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physics
mechanics

Questions and Answers of Mechanics

Calculate the torque (magnitude and direction) about point 0 due to the force F in each of the cases sketched in Fig. 10.37. In each case, the force F and the rod both lie in the plane of the page,
Calculate the net torque about point 0 for the two forces applied as in Fig. 10.38. The rod and both forces are in the plane of the page.
A square metal plate 0.180 m on each side is pivoted about an axis through point 0 at its center and perpendicular to the plate (Fig. 10.39). Calculate the net torque about this axis due to the three
Three forces are applied to a wheel of radius 0.350 m, as shown in Fig. 10.40. One force is perpendicular to the rim, one is tangent to it, and the other one makes a 40.00 angle with the radius. What
One force acting on a machine part is F = (-5.00 N)i + (4.00 N)j. The vector from the origin to the point where the force is applied is 1 = (-0.450m)i + (0.150m)j (a) In a sketch, show 1, F, and the
A Machinist is using a wrench to loosen a nut. The wrench is 25.0 cm long, and be exerts a 17.O-N force at the end of the handle at 37° with the handle (Fig. 10.41).(a) What torque does the
The flywheel of an engine has moment of inertia 2.50 kg m2 about its rotation axis. What constant torque is required to bring it up to an angular speed of 400 rev/min in 8.00 S, starting from rest?
A uniform 8.40-kg, spherical shell SO.O cm m diameter has four small 2.00-kg masses attached to its outer surface and equally spaced around it. This combination is spinning about an axis running
A machine part has the shape of a solid uniform sphere of mass 225 g and diameter 3.00 cm. It is spinning about a frictionless axle through its center, but at one point on its equator it is scraping
A cord is wrapped around the rim of a solid uniform wheel 0.250 m in radius and of mass 9.20 kg. A steady horizontal pull of 40.0 N to the right is exerted on the cord, pulling it off tangentially
A solid, uniform cylinder with mass 8.25 kg and diameter IS.0 cm is spinning at 220 rpm on a thin, frictionless axle that passes along the cylinder axis. You design a simple friction brake to stop
A stone is suspended from the free end of a wire that is wrapped around the outer rim of a pulley, similar to what is shown in Fig. 10.10. The pulley is a uniform disk with mass 10.0 kg and radius
A grindstone in the shape of a solid disk with diameter 0.520 m, and a mass of 50.0 kg is rotating at 850 rev/min, you press an ax against the rim with a normal force of 160 N (Fig. 10.43), and the
A 15.0-kg bucket of water is suspended by a very light rope wrapped around a solid uniform cylinder 0.300 m in diameter with mass 1.2.0 kg. The cylinder pivots on a frictionless axle through its
A 2.00-kg textbook rests on a frictionless, horizontal surface. A cord attached to the book passes over a pulley whose diameter is 0.150 m, to a hanging hook with mass 3.00 kg. The system is released
A 12.0-kg box resting on a horizontal frictionless surface is attached to 5.00-kg weight by a thin, light wire that passes over a frictionless pulley (Fig. 10.44). The pulley has the shape of a
A thin, uniform, 15.0-kg post, 1.75 m long, is held vertically using a cable and is attached to a 5.00-kg mass and a pivot at its bottom end (Fig. 10.45). The string attached to the S.OO-kg mass
A thin, horizontal rod with length I and mass M pivots about a vertical axis at one end A force with constant magnitude F is applied to the other end, causing the rod to rotate in a horizontal plane.
A 2.20.kg hoop 1.20 m in diameter is rolling to the right without slipping on a horizontal floor at a steady 3.00 rad/s. (a) How fast is its center moving? (b) What is the total kinetic energy of
A string is wrapped several times around the rim of a small hoop with radius 8.00 cm and mass 0.180 kg. The free end of the string is held in place and the hoop is released from rest (Fig. 10.46).
What fraction of the total kinetic energy is rotational for the following objects rolling without slipping on a horizontal surface? (a) A uniform solid cylinder; (b) A uniform sphere; (c) A
A hollow, spherical shell with mass 2.00 kg rolls without slipping down a 38.0 slope. (a) Find the acceleration, the friction force, and the minimum coefficient of friction needed 10 prevent
A solid ball is released from rest and slides down a hillside that slopes downward at 65.0" from the horizontal (a) What minimum value must the coefficient of static friction between the hill and
A uniform marble rolls down a symmetric bowl, starting from rest at the top of the left side. The top of each side is a distance h above the bottom of the bowl. The left half of the bowl is rough
A 392-N wheel comes off a moving truck and rolls without slipping along a highway. At the bottom of a hill it is rotating at 25.0 rad/s. The radius of the wheel is 0.600 m, and its moment of inertia
A Ball Rolling Uphill, A bowling ball rolls without slipping up a ramp that slopes upward at an angle p to the horizontal (see Example 10.7 in Section 10.3). Treat the ball as a uniform, solid
A playground merry-go-round has radius 2.40 m and moment of inertia 2100 kg m2 about a vertical axle through its center, and it turns with negligible friction. (a) A child applies an 18.o.N force
The engine delivers 175 hp to an aircraft propeller at 2400 rev/min. (a) How much torque does the aircraft engine provide? (b) How much work docs the engines do in one revolution of the propeller?
