beam is supported by a cable connected to the ceiling, as shown /in Fig. 11.45. The lower end of the beam rests on the floor.(a) What is the tension in the cable?(b) What is the
(a) In Fig. 11.46a6.00-mlong, uniform beam is hanging from a point 1.00 m to the right of its center. The beam weighs 140 N and makes an angle of 30.0° with the vertical. At the right-hand end of
A uniform, horizontal flagpole 5.00 m long with a weight of 200 N is hinged to a vertical wall at one end. A 600-N stuntwoman hangs from its other end. The flagpole is supported by a guy wire running
A holiday decoration consists of two shiny glass spheres with masses 0.0240 kg and 0.0360 kg suspended, as shown in Fig. 11.47, from a uniform rod with mass 0.120 kg and length 1.00 m. The rod is
A uniform rectangular plate of width d, height h, and weight W is supported with its top and bottom edges horizontal (Fig. 11.48). At the lower left comer there is a hinge and at the upper right
(a) If the steel rod of Example 11.5 (Section 11.4) has a circular cross section and a Poisson's ratio of 0.23, what is its change in diameter when the milling machine is hung from it?
A worker wants to turn over a uniform 125O-N rectangular crate by pulling at 53.0" on one of its vertical sides (Fig. 11.49). The floor is rough enough to prevent the crate from slipping.(a) What
One end of a uniform meter stick is placed against a vertical wall (Fig. 11.50). The other end is held by a lightweight cord that makes an angle 6 with the stick. The coefficient of static friction
Two friends are carrying a 200-kg crate up a flight of stairs. The crate is 1.25 m long and 0.500 m high, and its center of gravity is at its center. The stairs make a 45.0° angle with respect to
Forearm In the human arm, the forearm and hand pivot about the elbow joint. Consider a simplified model in which the biceps muscle is attached to the forearm 3.80 cm from the elbow joint. Assume that
Refer to the discussion of holding a dumbbell in Example 11.4 (Section 11.3). The maximum weight that can be held in this way is limited by the maximum allowable tendon tension T (determined by the
A uniform, 90.0-N table is 3.6 m long, 1.0 m high and 1.2 m wide. A 1500-N weight is placed 0.50 m from one end of the table, a distance of 0.60 m from each of the two legs at that end. Draw a
Flying Buttress (a) A symmetric building has a roof sloping upward at 35.0° above the horizontal on each side. If each side of the uniform roof weighs 10,000 N, find the horizontal force that this
You are trying to raise a bicycle wheel of mass m and radius R up over a curb of height h. To do this, you apply a horizontal force F (Fig. 11.52). What is the smallest magnitude of the force F that
The Farmyard Gate A gate 4.00 m wide and 2.00 m high weighs 500 N. Its center of gravity is at its center, and it is hinged at A and B. To relieve the strain on the top hinge, a wire CD is connected
If you put a uniform block at the edge of a table the center of the block must be over the table for the block not to fall off.(a) If you stack two identical blocks at the table edge, the center of
Two uniform 75.0-g marbles 2.00 cm in diameter are stacked as shown in Fig. 11.55 in a container that is 3.00 cm wide.(a) Find the force that the container exerts on the marbles at the points of
Two identical, uniform beams weighing 260 N each are connected at one end by a frictionless hinge. A light horizontal crossbar attached at the mid points of the beams maintains an angle of 53.0°
An engineer is designing a conveyor system for loading hay bales into a wagon (Fig. 11.57). Each bale is 0.25 m wide, 0.50 m high, and 0.80 m long (the dimension perpendicular to the plane of the
The hay bale of Problem 11.77 is dragged along a horizontal surface with constant speed by a force F (Fig. 11.58). The coefficient of kinetic friction is 0.35.(a) Find the magnitude of the force
A garage door is mounted on an overhead rail (Fig. 11.59). The wheels at A and B have rusted so that they do not roll, but rather slide along the track. The coefficient of kinetic friction is 0.52.
