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engineering
engineering mechanics statics

Questions and Answers of Engineering Mechanics Statics

The motorcycle travels up the hill at a constant speed of 15 m/s. Determine the magnitude of its acceleration as a function of x. y -X- y= 1 x² 1000 -X
The motorcyclist travels along the curve at a constant speed of 30 ft/s. Determine his acceleration when he is located at point A. Neglect the size of the motorcycle and rider for the calculation.
A racing car travels with a constant speed of 240 km/h around the elliptical race track. Determine the acceleration experienced by the driver at A. 2 km y B 4 km ; + 2 = 16 X
If the car passes point A with a speed of 20 m/s and begins to increase its speed at a constant rate of at = 0.5 m/s², determine the magnitude of the car's acceleration when s = 101.68 m and x = 0.
At a given instant the train engine at E has a speed of 20 m/s and an acceleration of 14 m/s² acting in the direction shown. Determine the rate of increase in the train's speed and the radius of
When the bicycle passes point A, it has a speed of 6 m/s, which is increasing at the rate of v̇ = (0.5) m/s². Determinethe magnitude of its acceleration when it is at point A. y +50 m y = 12 In X 20
The car has an initial speed v0 = 20 m/s at s = 0. If it increases its speed along the circular track at = (0.8s) m>/s2, where s is in meters, determine the time needed for the car to travel s =
The car starts from rest at s = 0 and increases its speed at at = 4 m/s2. Determine the time when the magnitude of acceleration becomes 20 m/s2. At what position s does this occur? p= 40 m_ S
The racing car travels with a constant speed of 240 km/h around the elliptical race track. Determine the acceleration experienced by the driver at B. 2 km y B 4 km WE 16 +²=1 X
A train is traveling with a constant speed of 14 m/s along the curved path. Determine the magnitude of the acceleration of the front of the train, B, at the instant it reaches point A (y = 0). y
The motorcycle is traveling at a constant speed of 60 km h. Determine the magnitude of its acceleration when it is at point A. y -25 m- A y² = 2x -X
A boat is traveling along a circular curve having a radius of 100 ft. If its speed at t = 0 is 15 ft/s and is increasing at v̇ = (0.8t) ft/s², determine the magnitude of its acceleration at the
When t = 0, the train has a speed of 8 m/s, which is increasing at 0.5 m/s2. Determine the magnitude of the acceleration of the engine when it reaches point A, at t = 20 s. Here the radius of
A boat is traveling along a circular path having a radius of 20 m. Determine the magnitude of the boat's acceleration when the speed is v= 5 m/s and the rate of increase in the speed is i = 2 m/s².
Starting from rest, a bicyclist travels around a horizontal circular path, ρ = 10 m, at a speed of v = (0.09t² + 0.1t) m/s, where t is in seconds. Determine the magnitudes of her velocity and
The ball is ejected horizontally from the tube with a speed of 8 m/s. Find the equation of the path, y = f(x), and then find the ball's velocity and the normal and tangential components of
A particle travels around a circular path having a radius of 50 m. If it is initially traveling with a speed of 10 m/s and its speed then increases at a rate of v̇ = (0.05 v) m/s²,determine the
Two cyclists, A and B, are traveling counterclockwise around a circular track at a constant speed of 8 ft/s at the instant shown. If the speed of A is increased at (at)A = (sA) ft/s2, where sA is in
The car is traveling at a constant speed of 30 m/s. The driver then applies the brakes at A and thereby reduces the car's speed at the rate of at = (-0.08v) m/s², where v is in m/s. Determine the
The car is traveling at a constant speed of 30 m/s. The driver then applies the brakes at A and thereby reduces the speed at the rate ofwhere t is in seconds. Determine the magnitude of the
A spiral transition curve is used on railroads to connect a straight portion of the track with a curved portion. If the spiral is defined by the equation y = (10-6)x3, where x and y are in feet,
Determine the magnitude of acceleration of the airplane during the turn. It flies along the horizontal circular path AB in 40 s, while maintaining a constant speed of 300 ft/s. A 60° В
The race car has an initial speed vA = 15 m/s at A. If it increases its speed along the circular track at the rate at = (0.4s) m/s², where s is in meters, determine the time needed for the car to
Particles A and B are traveling around a circular track at a speed of 8 m/s at the instant shown. If the speed of B is increasing by (at)B = 4 m/s2, and at the same instant A has an increase in speed
When the motorcyclist is at A, he increases his speed along the vertical circular path at the rate of v̇ = (0.3t) ft/s²,where t is in seconds and t = 0 at A. If he starts from restat A, determine
When the motorcyclist is at A, he increases his speed along the vertical circular path at the rate of v̇ = (0.04s) ft/s², where s is in ft and s = 0 at A. If he starts at vA = 2 ft/s, determine the
