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engineering
engineering mechanics statics

Questions and Answers of Engineering Mechanics Statics

A toboggan having a mass of 10 kg starts from rest at A and carries a girl and boy having a mass of 40 kg and 45 kg, respectively.When the toboggan reaches the bottom of the slope at B, the boy is
The crate has a mass m and rests on the barge which has a mass M and is initially at rest. The coefficient of kinetic friction between the crate and barge is μ. The rope is pulled (or jerked) such
The block of mass m travels at v₁ in the direction θ₁ shown at the top of the smooth slope. Determine its speed v₂ and its direction θ2 when it reaches the bottom. h X N 20₁ 202
Using the data in Prob. 15–49, determine the distance the crate slides on the barge before coming to rest.Prob. 15–49The crate has a mass m and rests on the barge which has a mass M and is
A railroad car weighs 30,000 lb and is traveling horizontally at 30 ft/s. At the same time another car weighing 10,000 lb is traveling 5 ft/s in the opposite direction. If the cars meet and couple
The 30-Mg freight car A and 15-Mg freight car B are moving towards each other with the velocities shown. Determine the maximum compression of the spring mounted on car A. Neglect rolling resistance.
A 40-lb box slides from rest down the smooth ramp onto the surface of a 20-lb cart. Determine the speed of the box at the instant it stops sliding on the cart. If someone ties the cart to the ramp at
Two cars A and B, each having a mass of 1.6 Mg, collide on the icy pavement of an intersection. The direction of motion of each car after collision is measured from snow tracks as shown. If the
Block A has a mass of 5 kg and is placed on the smooth triangular block B having a mass of 30 kg. If the system is released from rest, determine the distance B moves from point O when A reaches the
The 5-Mg truck and 2-Mg car are traveling with the freerolling velocities shown just before they collide. After the collision, the car moves with a velocity of 15km/h to the right relative to the
A box A, having a mass of 20 kg, is released from rest at the position shown and slides freely down the smooth inclined ramp. When it reaches the bottom of the ramp, it slides horizontally onto the
The two toy cars A and B have a weight of 0.4 lb and 0.6 lb, respectively. A spring having a stiffness of 30 lb/ft is attached to one of them and the cars are pressed together such that the spring is
The 15-kg block A has a velocity v = 10 m/s when it is s = 4 m from the 10-kg block B. If the unstretched spring has a stiffness k = 1000 N/m, determine the maximum compression of the spring due to
The four smooth balls each have the same mass m. If A and B are rolling forward with a velocity v and strike C, explain why after collision C and D each move off with a velocity v. Why doesn’t D
The four balls each have the same mass m. If A and B are rolling forward with velocity v and strike C, determine the velocity of each ball after the first three collisions. Take e = 0.5 between each
The 1-lb ball A is thrown so that when it strikes the 10-lb block B it is traveling horizontally at 20 ft/s. Determine the average normal force exerted between A and B if the impact occurs in 0.02 s.
The 1-lb ball A is thrown so that when it strikes the 10-lb block B it is traveling horizontally at 20 ft/s. If the coefficient of restitution between A and B is e = 0.6 and the coefficient of
The 1-lb ball A is thrown so that when it strikes the 10-lb block B it is traveling horizontally at 20 ft/ s. If the coefficient of restitution between A and B is e = 0.6, and the coefficent of
The scaffold S is raised by moving the roller at A toward the pin at B. If A is approaching B with a speed of 1.5 ft/s, determine the speed at which the platform rises as a function of θ. The 4-ft
If the hydraulic cylinder AB is extending at a constant rate of 1ft/s, determine the dumpster’s angular velocity at the instant θ = 30°. A B 12 ft. Off -15 ft-
Disk A has a mass of 250 g and is sliding on a smooth horizontal surface with an initial velocity (vA)1 = 2 m/s. It makes a direct collision with disk B, which has a mass of 175 g and is originally
Wheel A rolls without slipping over the surface of the fixed cylinder B. Determine the angular velocity of A if its center C has a speed of 2 m/s. How many revolutions will A make about its center
End A of the bar moves to the left with a constant velocity vA. Determine the angular velocity ω and angular acceleration α of the bar as a function of its position x. VA A ω,α X
Determine the angular velocity of rod AB when θ = 30°. The shaft and the center of the roller C move forward at a constant rate v = 5 m/s. v = 5 m/s B 100 mm C of -X
At the instant shown, θ = 60° and rod AB is subjected to a deceleration of 16 m/s2 when the velocity is 10 m/s. Determine the angular velocity and angular acceleration of link CD at this instant. v
