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engineering
engineering mechanics statics

Questions and Answers of Engineering Mechanics Statics

The smooth surface of the vertical cam is defined in part by the curve r = (0.2 cos θ + 0.3) m. If the forked rod is rotating with a constant angular velocity of θ̇ = 4 rad/s, determine the force
The spool, which has a mass of 2 kg, slides along the smooth horizontal spiral rod, r = (0.4θ) m, where θ is in radians. If its angular rate of rotation is constant and equals θ̇ = 6 rad/s,
Rod OA rotates counterclockwise at a constant angular rate θ̇ = 4 rad/s. The double collar B is pin connected together such that one collar slides over the rotating rod and the other collar
Solve Prob. 13–109 if motion is in the vertical plane.Prob. 13–109Rod OA rotates counterclockwise at a constant angular rate θ̇ = 4 rad/s. The double collar B is pin connected together
A 0.2-kg spool slides down along a smooth rod. If the rod has a constant angular rate of rotation θ̇ = 2 rad/s in the vertical plane, show that the equations of motion for the spool are r̈ -
The airplane executes the vertical loop defined by r² = [810(10³) cos 2θ] m². If the pilot maintains a constant speed v= 120m/s along the path, determine the normal force the seat exerts on him
The speed of a satellite launched into a circular orbit about the earth is given by Eq. 13–25. Determine the speed of a satellite launched parallel to the surface of the earth so that it travels in
The earth has an orbit with eccentricity 0.0167 around the sun. Knowing that the earth’s minimum distance from the sun is 146(106) km, find the speed at which the earth travels when it is at this
A communications satellite is in a circular orbit above the earth such that it always remains directly over a point on the earth’s surface. As a result, the period of the satellite must equal the
The satellite is in an elliptical orbit around the earth as shown. Determine its velocity at perigee P and apogee A, and the period of the satellite. P 2 Mm 8 Mm- A
The rocket is docked next to a satellite located 18 Mm above the earth’s surface. If the satellite is traveling in a circular orbit, determine the speed tangent to the earth’s surface which must
Prove Kepler’s third law of motion. Use Eqs. 13–19, 13–28, 13–29, and 13–31.Eqs. 13–19 1 r C cos 0 + GM₂ h² (13-19)
The rocket is traveling in free flight along the elliptical orbit. The planet has no atmosphere, and its mass is 0.60 times that of the earth. If the rocket has the orbit shown, determine the
The rocket is traveling in free flight along an elliptical trajectory A'A. The planet has a mass 0.60 times that of the earth. If the rocket has an apoapsis and periapsis as shown in the figure,
A satellite is to be placed into an elliptical orbit about the earth such that at the perigee of its orbit it has an altitude of 800 km, and at apogee its altitude is 2400 km. Determine its required
If the 50-kg crate is subjected to a force of P = 200 N, P determine its speed when it has traveled 15 m starting from rest. The coefficient of kinetic friction between the crate and the ground is
Determine the maximum speed that the jeep can travel over the crest of the hill and not lose contact with the road. p=250 ft
If the 50-kg crate starts from rest and attains a speed of P 6 m/s when it has traveled a distance of 15 m, determine the= force P acting on the crate.The coefficient of kinetic friction between the
A pilot weighs 150 lb and is traveling at a constant speed of 120 ft/s. Determine the normal force he exerts on the seat of the plane when he is upside down at A. The loop has a radius of curvature
As indicated by the derivation, the principle of work and energy is valid for observers in any inertial reference frame. Show that this is so, by considering the 10-kg block which rests on the smooth
When the driver applies the brakes of a light truck traveling 40 km/h, it skids 30 m before stopping. How far will the truck skid if it is traveling 80 km/h when the brakes are applied?