The airplane flies along the horizontal circular path AB in 60 s. If its speed at point A is 400 ft/s, which decreases at a rate of at = (–0.1t) ft/s2, where t is in seconds, determine the
Particles A and Bare traveling counterclockwise around a circular track at a constant speed of 8 m/s. If at the instant shown the speed of A begins to increase by (at)A = (0.4SA) m/s², where sA is
The train passes point B with a speed of 20 m/s which is decreasing at at = -0.5 m/s². Determine the magnitude of acceleration of the train at this point. A -400 m- B X y = 200 e 1000 X
A car travels around a circular track having a radius of r = 300 m such that when it is at point A it has a velocity of 5 m/s, which is increasing at the rate of v̇ = (0.06t) m/s2, where t is in
A particle P travels along an elliptical spiral path such that its position vector ris defined by {2 cos(0.1t)i + 1.5 sin(0.1t)j + (2t)k} m, where t is in seconds and the arguments for the sine and
If the speed of the crate at A is 15 ft s, which is increasing at a rate v̇ = 3 ft/s2, determine the magnitude of the acceleration of the crate at this instant. y 10 ft A 16 -X
The small washer is sliding down the cord OA. When it is at the midpoint, its speed is 28 m/s and its acceleration is 7 m/s2. Express the velocity and acceleration of the washer at this point in
Acar is traveling along the circular curve of radius r = 300 ft. At the instant shown, its angular rate of rotation is θ̇ = 0.4 rad/s, which is increasing at the rate of θ̈ = 0.2
If a particle's position is described by the polar coordinates r = 4(1 + sin t) m and θ = (2e-t) rad, where t is in secondsand the argument for the sine is in radians, determine theradial and
A particle moves along a path defined by polar coordinates r = (2et) ft and θ = (8t2) rad, where t is in seconds. Determine the components of its velocity and acceleration when t = 1 s.
A particle travels around a limaçon, defined by the equation r = b - a cos θ, where a and b are constants. Determine the particle’s radial and transverse components of velocity and acceleration
An airplane is flying in a straight line with a velocity of 200 mi/h and an acceleration of 3 mi/h2. If the propeller has a diameter of 6 ft and is rotating at a constant angular rate of 120 rad/s,
If a particle moves along a path such that r = (2 cost) ft and θ = (t/2) rad, where t is in seconds, plot the path r = f(θ) and determine the particle's radial and transversecomponents of velocity
The rod OA rotates clockwise with a constant angular velocity of 6 rad/s. Two pin-connected slider blocks, located at B, move freely on OA and the curved rod whose shape is a limaçon described by
Determine the magnitude of the acceleration of the slider blocks in Prob. 12–172 when θ = 150°.Prob. 12–172The rod OA rotates clockwise with a constant angular velocity of 6 rad/s. Two
The driver of the car maintains a constant speed of 40 m/s. Determine the angular velocity of the camera tracking the car when θ = 15°. r = (100 cos 20) m, OJ
The pin P is constrained to move along the curve defined by the lemniscate r = (4 sin 2θ) ft. If the angular position of the slotted arm OA is defined by 0 = (3t3/2) rad, where t is in seconds,
When θ = 15°, the car has a speed of 50 m/s which is increasing at 6 m/s2. Determine the angular velocity of the camera tracking the car at this instant. r = (100 cos 20) m 3.
A particle travels along the portion of the "four-leaf rose" defined by the equation r = (5 cos 2θ) m. If the angular velocity of the radial coordinate line is θ = (3t²) rad/s, where t is in
The time rate of change of acceleration is referred to as the jerk, which is often used as a means of measuring passenger discomfort. Calculate this vector, ȧ in terms of its cylindrical
A particle P moves along the spiral path r = (10/θ) ft, where is in radians. If it maintains a constant speed of v = 20 ft/s, determine vr, and vθ as functions of θ and evaluate each at θ = 1
If a particle’s position is described by the polar coordinates r = (2 sin 2θ) m and θ = (4t) rad, where t is in seconds, determine the radial and transverse components of its velocity and
The link is pinned at O, and as a result of its rotation it drives the peg P along the vertical guide. Calculate the magnitudes of the velocity and acceleration of P if θ = ct rad, where c is a
The mechanism within a machine is constructed so that the pin follows the path r= (300+200 cos θ) mm. Ifthe magnitudes of the pin'sdescribed by the equation θ̇ = 0.5 rad/s and θ̈ = 0, determine
The mechanism of a machine is constructed so that the roller at A follows the surface of the cam described by the equation r = (0.3 +0.2 cos θ) m. If θ̇ = 0.5 rad/s and θ̈ = 0, determine the
The position of a particle is described by r = (300e-0.5t) mm and θ = (0.3t2) rad, where t is in seconds. Determine the magnitudes of the particle's velocity and acceleration at the instant t = 1.5s.
