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engineering
engineering mechanics dynamics

Questions and Answers of Engineering Mechanics Dynamics

A motor gives disk A a clockwise angular acceleration αA = at2 + b. If the initial angular velocity of the disk is ω0, determine the magnitudes of the velocity and acceleration of block B when t =
The sphere starts from rest at θ = 0° and rotates with an angular acceleration α = kθ. Determine the magnitudes of the velocity and acceleration of point P on the sphere at the instant θ = θ1.
A tape having a thickness s wraps around the wheel which is turning at a constant rate ω. Assuming the unwrapped portion of tape remains horizontal, determine the acceleration of point P of the
The mechanism is used to convert the constant circular motion ω of rod AB into translating motion of rod CD.Determine the velocity and acceleration of CD for any angle θ of AB.
At the instant θ = θ1 the slotted guide is moving upward with acceleration a and velocity v. Determine the angular acceleration and angular velocity of link AB at this instant. Given: 01 = 50 deg
Determine the velocity of rod R for any angle θ of the cam C if the cam rotates with a constant angular velocity ω. The pin connection at O does not cause an interference with the motion of A on C.
The crankshaft AB is rotating at constant angular velocity ω. Determine the velocity of the piston P for the given θ. Given: Ⓒ= 150 8 = rad S 30 deg a = 0.2 ft b = 0.75 ft B
Determine the velocity of the rod R for any angle θ of cam C as the cam rotates with a constant angular velocity ω. The pin connection at O does not cause an interference with the motion of plate A
Bar AB rotates uniformly about the fixed pin A with a constant angular velocity ω. Determine the velocity and acceleration of block C when θ = θ1. A av L -7- B L T
The end A of the bar is moving downward along the slotted guide with a constant velocity vA. Determine the angular velocity ω and angular acceleration a of the bar as a function of its position y.
The slotted yoke is pinned at A while end B is used to move the ram R horizontally. If the disk rotates with a constant angular velocity ω, determine the velocity and acceleration of the ram. The
The bar is confined to move along the vertical and inclined planes. If the velocity of the roller at A is vA downward when θ = θ1. determine the bar's angular velocity and the velocity of roller B
The Geneva wheel A provides intermittent rotary motion ωA for continuous motion ωD of disk D. By choosing d = √2r, the wheel has zero angular velocity at the instant pin B enters or leaves one of
If h and θ are known, and the speed of A and B is vA = vB = v, determine the angular velocity ω of the body and the direction φ of vB. 3 A B VA h
The velocity of the slider block C is vC up the inclined groove. Determine the angular velocity of links AB and BC and the velocity of point B at the instant shown. Given: VC = 4 ft S L = 1 ft
The wheel is rotating with an angular velocity ω. Determine the velocity of the collar A for the given values of θ and φ. Given: 0 = 30 deg p = 60 deg @=8 rad S TA = 500 mm ΤΑ rB = 150 mm VB =
The shaper mechanism is designed to give a slow cutting stroke and a quick return to a blade attached to the slider at C. Determine the velocity of the slider block C at the instant shown, if link AB
The shaper mechanism is designed to give a slow cutting stroke and a quick return to a blade attached to the slider at C. Determine the velocity of the slider block C at the instant shown, if link AB
Rod AB is rotating with an angular velocity ωAB. Determine the velocity of the collar C for the given angles θ and φ. Given: @AB = 5 VB = 10 rad ft S S
If rod CD is rotating with an angular velocity ωDC, determine the angular velocities of rods AB and BC at the instant shown. Given: DC = 8 TBC = rad 01 = 45 deg 02 = 30 deg TAB = 150 mm TCD = S 400
The link AB has an angular velocity ωAB. Determine the velocity of block C at the instant shown when θ = 45 deg. Given: ФАВ = 2 rad S 0 = 45 deg r = 15 in r = 15 in
If, at a given instant, point B has a downward velocity of vB, determine the velocity of point A at this instant. Notice that for this motion to occur, the wheel must slip at A. Given: ES m VB =
At the instant shown, the truck is traveling to the right at speed v, while the pipe is rolling counterclockwise at angular velocity ω without slipping at B. Determine the velocity of the pipe’s
If disk D has constant angular velocity ωD, determine the angular velocity of disk A at the instant shown. Given: rad D = 2- S 0 = 60 deg $ = 45 deg 8 = 30 deg "a = 0.5 ft ra rd = 0.75 ft d = 2 ft