A 1.50.kg grinding wheel is in the form of a solid cylinder of radius 0.100 m. (a) What constant torque will bring it from rest to an angular speed of 1200 rev/n in 2.5 s? (b) Through what angle
An electric motor consumes 9.00 kJ of electrical energy in 1.00 min. If one-third of this energy goes into heat and other forms of internal energy of the motor, with the rest going to the molar
The carbide tips of the cutting teeth of a circular saw are 8.6 cm from the axis of rotation. (a) The no-load speed of the saw, when it is not cutting anything, is 4800 rev/min. Why is its no-load
An airplane propeller is 2.08 m in length (from tip to tip) and has a mass of 117 kg. When the airplane’s engine is first started, it applies a constant torque of 1950 N m to the propeller, which
(a) Compute the torque developed by an industrial motor whose output is 150 kW at an angular speed of 4000 rev/min. (b) A drum with negligible mass, 0.400 m in diameter is attached to the molar
A woman with mass 50 kg is standing on the rim of a large disk that is rotating at O.50rev/s about an axis through its center. The disk bas mass no kg and radius 4.0 m. calculate the magnitude of the
A 2.00-kg rock has horizontal velocity of magnitude 12.0 m/s when it is at point Pin Fig. 10.47.(a) At this instant, what are the magnitude and direction of its angular momentum relative to point
(a) Calculate the magnitude of the angular momentum of the earth in a circular omit around the sun. Is it reasonable to model it as a particle? (b) Calculate the magnitude of the angular momentum
Find the magnitude of the angular momentum of the second hand on a clock about an axis through the center of the clock face. The clock band bas a length of 15.0 cm and a mass of 6.00 g take the
A bellow, t bin-walled sphere of mass 12.0 kg and diameter 48.0 cm is rotating about an axle through its center. The angle (in radians) through which it turns as a function of time (in seconds) is
Under some circumstances, a star can collapse into an extremely dense object made mostly of neutrons and called a neutron star. The density of a neutron star is roughly 1014 times as great as that of
A small block on a frictionless, horizontal surface has a mass of 0.0250 kg. It is attached to a mass less cord passing through a bole in the surface (Fig. 10.48). The block is originally revolving
The Spinning Figure Skater the outstretched hands and arms of a figure skater preparing for a spin can be considered a slender rod pivoting about an axis through its center (Fig. 10.49). When the
A diver comes off a board with arms straight up and legs straight down, giving her a moment of inertia about her rotation axis of 18 kg nt. She then tucks into a small ball, decreasing this moment of
A large wooden turntable in the shape of a flat uniform disk bas a radius of 2.00 m and a total mass of 120 kg, the turntable is initially rotating at 3.00 rad/s about a vertical axis through its
A solid wood door 1.00 m wide and 2.00 m high is hinged along one side and bas a total mass of 40.0 kg. Initially open and at rest, the door is struck at its center by a handful of sticky mud with
A small 10.0.g bug stands at one end of a thin uniform bar that is initially at rest on a smooth horizontal table. The other end of the bar pivots about a nail driven into the table and can rotate
Asteroid Collision Suppose that an asteroid traveling straight toward the center of the earth were to collide with our planet at the equator and bury itself just below the surface. What would have to
A thin, uniform metal bar, 2.00 m long and weighing 90.0 N, is hanging vertically from the ceiling by a frictionless pivot. Suddenly it is struck 1.50 m below the ceiling by a small 3.00-kg ball,
Draw a top view of the gyroscope shown in Fig. 10.32. (a) Draw labeled arrows on your sketch for w L, and t Draw d produced by T. Draw T + dL Determine the sense of the precession by examining the
The rotor (flywheel) of a toy gyroscope has mass 0.140 kg. Its moment of inertia about its axis is 1.20 X 10-4 kg m2.The mass of the frame is 0.0250 kg. The gyroscope is supported on a single pivot
A Gyroscope on the Moon A certain gyroscope processes at a rate of 0.50 rad/s when used on earth. If it were taken to a lunar base, where the acceleration due or gravity is 0.165g, what would be its
A gyroscope is processing about a vertical axis. Describe what happens to the precession angular speed if the following changes in the variables are made, with all other variables remaining the same:
The earth processes once every 26,000 years and spins on its axis once a day. Estimate the magnitude of the torque that causes the precession of the earth. You may need some data from Appendix F.