The box slides down the helical ramp with a constant speed of v = 2 m/s. Determine the magnitude of its acceleration. The ramp descends a vertical distance of 1m for every full revolution. The mean
When θ = (2/3π) rad, the angular velocity and angular acceleration of the circular plate are θ = 1.5 rad/s andθ̈ = 3 rad/s², respectively. Determine the magnitudes of the velocity and
A particle moves in the x–y plane such that its position is defined by r = {2ti + 4t2j} ft, where t is in seconds. Determine the radial and transverse components of the particle’s velocity and
The box slides down the helical ramp such that r = 0.5 m, θ = (0.5t³) rad, and z = (2-0.2t2) m, where t is in seconds. Determine the magnitudes of the velocity and acceleration of the box at the
The motion of peg P is constrained by the lemniscate curved slot in OB and by the slotted arm OA. If OA rotates counterclockwise with an angular velocity of θ̇ = (3t³/2) rad/s, where t is in
The motion of the pin P is controlled by the rotation of the grooved link OA. If the link is rotating at a constant angular rate of θ̇ = 6 rad/s, determine the magnitudes of the velocity and
If the circular plate rotates clockwise with a constant angular velocity of θ̇ = 1.5 rad/s, determine the magnitudes of the velocity and acceleration of the follower rod AB when θ = (2/3π) rad.
For a short time the jet plane moves along a path in the shape of a lemniscate, r² = (2500 cos 20) km². At the instant θ = 30°, the radar tracking device is rotating atθ̇ = 5(10-³) rad/s with
The rod OA rotates counterclockwise with a constant angular velocity of θ̇ = 5 rad/s. Two pin-connected slider blocks, located at B, move freely on OA and the curved rod whose shape is a limaçon
The motion of peg P is constrained by the lemniscate curved slot in OB and by the slotted arm OA. If OA rotates counterclockwise with a constant angular velocity of θ̇ = 3 rad/s, determine the
If the cam rotates clockwise with a constant angular velocity of θ̇ = 5 rad/s, determine the magnitudes of the velocity and acceleration of the follower rod AB at the instant θ = 30°. The surface
At the instant θ = 30°, the cam rotates with a clockwiseangular velocity of θ̇ = 5 rad/s and angular acceleration of θ̈ = 6 rad/s². Determine the magnitudes of the velocity and acceleration of
A particle moves along an Archimedean spiral r = (80) ft, where is in radians. If θ̇ = 4 rad/s (constant), determine the radial and transverse components of the particle's velocity and acceleration
Determine the magnitude of the acceleration of the slider blocks in Prob. 12–185 when θ = 120°.Prob. 12–185The rod OA rotates counterclockwise with a constant angular velocity of θ̇ = 5
The arm of the robot move s so that r = 3 ft is constant, and its grip A moves along the path z = (3 sin 4θ) ft, where u is in radians. If θ = (0.5 t) rad, where t is in seconds, determine the
For a short time the arm of the robot is extending such that r= 1.5 ft/s when r = 3 ft, z = (4t²) ft, and θ = 0.5t rad, where t is in seconds. Determine the magnitudes of the velocity and
The slotted arm OA rotates counterclockwise about O such that when θ = π/4, arm OA is rotating with anangular velocity of θ̇ and an angular acceleration of 0.Determine the magnitudes of the
The car travels along a road, which for a short distance is defined by r = (200/θ) ft, where is in radians. If itmaintains a constant speed of v = 35 ft/s, determine theradial and transverse
Solve Prob. 12-189 if the particle has an angular acceleration θ̈ = 5 rad/s² when θ̇ = 4 rad/s at θ = π/2 rad.Prob. 12-189A particle moves along an Archimedean spiral r =
Determine the displacement of the block at B if A is pulled down 4 ft. A C B
The slotted arm OA rotates counterclockwise about O with a constant angular velocity of θ̇. The motion of pin B is constrained such that it moves on the fixed circular surface and along the slot in
Starting from rest, the cable can be wound onto the drum of the motor at a rate of vA = (3t2) m/s, where t is in seconds. Determine the time needed to lift the load 7 m. A D C B
The motor draws in the cable at C with a constant velocity of vc = 4 m/s. The motor draws in the cable at D with a constant acceleration of aD = 8 m/s². If vD = 0 when t = 0, determine (a) The
