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engineering
engineering mechanics statics

Questions and Answers of Engineering Mechanics Statics

The 0.2-kg ball is blown through the smooth vertical circular tube whose shape is defined by r = (0.6 sin θ) m, where is in radians. If θ = (πt²) rad,where t is in seconds, determine the
Determine the constant angular velocity θ̇ of the vertical shaft of the amusement ride if ϕ = 45°. Neglect the mass of the cables and the size of the passengers. 8 m 1.5 m
A small box of mass m is given a speed of = √1/4gr at the top of the smooth half cylinder. Determine the angle θ at which the box leaves the surface. A Ө Ө
The two blocks A and B have weights WA = 60 lb and WB = 10 lb. If the coefficient of kinetic friction between the incline and block A is μk = 0.2, determine the speed of A after it moves 3 ft down
The 2-Mg car is traveling along the curved road described by r = (50e2θ) m, where θ is in radians.If a camera is located at A and it rotates with an angularvelocity of θ̇ = 0.05 rad/s and an
The crash cushion for a highway barrier consists of a nest of barrels filled with an impact-absorbing material.The barrier stopping force is measured versus the vehicle penetration into the barrier.
The sack of mass m has a velocity of v0 when it is at a height h above the unstretched spring. Determine the maximum compression of the spring if it has stiffness k. WWW k
The steel ingot has a mass of 1800 kg. It travels along the conveyor at a speed v = 0.5 m/s when it collides with the “nested” spring assembly. Determine the maximum deflection in each spring
When the 12-lb block A is released from rest it lifts the two 15-lb weights B and C. Determine the maximum distance A will fall before its motion is momentarily stopped. Neglect the weight of the
If the cord is subjected to a constant force of F = 300 N and the 15-kg smooth collar starts from rest at A, determine the velocity of the collar when it reaches point B. Neglect the size of the
The 25-lb block has an initial speed of v0 = 10 ft/s when it is midway between springs A and B. After striking spring B, it rebounds and slides across the horizontal plane toward spring A, and
The force F, acting in a constant direction on the 20-kg block, has a magnitude which varies with positions of the block. Determine the speed of the block after it slides 3 m. When s = 0 the block is
At a given instant the 10-lb block A is moving downward with a speed of 6 ft s. Determine its speed 2 s later. Block B has a weight of 4 lb, and the coefficient of kinetic friction between it and the
The 5-lb cylinder is falling from A with a speed vA = 10 ft/s onto the platform. Determine the maximum displacement of the platform, caused by the collision. The spring has an unstretched length of
The catapulting mechanism is used to propel the 10-kg slider A to the right along the smooth track.The propelling action is obtained by drawing the pulley attached to rod BC rapidly to the left by
The “flying car” is a ride at an amusement park which consists of a car having wheels that roll along a track mounted inside a rotating drum. By design the car cannot fall off the track, however
The 2-kg block is subjected to a force having a constant direction and a magnitude F = (300/(1+ s)) N, where s is in meters. When s = 4 m, the block is moving to the left with a speed of 8 m/s.
The 30-lb box A is released from rest and slides down along a smooth ramp and onto the surface of a cart. If the cart is fixed from moving, determine the distance s from the end of the cart to where
The 2-lb block slides down the smooth parabolic surface, such that when it is at A it has a speed of 10 ft/s. Determine the magnitudes of the block’s velocity and acceleration when it reaches point
The 8-kg cylinder A and 3-kg cylinder B are released from rest. Determine the speed of A after it has moved 2 m starting from rest. Neglect the mass of the cord and pulleys. A Fo B
Marbles having a mass of 5 g are dropped from rest at A through the smooth glass tube and accumulate in the can at C. Determine the placement R of the can from the end of the tube and the speed at
Cylinder A has a mass of 3 kg and cylinder B has a mass of 8 kg. Determine the speed of A after it has moved 2 m starting from rest. Neglect the mass of the cord and pulleys. A о B
The 2-lb box slides on the smooth circular ramp. If the box has a velocity of 30 ft/s at A, determine the velocity of the box and normal force acting on the ramp when the box is located at B and C.