A 50.0-kg grindstone is a solid disk 0.520 m in diameter. You press an ax down on the rim with a normal force of 160 N (Fig. 10.43). The coefficient of kinetic friction between the blade and the
An experimental bicycle wheel is placed on a test stand so that it is free to turn on its axle. If a constant net torque of 5.00 Nm is applied to the tire for 2.00 s, the angular speed of the tire
Speedometer your car's speedometer converts the angular speed of the wheels to the linear speed of the car, assuming standard-size tires and no slipping on the pavement. (a) If your car's standard
A uniform hollow disk has two pieces of thin light wire wrapped around its outer rim and is supported from the cei1ing (Fig. 10.51). Suddenly one of the wires breaks and the remaining wire does not
A thin, uniform 3.80-kg bar, 80.0 cm long, has very small 2.50-kg balls glued on at either end (Fig. 10.52). It is supported horizontally by a thin, horizontal, frictionless axle passing through its
While exploring a castle, Exena the Exterminator is spotted by a dragon that chases her down a hallway. Exena runs into a room and attempts to swing the heavy door shut before the dragon gets he &
A thin rod of length l lies on the + x-axis with its left end at the origin. A string pulls on the rod with a force F directed toward a point P a distance h above the rod. Where along the rod should
Balancing Act Attached to one end of a long, then, uniform rod of length L and mass M is a small blob of clay of the same mass M. (a) Locate the position of the center of mass of the system of rod
You connect a light string to a point on the edge of a uniform vertical disk with radius R and mass M. The disk is free to rotate without friction about a stationary horizontal axis through its
The mechanism shown in Fig. 10.53 is used to raise a crate of supplies from a ship's hold. The crate has total mass 50 kg. A rope is wrapped I' around a wooden cylinder that turns on a metal axle.
A large 16.0-kg roll of paper with radius R = IS.O cm rests against the wall and is held in place by a bracket attached to a rod through the center of the 311 roll (Fig. 10.54). The rod turns without
A block with mass m = 5.00 kg slides down a surface inclined 36.90 to the horizontal (Fig. 10.55). The coefficient of kinetic friction is 0.25. A string attached to the block is wrapped around a
Two metal disks, one with radius R, = 2.50 cm and mass M, = O.SO kg and the other with radius R2 = 5.00 cm and mass M2 = 1.60 kg, are welded toge1her and mounted on a frictionless axis through their
A lawn roller in the form of a thin-walled, hollow cylinder with mass M is pulled horizontally with a constant horizontal force F applied by a handle attached to the axle. If it rolls without
Two weights are connected by a very light flexible cord that passes over a 50.O-N fric1ionless pulley of radius 0.300 m. The pulley is a solid uniform disk and is supported by a hook connected to the
A solid disk is rolling without slipping on a level surface at a constant speed of 2.50 m/s. (a) If the disk rolls up a 30.0" ramp, how far along the ramp will it move before it stops? (b) Explain
The Yo-yo A yo-yo is made from two uniform disks, each with mass m and radius R, connected by a light axle of radius b. A light, thin string is wound several times around the axle and then held
A thin-walled, hollow spherical shell of mass m and radius r starts from rest and rolls without slipping down the track shown in Fig. 10.57. Points A and B are on a circular part of the track having
Figure 10.58 shows three identical yo-yos initially at rest on a horizontal surface. For each yo-yo the string is pulled in the direction shown. In each case, there is sufficient friction for the
As shown in Fig. 10.46, a string is wrapped several times around the rim of a small hoop with radius 0.0800 m and mass 0.180 kg. The free end of the string is pulled upward in just the right way so
Starting from rest, a constant force F = 100 N is applied to the free end of a 50-m cable wrapped around the outer rim of a uniform solid cylinder, similar to the situation shown in Fig. 10.9(a). The
A uniform marble rolls without slipping down the path shown in Fig. 10.59, starting from rest. (a) Find the minimum height h required for the marble not to fall into the pit. (b) The moment of
Rolling Stones a solid, uniform, spherical boulder starts from rest and rolls down a 50.O-m-bigh hill, as shown in Fig. 10.60. The top half of the hill is rough enough to cause the boulder to roll
A solid, uniform ball rolls without slipping up a hill, as shown in Fig. 10.61. At the top of the hill, it is moving horizontally, and then it goes over the vertical cliff.(a) How far from the foot