The 50-lb load is hoisted by the pulley system and motor M. If the motor exerts a constant force of 30 lb on the cable, determine the power that must be supplied to the motor if the load has been
The 100-kg crate is subjected to the forces shown. If it is originally at rest, determine the distance it slides in order to attain a speed of v = 8 m/s. The coefficient of kinetic friction between
Determine the required height h of the roller coaster so that when it is essentially at rest at the crest of the hill A it will reach a speed of 100 km/h when it comes to the bottom B. Also, what
The rocket is traveling around the earth in free flight along the elliptical orbit AC. Determine its change in speed when it reaches A so that it travels along the elliptical orbit AB. C 8 Mm B W 8
The rocket shown is originally in a circular orbit 6 Mm above the surface of the earth. It is required that it travel in another circular orbit having an altitude of 14 Mm. To do this, the rocket is
The rocket is in free-flight circular orbit around the earth. Determine the time needed for the rocket to travel from the inner orbit at A to the outer orbit at A′. 8 Mm 19 Mm Α'
The rocket is initially in free-flight circular orbit around the earth. Determine the speed of the rocket at A. What change in the speed at A is required so that it can move in an elliptical orbit to
The rocket is in free flight along an elliptical trajectory A'A. The planet has no atmosphere, and its mass is 0.60 times that of the earth. If the orbit has the apoapsis and periapsis shown,
If the rocket is to land on the surface of the planet, determine the required free-flight speed it must have at A' so that the landing occurs at B. How long does it take for the rocket to land, in
The rocket is in a free-light elliptical orbit about the earth such that the eccentricity of its orbit is e and its perigee is r0. Determine the minimum increment of speed it should have in order to
If the rocket is to land on the surface of the planet, determine the required free-flight speed it must have at A′ so that the landing occurs at B. How long does it take for the rocket to land,
The rocket is traveling around the earth in free flight along an elliptical orbit AC. If the rocket has the orbit shown, determine the rocket’s velocity when it is at point A. Co B 8 Mm- 8 Mm -10
The space shuttle is launched with a velocity of 17 500 mi/h parallel to the tangent of the earth’s surface at point P and then travels around the elliptical orbit. When it reaches point A, its
The rocket is traveling in a free flight along an elliptical trajectory AA. The planet has no atmosphere, and its mass is 0.60 times that of the earth. If the rocket has the orbit shown, determine
If motor M exerts a force of F = (10t²+ 100) N on the cable, where t is in seconds, determine the velocity of the 25-kg crate when t = 4 s. The coefficients of static and kinetic friction between
The motor winds in the cable with a constant acceleration, such that the 20-kg crate moves a distance s = 6 m in 3 s, starting from rest. Determine the tension developed in the cable. The coefficient
The car having a mass of 2 Mg is originally traveling at 2 m/s. Determine the distance it must be towed by a force F = 4 kN in order to attain a speed of 5 m/s. Neglect friction and the mass of the
For protection, the barrel barrier is placed in front of the bridge pier. If the relation between the force and deflection of the barrier is F = (90(103)x1/2) lb, where x is in ft, determine the
The block has a weight of 1.5 lb and slides along the smooth chute AB. It is released from rest at A, which has coordinates of A(5 ft, 0, 10 ft). Determine the speed at which it slides off at B,
The 2-Mg car is being towed by a winch. If the winch exerts a force of T = 100(s + 1) N on the cable, where s is the displacement of the car in meters, determine the speed of the car when s =
A spring of stiffness k = 500 N/m is mounted against the 10-kg block. If the block is subjected to the force of F = 500 N, determine its velocity at s = 0.5 m. When s = 0, the block is at rest and
The collar has a mass of 5 kg and is moving at 8 m/s when x = 0 and a force of F = 60 N is applied to it. The direction of this force varies such that θ = 10x, where x is in meters and θ is
The force F, acting in a constant direction on the 20-kg block, has a magnitude which varies with the position s of the block. Determine how far the block must slide before its velocity becomes 15
The sports car is traveling along a 30° banked road having a radius of curvature of ρ = 500 ft. If the coefficient of static friction between the tires and the road is μs = 0.2, determine the
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 the rest.