A horizontal boom is supported at its left end by a frictionless pivot. It is held in place by a cable attached to the right-hand end of the boom. A chain and crate of total weight w hang from
Prior to being placed in its hole, a 5700-N, 9.0-m-long, uniform utility pole makes some nonzero angle with the vertical. A vertical cable attached 2.0 m below its upper end holds it in place while
A weight W is supported by attaching it to a vertical uniform metal pole by a thin cord passing over a pulley having negligible mass and friction. The cord is attached to the pole40.0 cm below the
Pyramid Builders. Ancient pyramid builders are balancing a uniform rectangular slab of stone tipped at an angle 6 above the horizontal using a rope (Fig. 11.61). The rope is held by five workers who
Hooke's Law for a Wire A wire of length 10 and cross-sectional Area A supports a hanging weight W. (a) Show that if the wire obeys Equation (11.7), it behaves like a spring of force constant AY/lo,
A 12.0-kg mass, fastened to the end of an aluminum wire with an unscratched length of 0.50 m, is whirled in a vertical circle with a constant angular speed of 120 rev/min. The cross-sectional area of
A metal wire 3.50 m long and 0.70 mm in diameter was given the following test A load weighing 20 N was originally hung from the wire to keep it taut. The position of the lower end of the wire was
A 1.05-m-Iong rod of negligible weight is supported at its ends by wires A and B of equal length (Fig. 11.62). The cross sectional area of A is 2.00 mm2 and that of B is 4.00 mm2€¢ Young's
An amusement park ride consists of airplane-shaped cars attached to steel rods (Fig. 11.63). Each rod has a length of 15.0 m and a cross sectional area of 8.00 cm2€¢(a) How much is the rod
A brass rod with a length of 1.40 m and a cross-sectional area of 2.00 cm2 is fastened end to end to a nickel rod with length L and cross-sectional area 1.00 cm2. The compound rod is subjected to
Stress on the Shin Bone. Compressive strength of our bones is important in everyday life. Young's modulus for bone is about 1.4 X 10 l0 Pa. Bone can take only about a 1.0% change in its length before
You hang a flood lamp from the end of a vertical steel wire. The flood lamp stretches the wire 0.18 mm and the stress is proportional to the strain. How much would it have stretched? (a) If the wire
A moon shiner produces pure ethanol (ethyl alcohol) late at night and stores it in a stainless steel tank in the form of a cylinder 0.300 m in diameter with a tight-fitting piston at the top. The
A bar with cross-sectional area A is subjected to equal and opposite tensile forces F at its ends. Consider a plane through the bar making an angle 6 with a plane at right angles to the bar (Fig.
A horizontal, uniform, copper rod has an original length 10, cross-sectional area A, Young's modulus Y, and mass m. It is supported by a frictionless pivot at its right end and by a cable at its left
A bookcase weighing 1500 N rests on a horizontal surface for which the coefficient of static friction is p = 0.40. The bookcase is 1.80 m tall and 2.00 m wide; its center of gravity is at its
Knocking Over a Post One end of a post weighing 400 N and with height h rests on a rough horizontal surface with p" = 0.30. The upper end is held by a rope fastened to the surface and making an angle
Minimizing the Tension A heavy horizontal girder of length L has several objects suspended from it. It is supported by a frictionless pivot at its left end and a cable of negligible weight that is
Two ladders, 4.00 m and 3.00 m long, are hinged at point A and tied together by a horizontal rope 0.90 m above the floor (Fig. 11.67). The ladders weigh 480 N and 360 N, respectively, and the center
A device for measuring compressibility consists of a cylinder filled with oil and fitted with a piston at one end. A block of sodium is immersed in the oil, and a force is applied to the piston.
Bulk Modulus of an Ideal Gas the equation of state (the equation relating pressure, volume, and temperature) for an ideal gas is pV = nRT, where n and R are constants. (a) Show that if the gas is
An angler hangs a 4.50-kg fish from a vertical steel wire 1.50 m long and 5.00 X 10-3 cm2 in cross-sectional area. The upper end of the wire is securely fastened to a support. (a) Calculate the
A beam of mass M and length L is supported horizontally at its ends by two cables making angles θ and Φ with the horizontal ceiling (Fig. 11.41).(a) Show that if the beam is uniform. These
A uniform solid cylinder Figure of mass M is supported on a ramp that rises at an angle θ T above the horizontal by a wire that is wrapped around its rim and pulls on it tangentially parallel
A 500.0-g bird is flying horizontally at 2.25 m/s, not paying much attention, when it suddenly flies into a stationary vertical bar, hitting it 25.0 cm below the top (Fig. 10.63). The bar is uniform,
A small block with mass 0.250 kg is attached to a string passing through a hole in a frictionless, horizontal surface (see Fig. 10.48). The block is originally revolving in a circle with a radius of
A horizontal plywood disk with mass 7.00 kg and diameter 1.00 m pivots on frictionless bearings about a vertical axis through its center. You attach a circular model-railroad track of negligible mass
A stiff uniform wire of mass Mo and length La is cut, bent, and the parts soldered together so that it forms a circular wheel having four identical spokes coming out from the center. None of the wire
In a physics laboratory you do the following ballistic pendulum experiment: You shoot a ball of mass m horizontally from a spring gun with a speed v. The hall is immediately caught a distance below a
A 55-kg runner runs around the edge of a horizontal turntable mounted on a vertical, frictionless axis through its center. The runner's velocity relative to the earth has magnitude 2.8 m/s. The
Recession of the Moon Careful measurements of the earth-moon separation indicate that our satellite is presently moving away from us at approximately 3.0 cm per year. Neglect any angular momentum
Center of Percussion A baseball hat rests on a frictionless, horizontal surface. The bat has a length of 0.900 m, a mass of 0.800 kg, and its center of mass is 0.600 m from the handle end of the hat
Consider a gyroscope with an axis that is not horizontal but is inclined from the horizontal by an angle fJ. Show that the precession angular frequency does not depend on the value of fJ but is given

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