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physics
mechanics

Questions and Answers of Mechanics

A 200-kg load is hung on a wire having a length of 4.00 m, cross-sectional area 0.200 - 10'4 m2, and Young’s modulus 8.00 - 1010 N/m2. What is its increase in length?
Assume that Young’s modulus is 1.50 - 1010 N/m2 for bone and that the bone will fracture if stress greater than 1.50 - 108 N/m2 is imposed on it. (a) What is the maximum force that can be exerted
Evaluate Young’s modulus for the material whose stress-versus-strain curve is shown in Figure 12.15.
A steel wire of diameter 1 mm can support a tension of 0.2 kN. A cable to support a tension of 20 kN should have diameter of what order of magnitude?
A child slides across a floor in a pair of rubber-soled shoes. The friction force acting on each foot is 20.0 N. The footprint area of each shoe sole is 14.0 cm2, and the thickness of each sole is
A 30.0-kg hammer strikes a steel spike 2.30 cm in diameter while moving with speed 20.0 m/s. The hammer rebounds with speed 10.0 m/s after 0.110 s. What is the average strain in the spike during the
If the shear stress in steel exceeds 4.00 X 108 N/m2, the steel ruptures. Determine the shearing force necessary to (a) Shear a steel bolt 1.00 cm in diameter and (b) Punch a 1.00-cm-diameter
A 2.00-m-long cylindrical steel wire with a cross-sectional diameter of 4.00 mm is placed over a light frictionless pulley, with one end of the wire connected to a 5.00-kg object and the other end
When water freezes, it expands by about 9.00%. What pressure increase would occur inside your automobile engine block if the water in it froze? (The bulk modulus of ice is 2.00 - 109 N/m2.)
The deepest point in the ocean is in the Mariana Trench, about 11 km deep. The pressure at this depth is huge, about 1.13 - 108 N/m2. (a) Calculate the change in volume of 1.00 m3 of seawater
A walkway suspended across a hotel lobby is supported at numerous points along its edges by a vertical cable above each point and a vertical column underneath. The steel cable is 1.27 cm in diameter
A lightweight, rigid beam 10.0 m long is supported by a cable attached to a spring of force constant k = 8.25 kN/m as shown in Figure P12.38. When no load is hung on the beam (Fg = 0), the length L
A bridge of length 50.0 m and mass 8.00 X 104 kg is supported on a smooth pier at each end as in Figure P12.39. A truck of mass 3.00 X 104 kg is located 15.0 m from one end. What are the forces on
A lintel of prestressed reinforced concrete is 1.50 m long. The cross-sectional area of the concrete is 50.0 cm2. The concrete encloses one steel reinforcing rod with cross-sectional area 1.50 cm2.
A uniform pole is propped between the floor and the ceiling of a room. The height of the room is 7.80 ft, and the coefficient of static friction between the pole and the ceiling is 0.576. The
A solid sphere of radius R and mass M is placed in a trough as shown in Figure P12.42. The inner surfaces of the trough are frictionless. Determine the forces exerted by the trough on the sphere at
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 (Fig. P12.43), the beam is uniform, weighs 200 N, and is 6.00 m long; the
A farm gate (Fig. P12.44) is 3.00 m wide and 1.80 m high, with hinges attached to the top and bottom. The guy wire makes an angle of 30.0° with the top of the gate and is tightened by a
A uniform sign of weight Fg and width 2L hangs from a light, horizontal beam, hinged at the wall and supported by a cable (Fig. P12.45). Determine(a) The tension in the cable and(b) The components of
A 1 200-N uniform boom is supported by a cable as in Figure P12.46. The boom is pivoted at the bottom, and a 2 000-N object hangs from its top. Find the tension in the cable and the components of the
A crane of mass 3 000 kg supports a load of 10 000 kg as in Figure P12.47, the crane is pivoted with a frictionless pin at A and rests against a smooth support at B. Find the reaction forces at A and
A ladder of uniform density and mass m rests against a frictionless vertical wall, making an angle of 60.0° with the horizontal. The lower end rests on a flat surface where the coefficient of static
A 10 000-N shark is supported by a cable attached to a 4.00-m rod that can pivot at the base. Calculate the tension in the tie-rope between the rod and the wall if it is holding the system in the
When a person stands on tiptoe (a strenuous position), the position of the foot is as shown in Figure P12.50a. The gravitational force on the body Fg is supported by the force n exerted by the floor
A person bending forward to lift a load €œwith his back€ (Fig P12.51a) rather than €œwith his knees€ can be injured by large forces exerted on the muscles
