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physics
mechanics
Vector Mechanics For Engineers Statics And Dynamics 8th Edition Ferdinand Beer, E. Russell Johnston, Jr., Elliot Eisenberg, William Clausen, David Mazurek, Phillip Cornwell - Solutions
The ball is ejected from the tube with a horizontal velocity of v1 = 8 ft/s as shown. If the coefficient of restitution between the ball and the ground is e = 0.8, determine(a) The velocity of the ball just after it rebounds from the ground and(b) The maximum height to which the ball rises after
The cue ball A is given an initial velocity (VA)1 = 5 m/s. If it makes a direct collision with ball B (e = 0.8), determine the velocity of B and the angle θ just after it rebounds from the cushion at C (e = 0.6). Each ball has a mass of 0.4 kg. neglect he size of each ball.
The 20-lb box slides on the surface for which μk = 0.3. The box has a velocity v = 15 ft/s when it is 2 ft from the plate. If it strikes the smooth plate, which has a weight of 10 lb and is held in position by an unstretched spring of stiffness k = 400 lb/ft, determine the maximum compression
The sphere of mass m falls and strikes the triangular block with a vertical velocity v. It the block rests on a smooth surface and has a mass 3m, determine its velocity just after the collision. The coefficient of restitution is e.
Block A, having a mass m, is released from rest, falls a distance h and strikes the plate B having a mass 2m. If the coefficient of restitution between A and B is e, determine the velocity of the plate just after collision. The spring has a stiffness k.
Before cranberry can make it to your dinner plate, it must pass a bouncing test which rates it quality. If cranberries having an e > 0.8a are to be accepted, determined the dimensions d and h for the barrier so that when a cranberry falls from rest at A it strikes the plate at Band bounces over
If disk A is sliding along the tangent to dist B and strikes B with a velocity v, determine the velocity of B after the collision and compute the loss of kinetic energy during the collision. Neglect friction. Disk B is originally at rest. The coefficient of restitution is e, and each disk has the
Two smooth coins A and B, each having the same mass, slide on a smooth surface with the motion shown, determine the speed of each coin after collision if they move off along the dashed paths. Hint: sine the line of impact has not been defined, apply the conservation of momentum along the x and y
Two coins A and b have the initial velocities shown just before they collide at point O. If they have weights of WA = 13.2 (10-3) lb WN = 6.60 (10-3) lb and the surface upon which they slide is smooth, determine their speeds just after impact. The coefficient of restitution is e = 0.65.
Two smooth disks A and B each have a mass of 0.5 kg. If both disks are moving with the velocities shown when they collide, determine their final velocities just after collision. The coefficient of restitution is e = 0.75.
Two smooth disks A and B each have a mass of 0.5 kg. If both disks are movie with the velocities shown when they collide, determine the coefficient of restitution between the disks if after collision B travels along a line, 30o counterclockwise from the y axis.
Two smooth disks A and B have the intial velocities shown just before they collide at O. If they have masses mA = 8 kg and mg = 6 kg, determine their speeds just after impact. The coefficient of restitution is e = 0.5.
The €œstone€ A used in the sport of curling slides over the ice track and strikes another €œstone€ B as shown. If each €œstone€ is smooth and has weight of 47 lb, and the coefficient of restitution between the
Ball A strikes ball B with an initial velocity of (VA) 1, as shown, If both balls have the same mass and the collision is perfectly elastic, determine the angle θ after collision. Ball B is originally at rest. Neglect the size of each ball.
Determine the angular momentum of the 2-lb particle A about point O, Use a Cartesian vector solution.
Determine the angular momentum HO of the particle about point O.
Determine the angular momentum HO of each of the particle about point O
Determine the angular momentum Hp of each of the particles about point P
Determine the angular momentum HO of the particle about point O.
Determine the angular momentum HP of the particle about point P
Determine the total angular momentum HO for the system of three particles about point O. All the particles are moving in the x-y plane.
Determine the angular momentum HO of each of the two particles about point O. use a scalar solution.
Determine the angular momentum, HP of each of the two particles about point P. use a scalar solution.
The ball B has a mass of 10 kg and is attached to the end of a rod whose mass may be neglected. If the rod is subjected to a torque M = (3t2 + 5t + 2) N m, where t is in seconds, determine the speed of the ball when t = 2s. The ball has a speed v = 2 m/s when t = 0.
The 3-lb ball located at A is released from rest and travels down the curved path. If the ball exerts a normal force of 5 lb on the path when it reaches point B, determine the angular momentum of the ball about the center of curvature, are point B must be determined.