Determine the displacement of the log if the truck at C pulls the cable 4 ft to the right. B C
The cable at A is being drawn toward the motor at vA = 8 m/s. Determine the velocity of the block. SB SC SA- C B A VA
Determine the constant speed at which the cable at A must be drawn in by the motor in order to hoist the load 6 m in 1.5 s. A D C B
Determine the speed of the block at B. € 6 m/s A B
If the end A of the cable is moving at vA = 3 m/s, determine the speed of block B. D B A VA = 3 m/s
Determine the time needed for the load at B to attain a speed of 10 m/s, starting from rest, if the cable is drawn into the motor with an acceleration of 3 m/s2. SB SC -SA- C B A
Determine the speed of B if A is moving downward with a speed of vA = 4 m/s at the instant shown. B A √e₁= = 4 m/s
The roller at A is moving with a velocity of vA = 4 m/s and has an acceleration of aA = 2 m/s2 when xA = 3 m. Determine the velocity and acceleration of block B at this instant. VA = 4 m/s XA- 4 m B
Determine the constant speed at which the cable at A must be drawn in by the motor in order to hoist the load at B 15 ft in 5 s. B B
The hoist is used to lift the load at D. If the end A of the chain is traveling downward at vA = 5 ft/s and the end B is traveling upward at VB = 2 ft/s, determine the velocity of the load at D.
If the hydraulic cylinder H draws in rod BC at 2 ft/s, determine the speed of slider A. H B C A SC SA- C
The cylinder C is being lifted using the cable and pulley system shown. If point A on the cable is being drawn toward the drum with a speed of 2 m/s, determine the speed of the cylinder. A с S
The cylinder C can be lifted with a maximum acceleration of aC = 3 m/s2 without causing the cables to fail. Determine the speed at which point A is moving toward the drum when s = 4 m if the cylinder
The motor draws in the cord at B with an acceleration of aB = 2 m/s2. When sA = 1.5 m, vB = 6 m/s. Determine the velocity and acceleration of the collar at this instant. 2m Nambay SA A B OF
If block B is moving down with a velocity vB and has an acceleration aB, determine the velocity and acceleration of block A in terms of the parameters shown. A SA- B Th VB, aB
The roller at A is moving upward with a velocity of VA = 3 ft/s and has an acceleration of aA = 4 ft/s² when SA = 4 ft. Determine the velocity and acceleration of block B at this instant. B -3 ft =
The block B is suspended from a cable that is attached to the block at E, wraps around three pulleys, and is tied to the back of a truck. If the truck starts from rest when xD is zero, and moves
At the instant shown, the car at A is traveling at 10 m/s around the curve while increasing its speed at 5 m/s2. The car at B is traveling at 18.5 m/s along the straightaway and increasing its speed
Two planes, A and B, are flying at the same altitude. If their velocities are vA = 500 km/h and vB = 700 km/h such that the angle between their straight-line courses is θ = 60°, determine the
The boat can travel with a speed of 16 km/h in still water. The point of destination is located along the dashed line. If the water is moving at 4 km/h, determine the bearing angle θ at which the
At the instant shown, cars A and B are traveling at speeds of 55 mi/h and 40 mi/h, respectively. If B is increasing its speed by 1200 mi/h2, while A maintains a constant speed, determine the velocity
Two boats leave the pier P at the same time and travel in the directions shown. If vA = 40 ft s and vB = 30 ft/s, determine the magnitude of the velocity of boat A relative to boat B. How long after
Car A travels along a straight road at a speed of 25 m/s while accelerating at 1.5 m/s². At this same instant car C is traveling along the straight road with a speed of 30 m/s while decelerating at
Car B is traveling along the curved road with a speed of 15 m/s while decreasing its speed at 2 m/s². At this same instant car C is traveling along the straight road with a speed of 30 m/s while
Cars A and B are traveling around the circular race track. At the instant shown, A has a speed of 90 ft/s and is increasing its speed at the rate of 15 ft/s², whereas B has a speed of 105 ft/s and

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