A uniform rod of weight Fg and length L is supported at its ends by a frictionless trough as shown in Figure P12.52.(a) Show that the center of gravity of the rod must be vertically over point O when
A force acts on a rectangular cabinet weighing 400 N, as in Figure P12.53.(a) If the cabinet slides with constant speed when F = 200 N and h = 0.400 m, find the coefficient of kinetic friction and
Consider the rectangular cabinet of Problem 53, but with a force F applied horizontally at the upper edge. (a) What is the minimum force required to start to tip the cabinet? (b) What is the
A uniform beam of mass m is inclined at an angle θ to the horizontal. Its upper end produces a ninety degree bend in a very rough rope tied to a wall, and its lower end rests on a rough floor
Figure P12.56 shows a truss that supports a downward force of 1 000 N applied at the point B. The truss has negligible weight. The piers at A and C are smooth.(a) Apply the conditions of equilibrium
A stepladder of negligible weight is constructed as shown in Figure P12.57. A painter of mass 70.0 kg stands on the ladder 3.00 m from the bottom. Assuming the floor is frictionless, find(a) The
A flat dance floor of dimensions 20.0 m by 20.0 m has a mass of 1 000 kg. Three dance couples, each of mass 125 kg, start in the top left, top right, and bottom left corners. (a) Where is the
A shelf bracket is mounted on a vertical wall by a single screw, as shown in Figure P12.59. Neglecting the weight of the bracket, find the horizontal component of the force that the screw exerts on
Figure P12.60 shows a vertical force applied tangentially to a uniform cylinder of weight Fg. The coefficient of static friction between the cylinder and all surfaces is 0.500. In terms of Fg find
A wire of length L, Young’s modulus Y, and cross-sectional area A is stretched elastically by an amount ΔL. By Hooke’s law (Section 7.4), the restoring force is ─ k ΔL. (a) Show
Two racquetballs are placed in a glass jar, as shown in Figure P12.62. Their centers and the point A lie on a straight line. (a) Assume that the walls are frictionless, and determine P1, P2, and
In exercise physiology studies it is sometimes important to determine the location of a person€™s center of mass. This can be done with the arrangement shown in Figure P12.63. A light plank
A steel cable 3.00 cm2 in cross-sectional area has a mass of 2.40 kg per meter of length. If 500 m of the cable is hung over a vertical cliff, how much does the cable stretch under its own weight?
(a) Estimate the force with which a karate master strikes a board if the hand’s speed at time of impact is 10.0 m/s, decreasing to 1.00 m/s during a 0.002 00-s time-of-contact with the board. The
A bucket is made from thin sheet metal. The bottom and top of the bucket have radii of 25.0 cm and 35.0 cm, respectively. The bucket is 30.0 cm high and filled with water. Where is the center of
An aluminum wire is 0.850 m long and has a circular cross section of diameter 0.780 mm. Fixed at the top end, the wire supports a 1.20-kg object that swings in a horizontal circle. Determine the
A bridge truss extends 200 m across a river (Fig. P12.68). The structure is free to slide horizontally to permit thermal expansion. The structural components are connected by pin joints, and the
A bridge truss extends 100 m across a river (Fig. P12.69). The structure is free to slide horizontally to permit thermal expansion. The structural components are connected by pin joints, and the
A cue strikes a cue ball and delivers a horizontal impulse in such a way that the ball rolls without slipping as it starts to move. At what height above the ball’s center (in terms of the radius of
A trailer with loaded weight Fg is being pulled by a vehicle with a force P, as in Figure P12.71. The trailer is loaded such that its center of mass is located as shown. Neglect the force of rolling
A bicycle is traveling downhill at a high speed. Suddenly, the cyclist sees that a bridge ahead has collapsed, so she has to stop. What is the maximum magnitude of acceleration the bicycle can have
A car moves with speed v on a horizontal circular track of radius R. A head-on view of the car is shown in Figure P12.73. The height of the car€™s center of mass above the ground is h, and
The tennis ball has a horizontal speed of 15 m/s when it is stuck by the racket. If it then travels away at an angle of 25o from the horizontal and reaches a maximum altitude of 10m, measured from
The 40-kg slider block is moving to the right with a speed of 1.5 m/s when it is acted upon by the forces F1 and F2. it these loading vary in the manner shown on the graph, determine the speed of the
Determine the velocities of blocks A and B 2 s after they are released from rest. Neglect the mass of the pulleys and cables.