The bar remains in contact with the floor and with point A. If point B moves to the right with a constant velocity vB, determine the angular velocity and angular acceleration of the bar as a function
When the bar is at the angle θ, the rod is rotating clockwise with constant angular velocity ω. Determine the velocity of the weight A at this instant. The cord is 20 ft long. 10 ft SA D A w, a 10
The crate is transported on a platform which rests on rollers, each having a radius r. If the rollers do not slip, determine their angular velocity if the platform moves forward with a velocity v. @
When the slider block C is in the position shown, the link AB has a clockwise angular velocity of 2 rad/s. Determine the velocity of block C at this instant. 15 in. A 45° B WAB = 2 rad/s 45° 15
The slider block C moves at 8 m/s down the inclined groove. Determine the angular velocities of links AB and BC, at the instant shown. A -45⁰ 2 m B C 2 m Vc = 8 m/s
The center of the wheel is moving to the right with a speed of 2 ft/s. If no slipping occurs at the ground, A, determine the velocity of points B and C. 1.5 ft C A 30° 2 ft/s B
The 5-lb box B is dropped from rest 5 ft from the top of the 10-lb plate P, which is supported by the spring having a stiffness of k = 30 lb/ft. If e = 0.6 between the box and plate, determine the
The 0.5-kg ball is fired from the tube at A with a velocity of v = 6 m/s. If the coefficient of restitution between the ball and the surface is e = 0.8, determine the height h after it bounces off
Using a slingshot, the boy fires the 0.2-lb marble at the concrete wall, striking it at B. If the coefficient of restitution between the marble and the wall is e = 0.5, determine the speed of the
A 300-g ball is kicked with a velocity of vA = 25 m/s at point A as shown. If the coefficient of restitution between the ball and the field is e = 0.4, determine the magnitude and direction θ of the
The two disks A and B have a mass of 3 kg and 5 kg, respectively. If they collide with the initial velocities shown, determine their velocities just after impact. The coefficient of restitution is e
Two identical balls A and B of mass m are suspended from cords of length L/2 and L, respectively. Ball A is released from rest when ϕ = 90° and swings down to ϕ = 0°, where it strikes B.
A ball of negligible size and mass m is given a velocity of v0 on the center of the cart which has a mass M and is originally at rest. If the coefficient of restitution between the ball and
The two hockey pucks A and B each have a mass of 250 g. If they collide at O and are deflected along the colored paths, determine their speeds just after impact. Assume that the icy surface over
It is observed that hailstones strike the surface of a frozen lake at an angle of 60° with the horizontal and rebound at an angle of 45°. Determine the coefficient of restitution. 不 0.5
The girl throws the 0.5-kg ball toward the wall with an initial velocity vA = 10 m/s. Determine (a) The velocity at which it strikes the wall at B, (b) The velocity at which it rebounds
The 0.2-lb ball bearing travels over the edge A with a velocity of vA = 3 ft/s. Determine the speed at which it rebounds from the smooth inclined plane at B.Take e = 0.8. V₁ = 3 ft/s 45° B
Two disks A and B each have a weight of 2 lb and the initial velocities shown just before they collide. If the coefficient of restitution is e = 0.5, determine their speeds just after impact. (UB)1 =
The two spheres A and B each have a mass of 400 g. The spheres are fixed to the horizontal rods and their initial velocity is 2 m/s. If a couple moment of M = 0.6 N · m is applied to the frame,
If the hailstones in Prob. 15–87 rise to a height of 0.5 m after rebounding, determine their velocity just before impact. Prob. 15–87It is observed that hailstones strike the surface of a
The two billiard balls A and B are originally in contact with one another when a third ball C strikes each of them at the same time as shown. If ball C remains at rest after the collision, determine
The 2-kg ball rotates around a 0.5-m-diameter circular path with a constant speed. If the cord length is shortened from 1 = 1 m to ∫' = 0.5 m, by pulling the cord through the tube, determine the
At the instant r = 1.5 m, the 5-kg disk is given a speed of v = 5 m/s, perpendicular to the elastic cord. Determine the speed of the disk and the rate of shortening of the elastic cord at the instant
If the rod of negligible mass is subjected to a couple moment of M = (30t2) N·m and the engine of the carsupplies a traction force of F = (15t) N to the wheels,where t is in seconds, determine the
The chute is used to divert the flow of water, Q = 0.6 m³/s. If the water has a cross-sectional area of 0.05 m², determine the force components at the pin D and roller C necessary for equilibrium.