If the link AB is rotating about the pin at A with angular velocity ωAB, determine the velocities of blocks C and E at the instant shown. Given: CAB = 5 a = 1 ft b = 2 ft c = 3 ft rad 8 = 30 deg d =
The planetary gear system is used in an automatic transmission for an automobile. By locking or releasing certain gears, it has the advantage of operating the car at different speeds. Consider the
If the end of the cord is pulled downward with speed vC, determine the angular velocities of pulleys A and B and the speed of block D. Assume that the cord does not slip on the pulleys. Given: VC =
If bar AB has an angular velocity ωAB, determine the velocity of the slider block C at the instant shown. Given: OAB = 6 TAB = rad 0 = 45 deg = 30 deg S = 200 mm TBC 500 mm ФАВ B TAB Гвс
At the instant shown, the truck is traveling to the right at speed v = at, while the pipe is rolling counterclockwise at angular velocity ω = bt, without slipping at B. Determine the velocity of the
Part of an automatic transmission consists of a fixed ring gear R, three equal planet gears P, the sun gear S, and the planet carrier C, which is shaded. If the sun gear is rotating with angular
When the crank on the Chinese windlass is turning, the rope on shaft A unwinds while that on shaft B winds up. Determine the speed of block D if the crank is turning with an angular velocity ω. What
At the instant shown, the truck is traveling to the right at speed vt. If the spool does not slip at B, determine its angular velocity if its mass center appears to an observer on the ground to be
In an automobile transmission the planet pinions A and B rotate on shafts that are mounted on the planet pinion carrier CD. As shown, CD is attached to a shaft at E which is aligned with the center
The wheel is rotating with an angular velocity ω. Determine the velocity of the collar A at the instant θ and φ using the method of instantaneous center of zero velocity. Given: TA = 500 mm rB
The cylinder B rolls on the fixed cylinder A without slipping. If the connected bar CD is rotating with an angular velocity ωCD. Determine the angular velocity of cylinder B. Given: COCD = 5 rad S =
The slider mechanism is used to increase the stroke of travel of one slider with respect to that of another. As shown, when the slider A is moving forward, the attached pinion F rolls on the fixed
The shaper mechanism is designed to give a slow cutting stroke and a quick return to a blade attached to the slider at C. Determine the velocity of the slider block C at the instant shown, if link AB
If, at a given instant, point B has a downward velocity vB determine the velocity of point A at this instant using the method of instantaneous center of zero velocity. Notice that for this motion to
At the instant shown, the truck is traveling to the right with speed vB, while the pipe is rolling counterclockwise with angular velocity ω without slipping at B. Determine the velocity of the
The instantaneous center of zero velocity for the body is located at point IC. If the body has an angular velocity ω, as shown, determine the velocity of B with respect to A. Given: rad (0 = 4- S a
If disk D has a constant angular velocity ωD, determine the angular velocity of disk A at the instant θ, using the method of instantaneous center of zero velocity. Given: r = 0.5 ft 8 = 60 deg r1 =
At the instant shown, the disk is rotating with angular velocity ω. Determine the velocities of points A, B, and C. Given: rad @=4 4- S r = 0.15 m
The slider block C is moving with speed vC up the incline. Determine the angular velocities of links AB and BC and the velocity of point B at the instant shown. Given: VC = 4 = ft S TAB = 1 ft TBC =
Show that if the rim of the wheel and its hub maintain contact with the three tracks as the wheel rolls, it is necessary that slipping occurs at the hub A if no slipping occurs at B. Under these
The epicyclic gear train is driven by the rotating link DE, which has an angular velocity ωDE. If the ring gear F is fixed, determine the angular velocities of gears A, B, and C. Given: ΤΑ 50
Determine the angular velocity of link AB at the instant shown if block C is moving upward at speed vC. Given: VC = 12 c = 4 in b = 5 in in S 0 = 30 deg Ø = 45 deg WAB B
At a given instant the top B of the ladder has acceleration aB and velocity vB both acting downward. Determine the acceleration of the bottom A of the ladder, and the ladder’s angular acceleration
If the collar at C is moving downward to the left with speed vC, determine the angular velocity of link AB at the instant shown. Given: VC = 8 m S a = 500 mm b = 350 mm 8 = 60 deg $ = 45 deg
At a given instant the top end A of the bar has the velocity and acceleration shown. Determine the acceleration of the bottom B and the bar’s angular acceleration at this instant. Given: VA = 5 aA