The 5-kg package is released from rest at A. It slides down the smooth plane onto the rough surface having a coefficient of kinetic friction of μk = 0.2 determine the total time of travel before
Block a weighs 10 lb and block b weighs 3 lb. If B is moving downward with a velocity (vb)1 = 3 ft/s at t = 0, determine the velocity of A when t = 1 s.c
Block a weighs 10 lb and block B weighs 3 lb. If B is moving downward with a velocity (μB) 1 = 3 ft/s at t = 0, determine the velocity of a when t = 1s. The coefficient of kinetic friction between
The winch delivers a horizontal towing force F to its cable at a which varies as shown in the graph. Determine the speed of the 70-kg bucket B when t = 18s. Originally the bucket is moving upward at
The winch delivers a horizontal towing force F to its cable at A which varies as shown in the graph. Determine the speed of the 80-kg bucket B when t = 24s. Originally the bucket is moving downward
The log has a mass of 500 kg and rests on the ground for which the coefficients of static and kinetic friction are μs = 0.5 and μk = 0.4 respectively. The winch delivers a horizontal towing
A railroad car having a mass of 15 Mg is coasting at 1.5 m/s on a horizontal track. At the same time another car having a mass of 12 Mg is coasting at 0.75 m/s in the opposite direction. It the cars
The car A has a weight of 4500 lb and is traveling to the right at 3 ft/s. Meanwhile a 3000-lb car B is traveling at 6 ft/s to the left. If the cars crash head-on and become entangled, determine
The two blocks A and B each have a mass of 5 kg and are suspended from parallel cords. A spring having a stiffness of K = 60 N/n, is attached to B and is compressed 0.3 m against A and B as shown.
The bus B has a weigh of 15 000 lb and is traveling to the right at 5 ft/s. Meanwhile a 3000-lb car A is traveling at 4 ft/s to the left. If the vehicles crash head-on and become entangled, determine
Two men A and B, each having a weight of 160 lb, stand on the 200-lb, cart. Each runs with a speed of 3 ft/s measured relative to the cart. Determine the final speed of the cart if(a) A runs and
A man wearing ice skates throws and 8-kg block with an initial velocity of 2 m/s, measured relative to himself, in the direction shown. If he is originally at rest and completes the throw in 1.5 s
The barge weighs 45 000 lb and supports two automobiles A and B which weigh 4000 lb and 3000 lb, respectively, if the automobiles start from rest and drive towards each other, accelerating at BA = 4
The barge B weighs 30 000 lb and supports and automobile weighing 3000 lb. if the barge is not tied to the pier P and someone drives the automobile to the other side of the barge for unloading
The block A has a mass of 2 kg and slides into an open ended box B with a velocity of 2 m/s. If the box has a mass of 3 kg and rests on top of a plate P that has a mass of 3 kg, determine the
The block A has a mass of 2 kg and slides into and open ended box B with a velocity of 2m/s. If the box has a mass of 3 kg and rests on top of a plate P that has a mass of 3 kg, determine the
The man M weighs 150 lb and jumps onto the boat B which has a weigh of 200 lb. if he has a horizontal component of velocity relative to the boat of 3 ft/s, just before he enters the boat, and the
The man M weighs 150 lb and jumps onto the boat B which is originally at rest. If he has a horizontal component of velocity of 3 ft/s just before he enters the boat, determine the weight of the boat
A boy A having a weight of 80 lb and girl B having a weight of 65 lb stand motionless at the ends of the toboggan, which has a weigh of 20 lb. if A walks to B and stops, and both walk back together
The 10-lb projectile is fired from ground level with an initial velocity of vA = 80 ft/s in the direction shown. When it reaches its highest point B it explodes into two 5-lb fragments. If one
Two boxes A and B, each having a weight of 160 lb, sit on the 500-lb conveyor which is free to roll on the ground. If the belt starts from rest and begins to run with a speed of 3 ft/s, determine the
The 10-kg block is held at rest on the smooth inclined plane by the stop block at A. if the 10-g bullet is traveling at 300 m/s when it becomes embedded in the 10-kg block, determine the distance the
A tugboat T having a mass of 19 Mg is tied to a barge B having a mass 75 Mg. If the rope is elastic such that it has a stiffness k = 600 kN/m, determine the maximum stretch in the rope during the
The 20-lb cart B is supported on rollers of negligible size, if a 10-lb suitcase A is thrown horizontally on it at 10ft/s, determine the length of time that A slides relative to B, and the final
The 20-lb cart B is supported on rollers of negligible size. If a 10-lb suitcase A is thrown horizontally on it at 10 ft/s, determine the time t and the distance B moves before A stops relative to B.
