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engineering
engineering mechanics dynamics

Questions and Answers of Engineering Mechanics Dynamics

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 it
Measurements of a shot recorded on a videotape during a basketball game are shown. The ball passed through the hoop even though it barely cleared the hands of the player B who attempted to block it.
The catapult is used to launch a ball such that it strikes the wall of the building at the maximum height of its trajectory. If it takes time t1 to travel from A to B, determine the velocity vA at
A particle is moving along the curve y = x − (x2/a). If the velocity component in the x direction is vx = v0. and changes at the rate a0, determine the magnitudes of the velocity and
The buckets on the conveyor travel with a speed v. Each bucket contains a block which falls out of the bucket when θ = θ1. Determine the distance d to where the block strikes the conveyor. Neglect
The stones are thrown off the conveyor with a horizontal velocity v0 as shown. Determine the distance d down the slope to where the stones hit the ground at B. Given: Vo = 10 8 = 32.2 S ft 2 S h =
Determine the smallest angle θ, measured above the horizontal, that the hose should be directed so that the water stream strikes the bottom of the wall at B. The speed of the water at the nozzle is
The fireman standing on the ladder directs the flow of water from his hose to the fire at B. Determine the velocity of the water at A if it is observed that the hose is held at angle θ.Given: 8 = 20
The projectile is launched with a velocity v0. Determine the range R, the maximum height h attained, and the time of flight. Express the results in terms of the angle θ and v0. The acceleration due
A ball bounces on the θ inclined plane such that it rebounds perpendicular to the incline with a velocity vA. Determine the distance R to where it strikes the plane at B. Given: 8 = 30 deg ft VA
The snowmobile is traveling at speed v0 when it leaves the embankment at A. Determine the time of flight from A to B and the range R of the trajectory. Given: VO = 10 d = 4 EI 9 = 40 deg c = 3 8 =
The path of a particle is defined by y2 = 4kx, and the component of velocity along the y axis is vy = ct, where both k and c are constants. Determine the x and y components of acceleration.
The man at A wishes to throw two darts at the target at B so that they arrive at the same time. If each dart is thrown with speed v0, determine the angles θC and θD at which they should be thrown
The water sprinkler, positioned at the base of a hill, releases a stream of water with a velocity v0 as shown. Determine the point B(x, y) where the water strikes the ground on the hill.Assume that
The projectile is launched from a height h with a velocity v0. Determine the range R. y R -X
A car moves along a circular track of radius ρ such that its speed for a short period of time 0 ≤ t ≤ t2, is v = b t + c t2. Determine the magnitude of its acceleration when t = t1. How far has
A boy at O throws a ball in the air with a speed v0 at an angle θ1. If he then throws another ball at the same speed v0 at an angle θ21, determine the time between the throws so the balls collide
At a given instant the jet plane has speed v and acceleration a acting in the directions shown. Determine the rate of increase in the plane’s speed and the radius of curvature ρ of the path.