The fountain shoots water in the direction shown. If the water is discharged at 30° from the horizontal, and the cross-sectional area of the water stream is approximately 2 in2, determine the force
The projectile having a mass of 3 kg is fired from a cannon with a muzzle velocity of v0 = 500 m/s. Determine the projectile’s angular momentum about point O at the instant it is at the maximum
Water is discharged from a nozzle with a velocity of 12 m/s and strikes the blade mounted on the 20-kg cart. Determine the tension developed in the cord, needed to hold the cart stationary, and the
The fan blows air at 6000 ft3/min. If the fan has a weight of 30 lb and a center of gravity at G, determine the smallest diameter d of its base so that it will not tip over. The specific weight of
Water is discharged at 16 m/s against the fixed cone diffuser. If the opening diameter of the nozzle is 40 mm, determine the horizontal force exerted by the water on the diffuser. ρw = 1 Mg/m3.
The nozzle has a diameter of 40 mm. If it discharges water uniformly with a downward velocity of 20 m/s against the fixed blade, determine the vertical force exerted by the water on the blade. ρw =
Aggregates fall off the conveyor belt at 500 kg/s and into the barge. Determine the force the rope at A exerts on the barge to hold it in place. 5 m/s A 8'm
The tractor together with the empty tank has a total mass of 4 Mg. The tank is filled with 2 Mg of water. The water is discharged at a constant rate of 50 kg/s with a constant velocity of 5 m/s,
The toy sprinkler for children consists of a 0.2-kg cap and a hose that has a mass per length of 30 g/m. Determine the required rate of flow of water through the 5-mm-diameter tube so that the
Sand drops onto the 2-Mg empty rail car at 50 kg/s from a conveyor belt. If the car is initially coasting at 4 m/s, determine the speed of the car as a function of time. 4 m/s
The fireboat is equipped with two water cannons. The one at A has a nozzle diameter of 6 in, and can pump 3000 gal/min, and the one at B has a nozzle diameter of 3 in. and can pump 1000 gal/min.
The jet is traveling at a speed of 720 km/h. If the fuel is being spent at 0.8 kg/s, and the engine takes in air at 200 kg/s, whereas the exhaust gas (air and fuel) has a relative speed of 12,000
The 1.5-m-long smooth chain hangs over the edge of the table. If the chain is released from rest, determine its speed just after the last link clears the table. The chain has a mass per unit length
A rocket is in deep space, and on earth it has an empty weight of 500 lb and carries 300 lb of fuel. If the fuel is burned at the rate of 15 lb/s and ejected with a relative velocity of 4400 ft/s,
The hemispherical bowl of mass m is held in equilibrium by the vertical jet of water discharged through a nozzle of diameter d. If the discharge of the water through the nozzle is Q, determine the
The bin deposits gravel onto the conveyor belt at the rate of 1500 lb/min. If the speed of the belt is 5 ft/s, determine how much greater the tension in the top portion of the belt must be than that
When the gear rotates 20 revolutions, it achieves an angular velocity of ε = 30 rad/s, starting from rest.Determine its constant angular acceleration and the timerequired.
The hoisting gear A has an initial angular velocity of 60 rad/s and a constant deceleration of 1 rad/s². Determine the velocity and deceleration of the block which is being hoisted by the hub on
The angular velocity of the disk is defined by ω = (5t2 + 2) rad/s, where t is in seconds. Determine the magnitudes of the velocity and acceleration of point A on the disk when t = 0.5 s. A 0.8 m
Starting at (ωA)0 = 3 rad/s, when θ = 0, s = 0, pulley A is given an angular acceleration α = (0.6θ) rad/s², where θ is in radians. Determine the speed of block B when it has risen s = 0.5 m.