When the 150-lb skier is at point A he has a speed of 5 ft/s. Determine his speed when he reaches point B on the smooth slope. For this distance the slope follows the cosine curve shown. Also, what
Roller coasters are designed so that riders will not experience a normal force that is more than 3.5 times their weight against the seat of the car. Determine the smallest radius of curvature ρ of
The 150-lb skater passes point A with a speed of 6ft/s. Determine his speed when he reaches point B and the normal force exerted on him by the track at this point. Neglect friction. B 25 ft y² =
If the 75-kg crate starts from rest at A, and its speed is 6m/s when it passes point B, determine the constant force F exerted on the cable. Neglect friction and the size of the pulley. A -6 m- B -2
If the force exerted by the motor M on the cable is 250 N, determine the speed of the 100-kg crate when it is hoisted to s = 3 m.The crate is at rest when s = 0. M S
The 10-lb block is pressed against the spring so as to compress it 2 ft when it is at A. If the plane is smooth, determine the distance d, measured from the wall, to where the block strikes the
If the 75-kg crate starts from rest at A, determine its speed when it reaches point B.The cable is subjected to a constant force of F = 300 N. Neglect friction and the size of the pulley. A 6 m- B -2
The jeep has a weight of 2500 lb and an engine which transmits a power of 100 hp to all the wheels. Assuming the wheels do not slip on the ground, determine the angle of the largest incline the jeep
An automobile having a mass of 2 Mg travels up a 7° slope at a constant speed of v = 100 km/h If mechanical friction and wind resistance are neglected, determine the power developed by the engine if
Determine the power input for a motor necessary to lift 300 lb at a constant rate of 5 ft/s The efficiency of the motor is ε = 0.65.
Using the biomechanical power curve shown, determine the maximum speed attained by the rider and his bicycle, which have a total mass of 92 kg, as the rider ascends the 20° slope starting from rest.
The man having a weight of 150 lb is able to run up a 15-ft-high flight of stairs in 4 s. Determine the power generated. How long would a 100-W light bulb have to burn to expend the same amount of
A rocket having a total mass of 8 Mg is fired vertically from rest. If the engines provide a constant thrust of T = 300 kN, determine the power output of the engines as a function of time. Neglect
The 1000-lb elevator is hoisted by the pulley system and motor M. If the motor exerts a constant force of 500 lb on the cable, determine the power that must be supplied to the motor at the instant
The sports car has a mass of 2.3 Mg and accelerates at 6 m/s², starting from rest. If the drag resistance on the car due to the wind is FD = (10v) N, where is the velocity in m/s, determine the
The elevator E and its freight have a total mass of 400 kg. Hoisting is provided by the motor M and the 60-kg block C. If the motor has an efficiency of ε = 0.6, determine the power that must be
The motor is used to lift the loaded 500-kg elevator with a constant velocity vE = 8 m/s. If the motor draws 60 kW of electrical power, determine the motor’s efficiency. Neglect the mass of the
The Milkin Aircraft Co. manufactures a turbojet engine that is placed in a plane having a weight of 13000 lb. If the engine develops a constant thrust of 5200 lb, determine the power output of the
A truck has a weight of 25 000 lb and an engine which transmits a power of 350 hp to all the wheels.Assuming that the wheels do not slip on the ground, determine the angle θ of the largest incline
The sports car has a mass of 2.3 Mg, and while it is traveling at 28 m/s the driver causes it to accelerate at 5 m/s2. If the drag resistance on the car due to the wind is FD = (0.3 v2)N, where v is
The 500-kg elevator starts from rest and moves upward with a constant acceleration ac = 2 m/s2. Determine the power output of the motor M when t = 3 s. Neglect the mass of the pulleys and cable. M
To dramatize the loss of energy in an automobile when it stops, consider a car having a weight of 5000 lb that is traveling at 35 mi/h. If the car is brought to a stop, determine how long a 100-W
An escalator is moving forward and upward with a speed of 2 ft/s. If the steps are 8 in. high and 15 in. in length, determine the required horsepower of a motor needed to lift an average load of 180
The material hoist and the load have a total mass of 800 kg and the counterweight C has a mass of 150 kg. At a given instant, the hoist has an upward velocity of 2 m/s and an acceleration of 1.5
The material hoist and the load have a total mass of 800 kg and the counterweight C has a mass of 150 kg. If the upward speed of the hoist increases uniformly from 0.5 m/s to 1.5 m/s in 1.5 s,
The 50-lb block rests on the rough surface for which the coeffi cient of kinetic friction is μk = 0.2. A force F = (40 + s2) lb, where s is in ft, acts on the block in the direction shown. If the