The small cylinder C has as mass of 10 kg and is attached to the end of a rod whose mass may be neglected. If the frame is subjected to a couple M = (8t2 + 5) N, m where t is in seconds, and the cylinder is subjected to a force of 60 N, which is always direct as shown, determine the speed of the
The four 5-lb spheres are rigidly attached to the crossbar frame having a negligible weight. If a couple moment M = (0.5t + 0.8) lb-ft, where t is in seconds, is applied as shown, determine the speed of each of the spheres in 4 seconds starting from rest. Neglect the size of the spheres.
An earth satellite of mass 700 kg is launched into a free-flight trajectory about the earth with an initial speed of vA = 10 km/s when the distance from the center of the earth is tA = 15 Mm. if the launch angle at this position is ǿ A= 70o, determine the speed vH of the satellite and its
The ball B has a weight of 5 lb and is originally rotating in a circle. As shown, the cord AB has a length of 3 ft and passes through the hole A, which is 2 ft above the plane of motion. If 1.5 ft of cord is pulled through the hole, determine the speed of the ball when it moves in a circular path
A 4-lb ball B is traveling around in a circle of radius r1 = 3 ft with a speed (vB) 1 = 6 ft/s. If the attached cord is pulled down through the hole with a constant speed vr = 2ft/s, determine the ball€™s speed at the instant r2 = 2 ft. How much work has to be done to pull down the cord?
A 4-lb ball B is traveling around in a circle of radius r1 = 3 ft with a speed (vB)1 = 6 ft/s. If the attached cord is pulled down through the hole with a constant speed vr = 2ft/s, determine how much time is required for the ball to reach a speed 12 ft/s, How far r2 is the ball from the hole when
An amusement park ride consists of a car which is attached to the cable OA. The car rotates in a horizontal circular path and is brought to a speed v1 = 4 ft/ when r = 12 ft. The cable is then pulled in at the constant rate of 0.5 ft/s, Determine the speed of the car in 3 s.
A child having a mass of 50 kg holds her legs up as shown as she swings downward from rest at 01 = 30o. Her center of mass is located at point G1. When she is at the bottom position θ = 0o, she suddenly lets her legs come down, shifting her center of mass to position G2. Determine her speed
The 800-lb roller-coaster car starts from rest on the track having the shape of a cylindrical helix. If the helix descends 8ft for every one revolution, determine the speed of the car in t = 4s. Also, how far has the car descended in this time? Neglect friction and the size of the car.
The 150-lb fireman is holding a hose which has a nozzle diameter of 1 in and hose diameter of 2 in. If the velocity of the water at discharge is 60 ft/s, determine the resultant normal and frictional force acting on the man€™s feet at the ground. Neglect the weight of the hose and the
A small block having a mass 0.1 kg is given a horizontal velocity of v1 = 0.4 m/s when r1 = 500 mm. It slides along the smooth conical surface. Determine the distance h it must descent for it to reach a speed of v2 = 2 m/s. Also, what is the angle of descent θ, that is, the angle measured
A jet of water having a cross-sectional area of 4 in2 strikes the fixed blade with a speed of 25 ft/s. Determine the horizontal and vertical components of force which the blade exerts on the water. Yv = 62.4 lb/ft3.
Water is flowing from the 150-mm-diameter fire hydrant with a velocity vB = 15 m/s. Determine the horizontal and vertical components of force and the moment developed at the base joint A, if the static (gauge) pressure at A is 50 kPa. The diameter of the fire hydrant at A is 200 mm Pv = 1 Mg/m3.
The blade divides the jet of water having a diameter of 3 in. If one-fourth of the water flows downward while the other three-fourths flows upwards, and the total flow is Q = 0.5 ft3/s, determine the horizontal and vertical components of force exerted on the blade by the jet Yw = 62.4 lb/ft3
The fan draws air through a vent with a speed of 12 ft/s. If the corss-sectional area of the vent is 2 ft2, determine the horizontal thrust on the blade. The specific weight of the air is The specific weight of the air is ya = 0.076 lb/ft3.