The flywheel rotates with an angular velocity of ω = (4 θ¹/2) rad/s, where θ is in radians. Determine the time it takes to achieve an angular velocity of ω = 150 rad/s. When t = 0, θ = 1 rad. W
The flywheel rotates with an angular velocity of w= (0.005θ²) rad/s, where is in radians. Determinethe angular acceleration when the wheel has rotated20 revolutions. 0
The disk is originally rotating at ω0 = 8 rad/s. If it is subjected to a constant angular acceleration of α = 20 rad/s2, determine the magnitudes of the velocity and the n and t components of
The bucket is hoisted by the rope that wraps around a drum wheel. If the angular displacement of the wheel is θ = (0.5t³ + 15t) rad, where t is in seconds, determine the velocity and acceleration
The disk is originally rotating at ω0 = 8 rad/s. If it is subjected to a constant angular acceleration of α = 6 rad/s2, determine the magnitudes of the velocity and the n and t components of
At the instant shown, the board has an accelerationof 0.5 m/s² to the right, while at the same instant pointson the outer rim of each drum have an acceleration witha magnitude of 3 m/s². If the
The angular acceleration of the disk is defined by α = 3t2 + 12 rad/s, where t is in seconds. If the disk is originally rotating at ω0 = 12 rad/s, determine the magnitude of the velocity and the n
The center of the pulley is being lifted vertically with an acceleration of 4 m/s² at the instant it has a velocity of 2 m/s. If the cable does not slip on the pulley's surface, determine the
The disk is driven by a motor such that the angular position of the disk is defined by θ = (20t + 4t2) rad where t is in seconds. Determine the number of revolutions, the angular velocity, and
If bar AB has an angular velocity ωAB = 6 rad/s, determine the velocity of the slider block C at the instant shown. WAB = 6 rad/s A B 200 mm 0 = 45° 500 mm 30°
For a short period of time, the motor turns gear A with a constant angular acceleration of αΑ = 4.5 rad/s², starting from rest. Determine the velocity of the cylinder and the distance it travels
If roller A moves to the right with a constant velocity of VΑ = 3 m/s, determine the angular velocity of the link and the velocity of roller B at the instant θ = 30°. B 1.5 m 0 = 30% VA = 3 m/s
At the instant shown, link AB has an angular velocity ωAB = 2 rad/s and an angular acceleration αAB = 6 rad/s². Determine the acceleration of the pin at C and the angular acceleration of link CB
The disk is moving to the left such that it has an angular acceleration α = 8 rad/s² and angular velocity ω = 3 rad/s at the instant shown. If it does not slip at A, determine the acceleration of
A wheel has an angular acceleration of α = (0.5 θ) rad/s², where θ is in radians. Determine the magnitude of the velocity and acceleration of a point P located on its rim after the wheel has
For a short time, gear A of the automobile starter rotates with an angular acceleration of αA = (450t2 + 60) rad/s2, where t is in seconds. Determine the angular velocity and angular displacement of
The wheel rolls without slipping with an angular velocity of ω = 10 rad/s. Determine the magnitude of the velocity of point B at the instant shown. B 0.6 m
A wheel has an initial angular velocity of 10 rev/s and a constant angular acceleration of 3 rad/s2. Determine the number of revolutions required for the wheel to have an angular velocity of 20
At the given instant member AB has the angular motions shown. Determine the velocity and acceleration of the slider block C at this instant. -5 in.- B 7 in. -3 rad/s 2 rad/s² A 5 in.
For a short time, gear Aof the automobile starter rotates with an angular acceleration of αA = (50ω1/2) rad/s2, where is in . Determine the angular velocity of gear B after gear A has rotated 50
Determine the angular velocity of the spool. The cable wraps around the inner core, and the spool does not slip on the platform P. 2 ft/s 2 ft B ift- 4 ft/s P
The 50-mm-radius pulley A of the clothes dryer rotates with an angular acceleration of αA = (27θ1/2A ) rad/s2, where θA is in radians. Determine its angular acceleration when t = 1 s, starting
If crank OA rotates with an angular velocity of ω = 12 rad/s, determine the velocity of piston B and the angular velocity of rod AB at the instant shown. 0.3 m 12 rad/s 0.6 m 30° B
If rod AB slides along the horizontal collar with a velocity of 60 ft/s, determine the angular velocity of link BC and the velocity of point C at the instant shown. 0.5 ft 30° 2.5 ft B 60 ft/s A
If the 50-mm-radius motor pulley A of the clothes dryer rotates with an angular acceleration of αA = (10 + 50t) rad/s2, where t is in seconds, determine its angular velocity when t = 3 s, starting
The disk is originally rotating at ω0 = 8 rad/s. If it is subjected to a constant angular acceleration αc = 6 rad/s², determine the magnitudes of the velocity and the n and t components of
The blade on the horizontal-axis windmill is turning with an angular velocity of ω0 = 2 rad/s. Determine the distance point P on the tip of the blade has traveled if the blade attains an angular
End A of the link has a velocity of vΑ = 3 m/s. Determine the velocity of the peg at B at this instant. The peg is constrained to move along the slot. B 2 m 45° 30° VA = 3 m/s A
The blade on the horizontal-axis windmill is turning with an angular velocity of ω0 = 2 rad/s. If it is given an angular acceleration of αc = 0.6 rad/s², determine the angular velocity and the
Determine the angular velocity of the rod and the velocity of point C at the instant shown. 4 m A VA = 6 m/s 2.5 m 2.5 m B

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