If the 10-kg ball has a velocity of 3 m/s when it is at the position A, along the vertical path, determine the tension in the cord and the increase in the speed of the ball at this position. 2m 0 =
The 2-Mg truck is traveling at 15 m s when the brakes on all its wheels are applied, causing it to skid for a distance of 10 m before coming to rest. Determine the constant horizontal force developed
The tractor is used to lift the 150-kg load B with the 24-m- long rope, boom, and pulley system. If the tractor travels to the right with an acceleration of 3 m/s² and has a velocity of 4 m/s at the
The tractor is used to lift the 150-kg load B with the 24-mlong rope, boom, and pulley system. If the tractor travels to the right at a constant speed of 4 m/s, determine the tension in the rope when
If a horizontal force P = 35 lb is applied to block A, determine the acceleration of block B. Neglect friction. Block A weighs 15 lb, and block B weighs 8 lb. Show that aA = aB tan 15°. B 15° A P
Cars A and B are traveling at the speeds shown. If B is accelerating at 1200 km/h² while A maintains a constant speed, determine the velocity and acceleration of A with respect to B. B 20 km/h 65
The 6-lb particle is subjected to the action of its weight and forces F₁ = {2i + 6j - 2tk} lb, F₂ = {ti - 4tj - 1k} lb, and F3 = {-2ti} lb, where t is in seconds. Determine the distance the ball
If the coefficient of kinetic friction between the 50-kg crate and the ground is μk = 0.3, determine the distance the crate travels and its velocity when t = 3 s. The crate starts from rest, and P =
The motor winds in the cable with a constant acceleration, such that the 20-kg crate moves a distance s = 6 m in 3 s, starting from rest. Determine the tension developed in the cable. The coefficient
A spring of stiffness k = 500 N/m is mounted against the 10-kg block. If the block is subjected to the force of F = 500 N, determine its velocity at s = 0.5 m. When s = 0, the block is at rest and
If the 50-kg crate starts from rest and achieves a velocity of v = 4 m/s when it travels a distance of 5 m to the right, determine the magnitude of force P acting on the crate. The coefficient of
If motor M exerts a force of F = (10t² + 100) N on the cable, where t is in seconds, determine the velocity of the 25-kg crate when t = 4 s. The coefficients of static and kinetic friction between
From a videotape, it was observed that a player kicked a football 126 ft during a measured time of 3.6 seconds. Determine the initial speed of the ball and the angle at which it was kicked. 0 -126 ft
The jet belt and man have a total weight of 210 lb. If the engines provide a constant thrust having x and y components of Fx = 35 lb and Fy = 300 lb, determine the total distance the man travels when
The block rests at a distance of 2 m from the center of the platform. If the coefficient of static friction between the block and the platform is , μs = 0.3, determine the maximum speed which the
If blocks A and B of mass 10 kg and 6 kg, respectively, are placed on the inclined plane and released, determine the force developed in the link. The coefficients of kinetic friction between the
The 10-lb block has a speed of 4 ft>s when the force of F = (8t2) lb is applied. Determine the velocity of the block when t = 2 s. The coefficient of kinetic friction at the surface is μk = 0.2.
If P = 400 N and the coefficient of kinetic friction between the 50-kg crate and the inclined plane is μk = 0.25, determine the velocity of the crate after it travels 6 m up the plane. The crate
Determine the maximum speed that the jeep can travel over the crest of the hill and not lose contact with the road. p=250 ft
If the 50-kg crate starts from rest and travels a distance of 6 m up the plane in 4 s, determine the magnitude of force acting on the crate. The coefficient of kinetic friction between the crate and
The sports car is traveling along a 30° banked road having a radius of curvature of ρ = 500 ft. If thecoefficient of static friction between the tires and the roadis μs = 0.2, determine the
In the event of an emergency, a nuclear reactor is shut down by dropping the control rod R, having a weight of 20 lb, into the reactor core C. If the rod is immersed in “heavy” water, which
Determine the time needed to pull the cord at B down 4 ft starting from rest when a force of 10 lb is applied to the cord. Block A weighs 20 lb. Neglect the mass of the pulleys and cords. B sil 10
A pilot weighs 150 lb and is traveling at a constant speed of 120 ft/s. Determine the normal force he exerts on the seat of the plane when he is upside down at A. The loop has a radius of curvature
The motorcycle has a mass of 0.5 Mg and a negligible size. It passes point A traveling at a speed of 15 m/s, which is increasing at a constant rate of 1.5 m/s². Determine the resultant frictional
The 10-lb block has a speed of 4 ft/s when the force of F = (8t2) lb is applied. Determine the velocity of the block when it moves s = 30 ft. The coefficient of kinetic friction at the surface is μk