The car travels along the curve having a radius of R. If its speed is uniformly increased from v1 to v2 in time t, determine the magnitude of its acceleration at the instant its speed is v3. Given:
A car is traveling along a circular curve that has radius ρ. If its speed is v and the speed is increasing uniformly at rate at, determine the magnitude of its acceleration at this instant. Given: p
The jet plane travels along the vertical parabolic path. When it is at point A it has speed v which is increasing at the rate at. Determine the magnitude of acceleration of the plane when it is at
A particle is moving along a curved path at a constant speed v. The radii of curvature of the path at points P and P' are ρ and ρ', respectively. If it takes the particle time t to go from P to P',
The satellite S travels around the earth in a circular path with a constant speed v1. If the acceleration is a, determine the altitude h. Assume the earth’s diameter to be d. Units Used: Mm 103 =
A boat is traveling along a circular path having radius ρ. Determine the magnitude of the boat’s acceleration when the speed is v and the rate of increase in the speed is at. Given: p = 20 m V =
Starting from rest, a bicyclist travels around a horizontal circular path of radius ρ at a speed v = b t2 + ct. Determine the magnitudes of his velocity and acceleration when he has traveled a
The car B turns such that its speed is increased by dvB/dt = b ect. If the car starts from rest when θ = 0, determine the magnitudes of its velocity and acceleration when t = t1. Neglect the size of
The Ferris wheel turns such that the speed of the passengers is increased by at = bt. If the wheel starts from rest when θ = 0°, determine the magnitudes of the velocity and acceleration of the
A package is dropped from the plane which is flying with a constant horizontal velocity vA. Determine the normal and tangential components of acceleration and the radius of curvature of the path of
The automobile is originally at rest at s = 0. If it then starts to increase its speed at dv/dt = bt2, determine the magnitudes of its velocity and acceleration at s = s1. Given: d = 300 ft P p = 240
The car B turns such that its speed is increased by dvB/dt = bect. If the car starts from rest when θ = 0, determine the magnitudes of its velocity and acceleration when the arm AB rotates to θ =
A particle P moves along the curve y = b x2 + c with a constant speed v. Determine the point on the curve where the maximum magnitude of acceleration occurs and compute its value. Given: b = 1 1 m c
The truck travels in a circular path having a radius ρ at a speed v0. For a short distance from s = 0, its speed is increased by at = bs. Determine its speed and the magnitude of its acceleration
The particle travels with a constant speed v along the curve. Determine the particle’s acceleration when it is located at point x = x1. Given: V v = 300 mm S 2 k = 20x 10 mm = x1 200 mm
At a given instant the train engine at E has speed v and acceleration a acting in the direction shown. Determine the rate of increase in the train's speed and the radius of curvature ρ of the path.
The automobile is originally at rest at s = 0. If its speed is increased by dv/dt = bt2, determine the magnitudes of its velocity and acceleration when t = t1. Given: b = 0.05 ft 4 S t₁ = 18 s t1 p
Cars move around the “traffic circle” which is in the shape of an ellipse. If the speed limit is posted at v, determine the maximum acceleration experienced by the passengers.Given: V =
Cars move around the “traffic circle” which is in the shape of an ellipse. If the speed limit is posted at v, determine the minimum acceleration experienced by the passengers.Given: V =
The motorcycle is traveling at v0 when it is at A. If the speed is then increased at dv/dt = at, determine its speed and acceleration at the instant t = t1. Given: k = 0.5 m at = 0.1 Vo = 1 t1 = 5
If a particle’s position is described by the polar coordinates r = asinbθ and θ = ct, determine the radial and tangential components of its velocity and acceleration when t = t1. Given: a = 2
The two particles A and B start at the origin O and travel in opposite directions along the circular path at constant speeds vA and vB respectively. Determine at t = t1,(a) The displacement along the
The car travels around the circular track having a radius r such that when it is at point A it has a velocity v1 which is increasing at the rate dv/dt = kt. Determine the magnitudes of its velocity
The race car has an initial speed vA at A. If it increases its speed along the circular track at the rate at = bs, determine the time needed for the car to travel distance s1. Given: VA =
The car travels around the portion of a circular track having a radius r such that when it is at point A it has a velocity v1 which is increasing at the rate of dv/dt = ks. Determine the magnitudes
The ball is ejected horizontally from the tube with speed vA. Find the equation of the path y = f (x), and then find the ball’s velocity and the normal and tangential components of acceleration
Particles A and B are traveling counter-clockwise around a circular track at constant speed v0. If at the instant shown the speed of A is increased by dvA/dt = bsA, determine the distance measured
The two particles A and B start at the origin O and travel in opposite directions along the circular path at constant speeds vA and vB respectively. Determine the time when they collide and the
A boy sits on a merry-go-round so that he is always located a distance r from the center of rotation. The merry-go-round is originally at rest, and then due to rotation the boy’s speed is increased