The material hoist and the load have a total mass of 800 kg and the counterweight C has a mass of 150 kg. At a given instant, the hoist has an upward velocity of 2 m/s and an acceleration of 1.5
The 10-lb collar starts from rest at A and is lifted with a constant speed of 2 ft/s along the smooth rod. Determine the power developed by the force F at the instant shown. 4 ft 0 -3 ft- A
The motor M is used to hoist the 500-kg elevator upward with a constant velocity vE = 8 m/s. If the motor draws 60 kW of electrical power, determine the motor’s efficiency. Neglect the mass of the
Sand is being discharged from the silo at A to the conveyor and transported to the storage deck at the rate of 360 000 lb/h. An electric motor is attached to the conveyor to maintain the speed of the
The 10-lb collar starts from rest at A and is lifted by applying a constant vertical force of F = 25 lb to the cord. If the rod is smooth, determine the power developed by the force at the instant θ
The 50-lb crate is given a speed of 10 ft/s in t = 4 s starting from rest. If the acceleration is constant, determine the power that must be supplied to the motor when t = 2 s. The motor has an
The 30-lb block A is placed on top of two nested springs B and C and then pushed down to the position shown. If it is then released, determine the maximum height h to which it will rise. KB = 200
The 5-kg collar has a velocity of 5 m/s to the right when it is at A. It then travels down along the smooth guide. Determine the speed of the collar when it reaches point B, which is located just
The girl has a mass of 40 kg and center of mass at G. If she is swinging to a maximum height defined by θ = 60°, determine the force developed along each of the four supporting posts such as AB at
The roller coaster car has a mass of 700 kg, including its passenger. If it starts from the top of the hill A with a speed vA = 3 m/s, determine the minimum height h of the hill crest so that the car
The 5-kg collar has a velocity of 5 m/s to the right when it is at A. It then travels along the smooth guide. Determine its speed when it reaches point B, which is located just before the end of the
The bob of the pendulum has a mass of 0.2 kg and is released from rest when it is in the horizontal position shown. Determine its speed and the tension in the cord at the instant the bob passes
Determine the smallest amount the spring at B must be compressed against the 0.5-lb block so that when it is released from B it slides along the smooth surface and reaches point A. y k = 5
The car C and its contents have a weight of 600 lb, whereas block B has a weight of 200 lb. If the car is released from rest, determine its speed when it travels 30 ft down the 20 incline. To measure
The roller coaster car having a mass m is released from rest at point A. If the track is to be designed so that the car does not leave it at B, determine the required height h. Also, find the speed
The roller coaster car has a mass of 700 kg, including its passenger. If it is released from rest at the top of the hill A, determine the minimum height h of the hill crest so that the car travels
The spring has a stiffness k = 200 N/m and an unstretched length of 0.5 m. If it is attached to the 3-kg smooth collar and the collar is released from rest at A, determine the speed of the collar
If the spring is compressed 3 in. against the 0.5-lb block and it is released from rest, determine the normal force of the smooth surface on the block when it reaches point x = 0.5 ft. k = 5
The spring has a stiffness k = 50 N/m and an unstretched length of 0.3 m. If it is attached to the 2-kg smooth collar and the collar is released from rest at A (θ = 0°), determine the speed of the
A 2-lb block rests on the smooth semicylindrical surface k at A. An elastic cord having a stiffness of k = 2 lb/ft is attached to the block at B and to the base of the semicylinder at C. If the block
When s = 0, the spring on the firing mechanism is unstretched. If the arm is pulled back such that s = 100 mm and released, determine the speed of the 0.3-kg ball and the normal reaction of the
When s = 0, the spring on the firing mechanism is unstretched. If the arm is pulled back such that s = 100 mm and released, determine the maximum angle θ the 0.3-kg ball will travel without leaving
A rocket of mass m is fired vertically from the surface of the earth, i.e., at r = r1. Assuming that no mass is lost as it travels upward, determine the work it must do against gravity to reach a
If the mass of the earth is Me, show that the gravitationalpotential energy of a body of mass m located a distance rfrom the center of the earth is Vg = -GMem/r. Recall thatthe gravitational force
The block has a mass of 20 kg and is released from rest when s = 0.5 m. If the mass of the bumpers A and B can be neglected, determine the maximum deformation of each spring due to the collision. s =