The buckets on the Pelton wheel are subjected to a 2-in-diameter just of water, which has a velocity of 150 ft/s. If each bucket is traveling at 95 ft/s when the water strikes it, determine the power developed by the wheel yw= 62.4 lb/ft3
The static pressure of water at C is 40 lb/in2. If water flows out of the pipe at A and B with velocities vA = 12 ft/s and vB = 25 ft/s, determine the horizontal and vertical components of force exerted on the elbow at C necessary to hold the pipe assembly in equilibrium. Neglect the weight of
The 200-kg boat is powered by the fan which develops a slipstream having a diameter of 0.75 m. If the fan ejects air with a speed of 14 m/s, measured relative to the boat, determine the initial acceleration of the boat if it is initially at rest. Assume that air has a constant density of pa = 1.22
A power lawn mower hovers very close over the ground. This is done by drawing air in at a speed of m/s through and intake unit A, which has a cross-sectional area of AA = 0.25m2, and then discharging it at the ground, B, where the cross-sectional area is AB = 0.35 m2. If air at A is subjected only
The elbow for a 5-in-diameter buried pipe is subjected to a static pressure of 10 lb/in2. The speed of the water passing through it is v = 8 ft/s. Assuming the pipe connection at A and B do not offer any vertical force resistance on the elbow, determine the resultant vertical force F that the soil
The car is used to scoop up water that is lying in a trough at the tracks. Determine the force needed to pull the car forward at constant velocity v for each of the three cases. The scoop has a cross-sectional area A and the density of water is pw.
A plow located on the from of a locomotive scoops up snow at the rate of 10 ft 3/s and stores it in the train. If the locomotive is traveling at a constant speed of 12 ft/s, determine the resistance to motion caused by the shoveling. The specific weight of snow is ys = 6lb/ft3.
The boat has a mass of 180 kg and is traveling forward on a river with a constant velocity of 70 km/h, measured relative to the river. The river is flowing in the opposite direction at 5 km/h. if a tube is placed in the water, as shown and it collects 40kf of water in the boat in 80s; determine the
The second stage of the two-stage rocket weighs, 2000 lb (empty) and is launched from the first stage with a velocity of 3000 mi/h. the fuel in the second stage weighs 1000 lb. If it is consumed at the rate of 50 lb/s and ejected with a relative velocity of 8000 ft/s, determine the acceleration of
The missile weighs 40 000 lb. The constant thrust provided by the turbojet engine is T = 15 000 lb. Additional thrust is provided by two rocket boosters B. The propellant in each booster is burned at a constant rate of 150 lb/s, with a relative exhaust velocity of 3000 ft/s. If the mass of the
The earthmover initially carries 10m3 of sand having a density of 1520 kg/m3. The sand is unloaded horizontally through a 2.5 m2 dumping port P at a rate of 900 kg/s measured relative to the port. Determine the resultant tractive force F at its front wheels if the acceleration of the earthmover is
The 10-Mg helicopter carries a bucket containing 500 kg of water, which is used to fight fires, if is hovers over the land in a fixed position and then releases 50 kg/s of water at 10m/s, measured relative to the helicopter, determine the initial upward acceleration the helicopter experiences as
The rocket has a mass of 65 Mg including the fuel. Determine the constant rate at which the fuel must be burned so that its thrust gives the rocket a speed or 200 ft/s in 10 s starting from rest. The fuel is expelled from the rocket at a relative speed of 3000 ft/s. Neglect the effects of air
The rocket has an initial mass mo including the fuel. For practical reasons desired for the crew, it is required that it maintain a constant upward acceleration ao. If the fuel is expelled from the rocket at a relative speed vevr determine the rate at which the fuel should be consumed to maintain
The 12-Mg jet airplane has a constant speed of 950 km/h when it is flying along a horizontal straight line. Air enters the intake scoops S at the rate of 50 m3/s. If the engine burns fuel at the rate of 0.4 kg/s and the gas (air and fuel) is exhausted relative to the plane with a speed of 450 m/s,
The jet is traveling at a speed of 500 mi/h, 30o with the horizontal. If the fuel is being spent at 3 lb/s, and the engine takes in air at 400 lb/s, whereas the exhaust gas (air and fuel) has a relative speed of 32 800 ft/s, determine the acceleration of the plane at this instant. The drag
The truck has a mass of 50 Mg when empty. When it is unloading 5 m3 of sand at a constant rate of 0.8m3/s, the sand flows out the back at a speed of 7 m/s, measured relative to the truck, in the direction shown. If the truck is free to roll, determine its initial acceleration just as the load
The car has a mass mo and is used to tow the smooth chain having a total length I and mass per unit of length m. If the chain is originally piled up, determine the tractive force F that must be supplied by the rear wheels of the car, necessary to maintain a constant speed b while the chain is being
Determine the magnitude of force F as a function of time, which must be applied to the end of the cord at A to raise the hook H with a constant speed v = 0.4 m/s. Initially the chain is at rest on the ground. Neglect the mass of the cord and the hook. The chain has mass of 2 kg/m.