At a given instant the bottom A of the ladder has acceleration aA and velocity vA, both acting to the left. Determine the acceleration of the top of the ladder, B, and the ladder’s angular
The rod of length rAB slides down the inclined plane, such that when it is at B it has the motion shown. Determine the velocity and acceleration of A at this instant. Given: TAB = 10 ft TCB = 4 ft aB
The wheel is moving to the right such that it has angular velocity ω and angular acceleration α at the instant shown. If it does not slip at A, determine the acceleration of point B. Given: @= 2 α
The disk rotates with angular velocity ω and angular acceleration α. Determine the angular acceleration of link CB at this instant. Given: @=5 rad S rad 2 S r = 0.5 ft α = 6 a = 2 ft b = 1.5 ft 0
Rod AB has the angular motion shown. Determine the acceleration of the collar C at this instant. Given: @AB = 3 rad S TAB = 0.5 m 01 = 30 deg rad 2 S *BC = 0.6 m CAB = 5 02 = 45 deg
At a given instant gears A and B have the angular motions shown. Determine the angular acceleration of gear C and the acceleration of its center point D at this instant. Note that the inner hub of
The tied crank and gear mechanism gives rocking motion to crank AC, necessary for the operation of a printing press. If link DE has the angular motion shown, determine the respective angular
At a given instant the wheel is rotating with the angular velocity and angular acceleration shown. Determine the acceleration of block B at this instant. Given: @ = 2 a = 6 rad S rad 2 S 1 = 1.5 m 8
The closure is manufactured by the LCN Company and is used to control the restricted motion of a heavy door. If the door to which is it connected has an angular acceleration α, determine the angular
The ends of the bar AB are confined to move along the paths shown. At a given instant, A has velocity vA and acceleration aA. Determine the angular velocity and angular acceleration of AB at this
The wheel rolls without slipping such that at the instant shown it has an angular velocity ω and angular acceleration α. Determine the velocity and acceleration of point B on the rod at this
Block B moves along the slot in the platform with constant speed v, measured relative to the platform in the direction shown. If the platform is rotating at constant rate ω, determine the velocity
The collar E is attached to, and pivots about, rod AB while it slides on rod CD. If rod AB has an angular velocity of ωAB and an angular acceleration of αAB both acting clockwise, determine the
While the swing bridge is closing with constant rotation ω, a man runs along the roadway at constant speed v relative to the roadway. Determine his velocity and acceleration at the instant shown.
Block B of the mechanism is confined to move within the slot member CD. If AB is rotating at constant rate ωAB, determine the angular velocity and angular acceleration of member CD at the instant
While the swing bridge is closing with constant rotation ω, a man runs along the roadway such that he is running outward from the center at speed v with acceleration a, both measured relative to the
A girl stands at A on a platform which is rotating with constant angular velocity ω. If she walks at constant speed v measured relative to the platform, determine her acceleration(a) When she
At a given instant, rod AB has the angular motions shown. Determine the angular velocity and angular acceleration of rod CD at this instant. There is a collar at C. Given: AB = 5 rad S αAB =
The gear has the angular motion shown. Determine the angular velocity and angular acceleration of the slotted link BC at this instant. The peg at A is fixed to the gear. Given: rad @=2- a =
A girl stands at A on a platform which is rotating with angular acceleration α and at the instant shown has angular velocity ω .If she walks at constant speed v measured relative to the platform,
The “quick-return” mechanism consists of a crank AB, slider block B, and slotted link CD. If the crank has the angular motion shown, determine the angular motion of the slotted link at this
The cars on the amusement-park ride rotate around the axle at A with constant angular velocity ωAf measured relative to the frame AB. At the same time the frame rotates around the main axle support
The girl has mass M and center of mass at G. If she is swinging to a maximum height defined by θ = θ1, determine the force developed along each of the four supporting posts such as AB at the
If the spring is compressed a distance δ against the block of weight W and it is released from rest, determine the normal force of the smooth surface on the block when it reaches the point x1.