The free-rolling ramp has a mass of 40 kg. A 10-kg crate is released from rest at A and slides down 3.5 m to point B. if the surface of the ramp is smooth, determine the ramp€™s speed when
The block has a mass of 50 kg and rests on the surface of the cart having a mass of 75 kg. If the spring which is attached to the cart and not the block is compressed 0.2 m and the system is released
The block has a mass of 50 kg and rests on the surface of the cart having a mass of 75 kg. If the spring which is attached to the cart and not the block is compressed 0.2 m and the system is released
Blocks A and B have masses of 40 kg and 60 kg, respectively. They are placed on a smooth surface and the spring connected between them is stretched 2m. If they are released from rest, determine the
An ivory ball having a mass of 200 g is released from rest at a height of 400 mm above a very large fixed metal surface. It the ball rebounds to a height of 325 mm above the surface, determine the
Block A has a mass of 3 kg and is sliding on a rough horizontal surface with a velocity (vA)1 = 2 m/s when it makes a direct collision with block B, which has a mass of 2 kg and is originally at
Disk A has a mass of 2 kg and is sliding forward on the smooth surface with a velocity (vA) 1 = 5 m/s when it strikes the 4-kg disk B1 which is sliding towards A at (vN) 1 = 2m/s, with direct central
The three balls each weigh 0.5 lb and have a coefficient of restitution of e = 0.85. if ball A is released from rest and strikes ball B and then ball B strikes ball C, determine the velocity of each
If two disks A and B have the same mass and are subjected to direct central impact such that the collision is perfectly elastic (e = 1), prove that the kinetic energy before collision equals the
Each ball has a mass m and the coefficient of restitution between the balls is e. If they are moving towards one another with a velocity v, determine their speeds after collision. Also, determine
The man A has a weight of 175 lb and jumps from rest h = 8 ft onto a platform P that has a weight of 60 lb. The platform is mounted on a spring, which has a stiffness k = 200 lb/ft. Determine(a) The
The man A has a weight of 175 lb and jumps from rest h = 8 ft onto a platform P that has a weight of 60 lb. The platform is mounted on a spring, which has a stiffness k = 200 lb/ft. If the
The three balls each have the same mass m. if A has a speed v just before a direct collision with Bv determine the speed of C after collision. The coefficient of restitution between each ball is e.
If the girl throws the ball with a horizontal velocity of 8 ft/s, determine the distance d so that the ball bounces once on the smooth surface and then lands in the cup at C. take e = 0.8
The ball is dropped from rest and falls distance of 4 ft before striking the smooth plane A. If e = 0.8, determine the distance d to where it again strikes the plane at B.
The ball is dropped from rest and falls a distance of 4 ft before striking the smooth plane at A. If it rebounds and in t = 0.5 s again strikes the plane at B, determine the coefficient of
The 2-kg ball is thrown at the suspended 20-kg block with a velocity of 4 m/s. If the coefficient of restitution between the ball and the block is e = 0.8, determine the maximum height h to which the
The 2-kg ball is thrown at the suspended 2-0-kg block with a velocity of 4 m/s. if the time of impact between the ball and the block is 0.005s, determine the average normal force exerted on the block
A ball is thrown onto a rough floor at an angle θ. If it rebounds at an angle ǿ and the coefficient of restitution e. Neglect the size of the ball. Hint: Show that during impact, the
A ball is thrown onto a rough floor at an angle of θ = 45o. If it rebounds at the same angle ǿ = 45o, determine the coefficient of kinetic friction between the floor and the ball. The
Plates A and B each have a mass of 4 kg and are restricted to move along the smooth guides. If the coefficient of restitution between the plates is e = 0.7, determine(a) The speed of both plates just
The 8-lb ball is released from rest 10 ft from the surface of a plat P which weighs 6 lbs. Determine the maximum compression in the spring if the impact is perfectly elastic.
It was observed that a tennis ball when served horizontally 7.5 above the ground strikes the smooth ground at B 20 ft away. Determine the initial velocity vA of the ball and the velocity vS (and
It was observed that a tennis ball when served horizontally 7.5 above the ground strikes the smooth ground at B, and bounces upward at θ = 30o. Determine the initial velocity vA the final
The ping-pong ball has a mass of 2 g. If it is struck with the velocity shown, determine how high h it rises above the end of the smooth table after the rebound. Take e = 0.8

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