The motion of a particle along a fixed path is defined by the parametric equations r = b, θ = ct and z = dt2. Determine the unit vector that specifies the direction of the binormal axis to the
A particle moves along the curve y = bsin(cx) with a constant speed v. Determine the normal and tangential components of its velocity and acceleration at any instant. Given: m V v = 2 = S b = 1 m C m
Particles A and B are traveling around a circular track at speed v0 at the instant shown. If the speed of B is increased by dvB/dt = aBt, and at the same instant A has an increase in speed dvA/dt =
The truck travels at speed v0 along a circular road that has radius ρ. For a short distance from s = 0, its speed is then increased by dv/dt = bs. Determine its speed and the magnitude of its
A go-cart moves along a circular track of radius ρ such that its speed for a short period of time,Determine the magnitude of its acceleration when t = t2. How far has it traveled in t = t2? Use
A particle is moving along a circular path having radius r such that its position as a function of time is given by θ = c sin bt. Determine the acceleration of the particle at θ = θ1. The particle
The slotted fork is rotating about O at a constant rate θ'. Determine the radial and transverse components of the velocity and acceleration of the pin A at the instant θ = θ1. The path is defined
A particle P travels along an elliptical spiral path such that its position vector r is defined by r = (a cos bt i + c sin dt j + et k). When t = t1, determine the coordinate direction angles α, β,
If a particle’s position is described by the polar coordinates r = a(1 + sin bt) and θ = cedt, determine the radial and tangential components of the particle’s velocity and acceleration when t =
The slotted fork is rotating about O at the rate θ' which is increasing at θ'' when θ = θ1. Determine the radial and transverse components of the velocity and acceleration of the pin A at this
A truck is traveling along the horizontal circular curve of radius r with a constant speed v. Determine the angular rate of rotation θ' of the radial line r and the magnitude of the truck’s
A particle moves in the x - y plane such that its position is defined by r = ati + bt2j. Determine the radial and tangential components of the particle’s velocity and acceleration when t = t1.
The slotted link is pinned at O, and as a result of the angular velocity θ' and the angular acceleration θ'' it drives the peg P for a short distance along the spiral guide r = aθ. Determine the
A particle travels along a portion of the “four-leaf rose” defined by the equation r = a cos(bθ). If the angular velocity of the radial coordinate line is θ' = ct2, determine the radial and
If a particle moves along a path such that r = acos(bt) and θ = ct, plot the path r = f(θ) and determine the particle’s radial and transverse components of velocity and acceleration. Given: a = 2
The slotted link is pinned at O, and as a result of the constant angular velocity θ' it drives the peg P for a short distance along the spiral guide r = aθ where θ is in radians. Determine the
A cameraman standing at A is following the movement of a race car, B, which is traveling along a straight track at a constant speed v. Determine the angular rate at which he must turn in order to
A truck is traveling along the horizontal circular curve of radius r with speed v which is increasing at the rate v'. Determine the truck’s radial and transverse components of acceleration. Given:
A particle is moving along a circular path having a radius r. Its position as a function of time is given by θ = bt2. Determine the magnitude of the particle’s acceleration when θ = θ1. The
The slotted link is pinned at O, and as a result of the constant angular velocity θ' it drives the peg P for a short distance along the spiral guide r = aθ. Determine the radial and transverse
A train is traveling along the circular curve of radius r. At the instant shown, its angular rate of rotation is θ', which is decreasing at θ''. Determine the magnitudes of the train’s velocity
The rod OA rotates counterclockwise with a constant angular velocity of θ'. Two pin-connected slider blocks, located at B, move freely on OA and the curved rod whose shape is a limaçon described by
At the instant shown, the water sprinkler is rotating with an angular speed θ' and an angular acceleration θ''. If the nozzle lies in the vertical plane and water is flowing through it at a
The arm of the robot has a variable length so that r remains constant and its grip. A moves along the path z = a sinb θ. If θ = ct, determine the magnitudes of the grip’s velocity and
The boy slides down the slide at a constant speed v. If the slide is in the form of a helix, defined by the equations r = constant and z = −(hθ)/(2π), determine the boy’s angular velocity about
The searchlight on the boat anchored a distance d from shore is turned on the automobile, which is traveling along the straight road at speed v and acceleration a. Determine the required angular
For a short distance the train travels along a track having the shape of a spiral, r = a/θ. If it maintains a constant speed v, determine the radial and transverse components of its velocity when θ
The rod OA rotates counterclockwise with a constant angular velocity of θ'. Two pin-connected slider blocks, located at B, move freely on OA and the curved rod whose shape is a limaçon described by
For a short distance the train travels along a track having the shape of a spiral, r = a/θ. If the angular rate θ' is constant, determine the radial and transverse components of its velocity and
For a short time the arm of the robot is extending so that r' remains constant, z = bt2 and θ = ct. Determine the magnitudes of the velocity and acceleration of the grip A when t = t1 and r = r1.