A 60-kg satellite travels in free flight along an elliptical orbit such that at A, where rA= 20 Mm, it has a speed vA = 40 Mm/h. What is the speed of the satellite when it reaches point B, where TB =
The spring is unstretched when s = 1m and the 15-kg block is released from rest at this position. Determine the speed of the block when s = 3m. The spring remains horizontal during the motion, and
The 20-lb smooth collar is attached to the spring that has an unstretched length of 4 ft. If it is released from rest at position A, determine its speed when it reaches point B. X 6 ft 3 ft A k = 50
The 10-kg block A is released from rest and slides down the smooth plane. Determine the compression x of the spring when the block momentarily stops. k = 5 kN/m 000000 30° 10 m
The 0.75-kg bob of a pendulum is fired from rest at position A by a spring which has a stiffness of k = 6 kN/m and is compressed 125 mm. Determine the speed of the bob and the tension in the cord
The roller coaster car has a speed of 15 ft/s when it is at the crest of a vertical parabolic track. Determine the car’s velocity and the normal force it exerts on the track when it reaches point
The spring has a stiffness k = 3 lb/ft and an unstretched length of 2 ft. If it is attached to the 5-lb smooth collar and the collar is released from rest at A, determine the speed of the collar just
When the 5-kg box reaches point A it has a speed vA = 10 m/s. Determine the normal force the box exerts on the surface when it reaches point B. Neglect friction and the size of the box. 9 m B - 9 m y
The 20-lb collar is constrained to move on the smooth rod. It is attached to the three springs which are unstretched when s = 0. If the collar is displaced s = 0.5 and released from rest, determine
A tank car is stopped by two spring bumpers A and B, having a stiffness of KA = 15(10³) lb/ft and kB = 20(10³) lb/ft, respectively. Bumper A is attached to the car, whereas bumper B is attached to
The cylinder has a mass of 20 kg and is released from rest when h = 0. Determine its speed when h = 3 m. Each spring has a stiffness k = 40 N/m and an unstretched length of 2 m. 2 m k www 2 m- k T h
If the 20-kg cylinder is released from rest at h = 0, determine the required stiffness k of each spring so that its motion is arrested or stops when h = 0.5 m. Each spring has an unstretched length
The cart and package have a mass of 20 kg and 5 kg, respectively. If the cart has a smooth surface and it is initially at rest, while the velocity of the package is as shown, determine the final
The truck travels in a circular path having a radius of 50 m at a speed of v = 4 m/s. For a short distance from s = 0, its speed is increased by v = (0.05s) m/s², where s is in meters. Determine its
The position of a particle along a straight line is given by s = (t³ - 9t² +15t) ft, where t is in seconds. Determine its maximum acceleration and maximum velocity during the time interval 0 ≤ t
Car B turns such that its speed is increased by (at)B = (0.5et) m/s², where t is in seconds. If the car startsfrom rest when θ = 0°, determine the magnitudes of itsvelocity and acceleration when t
Determine the time needed for the load at B toattain a speed of 8 m/s, starting from rest, if the cable isdrawn into the motor with an acceleration of 0.2 m/s². B B
Due to an external force, the particle travels along a straight track such that its position is described by the s-t graph. Construct the v-t graph for the same time interval. Take v=0, a=0 when t=0.
Starting from rest, a particle moving in a straight line has an acceleration of a = (2t - 6) m/s2, where t is in seconds. What is the particle’s velocity when t = 6 s, and what is its position when
If a particle has an initial velocity of v0 = 12 ft/s to the right, at s0 = 0, determine its position when t = 10 s, if a = 2 ft/s2 to the left.
A van travels along a straight road with a velocity described by the graph. Construct the s-t and a-t graphs during the same period. Take s = 0 when t = 0. v (ft/s) 80 主 v=-4t+ 80 20 ·t(s)
A particle travels along a straight line with a velocity v = (12 - 3t2) m/s, where t is in seconds. When t = 1 s, the particle is located 10 m to the left of the origin. Determine the acceleration
A particle travels along a straight line with a constant acceleration. When s = 4 ft, v = 3 ft/s and when s = 10 ft, v = 8 ft/s. Determine the velocity as a function of position.
The velocity of a particle traveling in a straight line is given by v = (6t - 3t2) m/s, where t is in seconds. If s = 0 when t = 0, determine the particle’s deceleration and position when t = 3 s.
A particle moving along a straight line is subjected to a deceleration a = (-2v³) m/s², where v is in m/s. If it has a velocity v = 8 m/s and a position s = 10m when t = 0, determine its velocity
A particle moves along a straight line such that its position is defined by s = (2t³ + 3t² - 12t - 10) m. Determine the velocity, average velocity, and the average speed of the particle when t = 3

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