A sports car can accelerate 6m/s2 and decelerate at 8 m/s2. If the maximum speed it can attain is 60 m/s, determine the shortest time it takes top travel 900 m starting from rest and then stopping when s = 900 m.
A 2-kg particle rests on a smooth horizontal plane and is acted upon by forces Fx = 0 and Fy = 3N. If x = 0, y = 0, vx = 6 m/s, and vy = 2 m/s when t = o, determine the equation y = f (x) which describes the path.
Determine the velocity of each block 2 s after the blocks are released from rest. Neglect the mass of the pulleys and cord.
To test the manufactured properties of 2-lb steel balis, each ball is released from rest as shown and strikes a 45o inclined surface. If the corf
The 90-lb force is required to drag the 200-lb block 60 ft up the rought inclined plane at constant velocity. If the force is removed when the block reaches point B, and the block is then released from rest, determine the block's velocity when it slides back down the plane and reaches point A.
The spring having a stiffness of 5 kN/m is compressed 400 mm. The stored energy in the spring is used to drive a machine which requires 80 W of power. Determine how long the spring can supply energy at the required rate.
The motor at C pulls in the cable with an acceleration ac= (3t)2 m/s, where t is in seconds. The motor at D draws in its cable at aD = 5m/s2. If both motors start at the same instant from rest when d = 3m, determine (a) The time needed for d = O, and (b) The relative velocity of block A with
The baggage truck A has a mass of 800 kg and is used to pull each of the 300-kg cars. Determine the tension in the couplings at B and C if the tractive force F on the truck is F = 480 N. What is the speed of the truck when t = 2 s, starting from rest? The car wheels are free to roll. Neglect the
The baggage truck A has a mass of 800 kg and is used to pull each of the 300-kg cars. If the tractive force F on the truck is F = 480 N, determine the initial acceleration of the truck. What is the acceleration of the truck. What is the acceleration of the truck if the coupling at C suddenly fails?
Assuming that the force acting on a 2.5-g bullet, as it passes horizontally through the barrel of a rigle, caries with time in the manner shown, determine the maximum net force, FO, applied to the bullet when it is fired. The muzzle velocity is 800 m/s when t = 0.75 m/s. Neglect friction between
Determine the speed of block B if the end of the cable at C is pulled downward with a speed of 10 ft/s. What is the relative velocity of the block with respect to C?
Packages having a mass of 2.5 kg ride on the surface of the conveyor belt. If the belt starts from rest and with constant acceleration increases to a speed of 0.75 m/s in 2 s, determine the maximum angle of tilt, 0, so that none of the packages slip on the inclined surface AB of the belt. The
A projectile, initially at the origin, moves along a straight-line path through a fluid medium such that its velocity is v = 1800 (1 - e -03e) mm/s, where t is in seconds. Determine the displacement of the projectile during the first 3 s.
The speed of a train during the first minute of its motion has been recorded as follows:Plot the v-t graph, approximating the curve as straight line segments between the given points. Determine the total distance traveled.
A train car, having a mass of 25 Mg, travels up a 10o incline with a constant speed of 80 km/h. Determine the power required to overcome the force of gravity.
The slotted arm AB drives the pin C through the spiral groove described by the equation r = (1.50) ft, where 0 is in radians. If the arm starts from rest when 0 = 60o and is driven at an angular rate of μ0 = (4t) rad/s, where t is in seconds, determine the radial and transverse components of
The chain has a mass of 3 kg/m. If the coefficient of kinetic friction between the chain and the plane is μk = 0.2, determine the velocity at which the end A will pass point B when the chain is released from rest.
The 6-lb ball is fired from a tube by a spring having a stiffness k = 20 lb/in. Determine how far the spring must be compressed to fire the ball from the compressed position to a height of 8 ft, at which point if has a velocity of 6 ft/s.
Disk A weighs 2 lb and is sliding on a smooth horizontal plane with a velocity of 3 ft/s. Disk B weighs 11 lb and is initially at rest. If after the impact A has a velocity of B after impact. How much kinetic energy is lost in the collision?