A car has a mass M and accelerates along a horizontal straight road from rest such that the power is always a constant amount P. Determine how far it must travel to reach a speed of v.
Each of the two elastic rubber bands of the slingshot has an unstretched length l. If they are pulled back to the position shown and released from rest, determine the speed of the pellet of mass M
Each of the two elastic rubber bands of the slingshot has an unstretched length l. If they are pulled back to the position shown and released from rest, determine the maximum height the pellet of
The collar of weight W is released from rest at A and travels along the smooth guide. Determine the speed of the collar just before it strikes the stop at B. The spring has an unstretched length L.
The firing mechanism of a pinball machine consists of a plunger P having a mass Mp and a spring stiffness k. When s = 0, the spring is compressed a distance δ. If the arm is pulled back such that s
The collar of weight W is released from rest at A and travels along the smooth guide. Determine its speed when its center reaches point C and the normal force it exerts on the rod at this point. The
The roller-coaster car has mass M, including its passenger, and starts from the top of the hill A with a speed vA. Determine the minimum height h of the hill crest so that the car travels around both
The spring has stiffness k and unstretched length L. If it is attached to the smooth collar of weight W and the collar is released from rest at A, determine the speed of the collar just before it
Two equal-length springs having stiffnesses kA and kB are “nested” together in order to form a shock absorber. If a block of mass M is dropped from an at-rest position a distance h above the top
Just for fun, two engineering students each of weight W, A and B, intend to jump off the bridge from rest using an elastic cord (bungee cord) having stiffness k. They wish to just reach the surface
The bob of mass M of a pendulum is fired from rest at position A. If the spring is compressed to a distance δ and released, determine (a) Its stiffness k so that the speed of the bob is zero when it
The roller-coaster car has a speed vA 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 B.
The Raptor is an outside loop roller coaster in which riders are belted into seats resembling ski-lift chairs. Determine the minimum speed v0 at which the cars should coast down from the top of the
The Raptor is an outside loop roller coaster in which riders are belted into seats resembling ski-lift chairs. If the cars travel at v0 when they are at the top of the hill, determine their speed
A block having a mass M is attached to four springs. If each spring has a stiffness k and an unstretched length δ, determine the maximum downward vertical displacement smax of the block if it is
The ball has weight W and is fixed to a rod having a negligible mass. If it is released from rest when θ = 0°, determine the angle θ at which the compressive force in the rod becomes zero.
A block of weight W slides down an inclined plane of angle θ with initial velocity v0. Determine the velocity of the block at time t1 if the coefficient of kinetic friction between the block and
A ball of weight W is thrown in the direction shown with an initial speed vA. Determine the time needed for it to reach its highest point B and the speed at which it is traveling at B. Use the
A block of weight W is given an initial velocity v0 up a smooth slope of angle θ. Determine the time it will take to travel up the slope before it stops. Given: W = 5 lb VO 10 = 8 = DO S 45 deg ft =
The choice of a seating material for moving vehicles depends upon its ability to resist shock and vibration. From the data shown in the graphs, determine the impulses created by a falling weight onto
The baseball has a horizontal speed v1 when it is struck by the bat B. If it then travels away at an angle θ from the horizontal and reaches a maximum height h, measured from the height of the bat,
A solid-fueled rocket can be made using a fuel grain with either a hole (a), or starred cavity (b), in the cross section. From experiment the engine thrust-time curves (T vs. t) for the same amount
A man hits the golf ball of mass M such that it leaves the tee at angle θ with the horizontal and strikes the ground at the same elevation a distance d away. Determine the impulse of the club C on
During operation the breaker hammer develops on the concrete surface a force which is indicated in the graph. To achieve this the spike S of weight W is fired from rest into the surface at speed v.
The jet plane has a mass M and a horizontal velocity v0 when t = 0. If both engines provide a horizontal thrust which varies as shown in the graph, determine the plane’s velocity at time t1.
The particle P is acted upon by its weight W and forces F1 = (ai + btj + ctk) and F2 = dt2i. If the particle originally has a velocity of v1 = (v1xi+v1yj+v1zk), determine its speed after time t1.
A man kicks the ball of mass M such that it leaves the ground at angle θ with the horizontal and strikes the ground at the same elevation a distance d away. Determine the impulse of his foot F on

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