Block A has a weight of 8 lb and block B has a weight of 6 lb. They rest on a surface for which the coefficient of kinetic friction is μk = 0.2. If the spring has a stiffness of k = 20 lb/ft, and it
The conveyor belt C is moving at 6 m/s. If the coefficient of static friction between the conveyor belt and the 10-kg box B is μs = 0.2, determine the shortest time the conveyor can stop so that the
Determine the constant angular velocity of the vertical θ̇ 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
Team A and team B consist of four members of total mass 320 kg and 330 kg, respectively. If the average coefficients of static and kinetic friction for team A are μs = 0.52 and μk = 0.5, and for
Block A has a mass of 60 kg and rests on block B, which has a mass of 30 kg. If the coefficients of static and kinetic friction are indicated in the figure, determine the largest horizontal force P
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 angular velocity of θ̇ = 0.05 rad/s and an
Solve Prob. 13-18 if the suitcase has an initial velocity down the ramp of vA = 10 ft/s and the coefficient of kinetic friction along AB is μk = 0.2.Prob. 13-18A 40-lb suitcase slides from rest 20
The motor lifts the 50-kg crate with an acceleration of 6 m/s2. Determine the components of force reaction and the couple moment at the fixed support A. A 4m B IXI 30° 6 m/s² X
The 400-kg mine car is hoisted up the incline using the cable and motor M. For a short time, the force in the cable is F = (3200t2) N, where t is in seconds. If the car has an initial velocity v₁ =
A 40-lb suitcase slides from rest 20 ft down the smooth ramp. Determine the point where it strikes the ground at C. How long does it take to go from A to C? AL 20 ft 30° 4 ft + B -R- C
Determine the acceleration of each block if A and B have a mass m and C has a mass 2 m. Neglect the mass of the cords and the pulleys. A m B m C 2 m
The 400-kg mine car is hoisted up the incline using the cable and motor M. For a short time, the force in the cable is F = (3200t2) N, where t is in seconds. If the car has an initial velocity v₁ =
The conveyor belt delivers each 12-kg crate to the ramp at A such that the crate’s speed is vA = 2.5 m>/s, directed down along the ramp. If the coefficient of kinetic friction between each crate
The 50-kg block A is released from rest. Determine the velocity of the 15-kg block B in 2 s. CO E D B A
The conveyor belt delivers each 12-kg crate to the ramp at A such that the crate’s speed is vA = 2.5 m/s, directed down along the ramp. If the coefficient of kinetic friction between each crate and
The force exerted by the motor M on the cabilses hown in the graph. Determine the velocity of the 200-lb crate A when t = 2.5 s. M 250 lb FO A₁ F (lb) 2.5 t (s)
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 if block B has a weight of 4 lb, and the coefficient of kinetic friction between it and
The 20-kg block A rests on the 60-kg plate B in the position shown. Neglecting the mass of the rope and pulley, and using the coefficients of kinetic friction indicated, determine the time needed for
At the instant shown the 100-lb block A is moving down the plane at 5 ft/s while being attached to the 50-lb block B. If the coefficient of kinetic friction between the block and the incline is μk =
The four 2-kg metal plates are stacked on top of one another. If the coefficient of static friction between any two plates is μs = 0.3, determine the smallest horizontal force F that can be applied
The 3-kg crate rests on the 10-kg cart where the coefficients of static and kinetic friction are μs = 0.25 and μk = 0.2, respectively. Determine the smallest constant force P needed to cause the
The safe S has a weight of 200 lb and is supported by the rope and pulley arrangement shown. If the end of the rope is given to a boy B of weight 90 lb, determine his acceleration if in the confusion
Block A has a mass of 20 kg and block B has a mass of 50 kg. If the spring is stretched 0.2 m at the instant shown, determine the acceleration of block B at this instant if it is(a) Originally at
The coefficient of static friction between the 200-kg crate and the flat bed of the truck is μs = 0.3. Determine the shortest time for the truck to reach a speed of 60 km h, starting from rest with
Determine the velocity of the cylinder A when t = 4 s if the system is released from rest. Cylinder A has a mass of 8 kg and cylinder B has a mass of 6 kg. Neglect the mass of the pulleys and cords.
The 1.5-kg block slides along a smooth plane and strikes a nonlinear spring with a speed of v = 4 m/s. The spring is termed "nonlinear" because it has a resistance of Fs = ks², where k = 900 N/m².
The motorcycle has a mass of 0.5 Mg and a negligible size. It passes point A traveling at a speed of 15 m/s, which is increasing at a constant rate of 1.5 m/s². Determine the resultant frictional
The motion of a truck is arrested using a bed of loose stones AB and a set of crash barrels BC. If experiments show that the stones provide a rolling resistance of 160 lb per wheel and the crash

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