A particle is moving along a circular path of 2-m radius such that its position as a function of time is given by θ = (5t2) rad, where t is in seconds. Determine the magnitude of the particle’s acceleration when θ = 30o. The particle starts from rest when θ = 0o
If the end of the cable at A is pulled down with a speed of 2 m/s, determine the speed at which block B rises.
A rifle has a mass of 2.5 kg. If it is loosely gripped and a 1.5-g bullet is fired from it with a horizontal muzzle velocity of 1400 m/s, determine the recoil velocity of the rifle just after firing.
The drinking fountain is designed such that the nozzle is located from the edge of the basin as shown. Determine the maximum and minimum speed at which water can be ejected from the nozzle so that is does not splash over the sides of the basin at B and C.
The 20-lb block B rests on the surface of a table for which the coefficient of kinetic friction is μk = 0.1. Determine the speed of the 10-lb block A after it has moved downward 2 ft from rest. Neglect the mass of the pulleys and cords.
The 5-lb ball, attached to the cord, is struck by the boy. Determine the smallest speed he must impart to the ball so that tit will swing around in a vertical circle, without causing the cord to become slack.
The winding drum D is drawing in the cable at an accelerated rate of 5 m/s2. Determine the cable tension if the suspended crate has a mass of 800 kg.
A crate has a weight of 1500 lb. If it is pulled along the ground at a constant speed for a distance of 20 ft, and the towing cable makes and angle of 15o with the horizontal, determine the tension in the cable and the work done by the towing force. The coefficient of kinetic friction between the
The collar of negligible size has a mass of 0.25 kg and is attached to a spring having an unstretched length of 100 mm. If the collar is released from rest at A and travels along the smooth guide, determine its speed just before it strikes B.
The particle P travels with a constant speed of 300 mm/s along the curve. Determine its acceleration when it is located at point (200 mm, 100 mm).
The block has a mass of 0.5 kg and moves within the smooth vertical slot. If the block starts from rest when the attached spring is in the unstretched position at A, determine the constant vertical force F which must be applied to the cord so that the block attains a speed vB = 2.5 m/s when it
The rocket sled has a mass of 4 Mg and travels from rest along the smooth horizontal track such that it maintains a constant power output of 450 kW. Neglect the loss of fuel mass and air resistance, and determine how far it must travel to reach a speed of v = 60 m/s.
The spool, which has a mass of 4 kg, slides along the rotating rod. At the instant shown, the angular rate of rotation of the rod is θ = 6 rad/s and this rotation is increasing at θ = 2 rad/s2. At this same instant, the spool has a velocity of 3 m/s and an acceleration of 1 m/s2, both
A skier from rest at A (30 ft, O) and descends the smooth slope, which may be approximated by a parabola. If she has a weight of 120 lb, determine the normal force she exerts on the ground at the instant she arrives at point B.
The small 2-lb collar starting from rest at A slides down along the smooth rod. During the motion, the collar is acted upon by force F = {10i + 6yj + 2zk} lb, where x, y, z are in feet. Determine the collar€™s speed when it strikes the wall at B.
A ball having a mass of 200 g is released from rest at a height of 400 mm above a very large fixed metal surface. If the ball rebounds to a height of 325 mm above the surface, determine the coefficient of restitution between the ball and the surface.
Packages having a mass of 6 kg slide down a smooth chute and land horizontally with a speed of 3 m/s on the surface of a conveyor belt. If the coefficient of kinetic friction between the belt and a package is μk = 0.2, determine the time needed to bring the package to rest on the belt if the
The blocks A and B weigh 10 and 30 lb, respectively. They are connected together by a light cord and ride in the frictionless grooves. Determine the speed of each block after block A moves 6 ft up alone the plane. The blocks are released from rest.
The motor M pulls in its attached rope with an acceleration aP = 6 m/s2. Determine the towing force exerted by M on the rope in order to move the 50.Kg crate up the inclined plane. The coefficient of kinetic friction between the crate and the plane is μk = 0.3. Neglect the mass of the pulleys
If a particle has an initial velocity vO = 12 ft/s to the right, and a constant acceleration of 2 ft/s2 to the left, determine the particle’s displacement in 10 s. Originally sO = 0.
A 3-lb block, initially at rest at point A, slides along the smooth parabolic surface. Determine the normal force acting on the block when it reaches B. Neglect the size of the block.
At a given instant the 10-lb block A is moving downward with a speed of 6 ft/s. Determine its seed 2s later. Block B has a weight of 4 lb, and the coefficient of kinetic friction between it and the horizontal plane is μk = 0.2. Neglect the mass of the pulleys and cord.
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