A 42.0-cm-diameter wheel, consisting of a rim and six spokes, is constructed from a thin, rigid plastic material having a linear mass density of 25.0 g/cm. This wheel is released from rest at the top
A high-wheel antique bicycle has a large front wheel with the foot-powered crank mounted on its axle and a small rear wheel turning independently of the front wheel; there is no chain connecting the
In a lab experiment you let a uniform ball roll down a curved track. The ball starts from rest and rolls without slipping. While on the track, the ball descends a vertical distance h. The lower end
In a spring gun, a spring of force constant 400 N/m is compressed 0.15 m. When fired, 80.0% of the elastic potential energy stored in the spring is eventually converted into the kinetic energy of a
If a wheel rolls along a horizontal surface at constant speed, the coordinates of a certain point on the rim of the wheel are x(t) = R[(2wt/T) - sin(2wt/T)] and y(t) = R[l- cos(2wt/T)], where R and T
A child rolls a 0.600-kg basketball up a long ramp. The basketball can be considered a thin-walled, hollow sphere. When the child releases the basketball at the bottom of the ramp, it has a speed of
A uniform, solid cylinder with mass M and radius 2R rests on a horizontal tabletop. A string is attached by a yoke to a frictionless axle through the center of the cylinder so that the cylinder can
A uniform drawbridge 8.00 m long is attached to the roadway by a frictionless hinge at one end, and it can be raised by a cable attached to the other end. The bridge is at rest, suspended at 60.0°
A 5.00-kg ball is dropped from a height of 12.0 m above one end of a uniform bar that pivots at its center. The bar has mass 8.00 kg and is 4.00 m in length. At the oilier end of the bar sits another
A uniform, 0.0300-kg rod of length 0.400 m rotates in a horizontal plane about a fixed axis through its center and perpendicular to the rod. Two small rings, each with mass 0.0200 kg, are mounted so
A uniform rod of length L rests on a frictionless horizontal surface. The rod pivots about a fixed frictionless axis at one end. The rod is initially at rest. A bullet traveling parallel to the
The solid wood door of a gymnasium is 1.00 m wide and 2.00 m high, has total mass 35.0 kg, and is hinged along one side. The door is open and at rest when a stray basketball hits the center of the
A target in a shooting gallery consists of a vertical square wooden board, 0.250 m on a side and with mass 0.750 kg that pivots on a horizontal axis along its top edge. The board is struck face-on at
Neutron Star Glitches Occasionally, a rotating neutron star (see Exercise 10.39) undergoes a sudden and unexpected speedup called a glitch. One explanation is that a glitch occurs when the crust of
A 2.40-kg, 50.0-cm-Iong uniform bar has a small 1.l0-kg mass glued to its left end and a small 2.20-kg mass glued to the other end. You want to balance this system horizontally on a fulcrum placed
The center of gravity of an irregular object is shown in Fig. H.20. You need to move the center of gravity 2.20 cm to the left by gluing on a tiny l.50-kg mass, which will then be considered as part
A box of negligible mass rests at the left end of a 2.00-m, 25.0-kg plank (Fig. 11.21). The width of the box is 75.0 cm, and sand is to be distributed uniformly throughout it. The center of gravity
A uniform 300-N trapdoor in a floor is hinged at one side. Find the net upward force needed to begin to open it and the total force exerted on the door by the hinges (a) If the upward force is
Raising a Ladder a ladder carried by a fire truck is 20.0 m long. The ladder weighs 2800 N and its center of gravity is at its center. The ladder is pivoted at one end (A) about a pin(Hg. 11.22); you
Two people are carrying a uniform wooden board that is 3.00 m long and weighs 160 N. If one person applies an upward force equal to 60 N at one end, at what point does the other person lift? Begin
Two people carry a heavy electric motor by placing it on a light board 2.00 m long. One person lifts at one end with a force of 400 N, and the other lifts the opposite end with a force of 600 N.(a)
A 60.0-cm, uniform, 50.0-N shelf is supported horizontally by two vertical wires attached to the sloping ceiling (Fig. 11.23). A very small 25.0-N tool is placed on the shelf midway between the
A 350-N, uniform, 1.50-m bar is suspended horizontally by two vertical cables at each end. Cable A can support a maximum tension of 500.0 N without breaking, and cable B can support up to 400.0 N.
A uniform ladder 5.0 m long rests against a frictionless, vertical wall with its lower end 3.0 m from the wall. The ladder weighs 160 N. The coefficient of static friction between the foot of the

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