The searchlight on the boat anchored a distance d from shore is turned on the automobile, which is traveling along the straight road at a constant speed v. Determine the angular rate of rotation of
The pin follows the path described by the equation r = a + bcos θ. At the instant θ = θ1. the angular velocity and angular acceleration are θ' and θ''. Determine the magnitudes of the pin’s
The mechanism of a machine is constructed so that for a short time the roller at A follows the surface of the cam described by the equation r = a + b cosθ. If θ' and θ'' are given, determine the
A car is traveling along the circular curve having a radius r. At the instance shown, its angular rate of rotation is θ', which is decreasing at the rate θ''. Determine the radial and transverse
The small washer is sliding down the cord OA. When it is at the midpoint, its speed is v and its acceleration is a'. Express the velocity and acceleration of the washer at this point in terms of its
The roller coaster is traveling down along the spiral ramp with a constant speed v. If the track descends a distance h for every full revolution, determine the magnitude of the roller coaster’s
The motor draws in the cable at C with a constant velocity vC. The motor draws in the cable at D with a constant acceleration of aD. If vD = 0 when t = 0, determine(a) The time needed for block A to
For a short time the position of the roller-coaster car along its path is defined by the equations r = r0, θ = at, and z = bcos θ. Determine the magnitude of the car’s velocity and acceleration
The cord is attached to the pin at C and passes over the two pulleys at A and D. The pulley at A is attached to the smooth collar that travels along the vertical rod. Determine the velocity and
A cameraman standing at A is following the movement of a race car, B, which is traveling around a curved track at constant speed vB. Determine the angular rate at which the man must turn in order to
A double collar C is pin-connected together such that one collar slides over a fixed rod and the other slides over a rotating rod. If the geometry of the fixed rod for a short distance can be defined
The cord of length L is attached to the pin at C and passes over the two pulleys at A and D. The pulley at A is attached to the smooth collar that travels along the vertical rod. When sB = b, the end
The crate C is being lifted by moving the roller at A downward with constant speed vA along the guide. Determine the velocity and acceleration of the crate at the instant s = s1. When the roller is
The man pulls the boy up to the tree limb C by walking backward. If he starts from rest when xA = 0 and moves backward with constant acceleration aA, determine the speed of the boy at the instant yB
The girl at C stands near the edge of the pier and pulls in the rope horizontally at constant speed vC. Determine how fast the boat approaches the pier at the instant the rope length AB is d. Given:
At the instant shown, cars A and B are traveling at speeds vA and vB respectively. If B is increasing its speed at v'A, while A maintains a constant speed, determine the velocity and acceleration of
Cars A and B are traveling around the circular race track. At the instant shown, A has speed vA and is increasing its speed at the rate of v'A, whereas B has speed vB and is decreasing its speed at
At the instant shown, cars A and B are traveling at speeds vA and vB respectively. If A is increasing its speed at v'A whereas the speed of B is decreasing at v'B, determine the velocity and
Two planes, A and B, are flying at the same altitude. If their velocities are vA and vB such that he angle between their straight-line courses is θ, determine the velocity of plane B with respect to
An aircraft carrier is traveling forward with a velocity v0. At the instant shown, the plane at A has just taken off and has attained a forward horizontal air speed vA, measured from still water. If
The boy A is moving in a straight line away from the building at a constant speed vA. At what horizontal distance d must he be from C in order to make the catch if the ball is thrown with a
Two boats leave the shore at the same time and travel in the directions shown with the given speeds. Determine the speed of boat A with respect to boat B. How long after leaving the shore will the
The airplane has a speed relative to the wind of vA. If the speed of the wind relative to the ground is vW, determine the angle θ at which the plane must be directed in order to travel in the

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