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engineering
engineering mechanics dynamics

Questions and Answers of Engineering Mechanics Dynamics

The arm is rotating at the rate θ' when the angular acceleration is θ'' and the angle is θ0. Determine the normal force it must exert on the particle of mass M if the particle is confined to move
The pilot of an airplane executes a vertical loop which in part follows the path of a “four-leaved rose,” r = a cos 2θ . If his speed at A is a constant vp, determine the vertical reaction the
The collar has mass M and travels along the smooth horizontal rod defined by the equiangular spiral r = aeθ. Determine the tangential force F and the normal force NC acting on the collar when θ =
Using a forked rod, a smooth cylinder C having a mass M is forced to move along the vertical slotted path r = aθ. If the angular position of the arm is θ = bt2, determine the force of the rod on
The ball has mass M and a negligible size. It is originally traveling around the horizontal circular path of radius r0 such that the angular rate of rotation is θ'0. If the attached cord ABC is
The forked rod is used to move the smooth particle of weight W around the horizontal path in the shape of a limacon r = a + bcosθ. If θ = ct2, determine the force which the rod exerts on the
The smooth particle has mass M. It is attached to an elastic cord extending from O to P and due to the slotted arm guide moves along the horizontal circular path r = b sin θ. If the cord has
Determine the normal and frictional driving forces that the partial spiral track exerts on the motorcycle of mass M at the instant θ, θ', and θ''. Neglect the size of the motorcycle. Units
The smooth particle has mass M. It is attached to an elastic cord extending from O to P and due to the slotted arm guide moves along the horizontal circular path r = b sin θ. If the cord has
The collar of weight W slides along the smooth vertical spiral rod r = bθ, where θ is in radians. If its angular rate of rotation θ' is constant, determine the tangential force P needed to cause
The collar of weight W slides along the smooth horizontal spiral rod r = bθ, where θ is in radians. If its angular rate of rotation θ' is constant, determine the tangential force P needed to cause
A smooth can C, having a mass M, is lifted from a feed at A to a ramp at B by a rotating rod. If the rod maintains a constant angular velocity of θ', determine the force which the rod exerts on the
The particle has mass M and is confined to move along the smooth horizontal slot due to the rotation of the arm OA. Determine the force of the rod on the particle and the normal force of the slot on
The particle has mass M and is confined to move along the smooth horizontal slot due to the rotation of the arm OA. Determine the force of the rod on the particle and the normal force of the slot on
The particle of weight W is guided along the circular path using the slotted arm guide. If the arm has angular velocity θ' and angular acceleration θ'' at the instant θ = θ1, determine the force
The spring-held follower AB has weight W and moves back and forth as its end rolls on the contoured surface of the cam, where the radius is r and z = asin(2θ). If the cam is rotating at a constant
The spring-held follower AB has weight W and moves back and forth as its end rolls on the contoured surface of the cam, where the radius is r and z = a sin(2θ). If the cam is rotating at a constant
The spool of mass M slides along the rotating rod. At the instant shown, the angular rate of rotation of the rod is θ', which is increasing at θ''. At this same instant, the spool is moving outward
The girl has a mass M. She is seated on the horse of the merry-go-round which undergoes constant rotational motion θ'. If the path of the horse is defined by r = r0, z = b sin(θ), determine the
Ball A is released from rest at height h1 at the same time that a second ball B is thrown upward from a distance h2 above the ground. If the balls pass one another at a height h3 determine the speed
A car starts from rest and moves along a straight line with an acceleration a = k s−1/3. Determine the car’s velocity and position at t = t1.Given: $9 = [₁ 3 S 6 m E = Y
The acceleration of a rocket traveling upward is given by ap = b + c sp. Determine the rocket’s velocity when sp = sp1 and the time needed to reach this altitude. Initially, vp = 0 and sp = 0 when
A particle has an initial speed v0. If it experiences a deceleration a = bt, determine its velocity when it travels a distance s1. How much time does this take? Given: vo Vo = 27 S b = -6 m 3 S $1 =
A stone A is dropped from rest down a well, and at time t1 another stone B is dropped from rest. Determine the time interval between the instant A strikes the water and the instant B strikes the
A particle is moving with velocity v0 when s = 0 and t = 0. If it is subjected to a deceleration of a −kv3= , where k is a constant, determine its velocity and position as functions of time.
A truck traveling along a straight road at speed v1, increases its speed to v2 in time t. If its acceleration is constant, determine the distance traveled. Given: VI = 20 km hr V2 = 120 km hr t = 15 s
The position of a particle along a straight line is given by sp = at3 + bt2 + ct. Determine its maximum acceleration and maximum velocity during the time interval t0 ≤ t ≤ tf. Given: a = 1 ft b =
A baseball is thrown downward from a tower of height h with an initial speed v0. Determine the speed at which it hits the ground and the time of travel. Given: h = 50 ft 8 = 32.2 2 S Vo ft = 18. S
Starting from rest, a particle moving in a straight line has an acceleration of a = (bt + c). What is the particle’s velocity at t1 and what is its position at t2? Given: b = 2 w|B 3 S c =
The acceleration of a particle as it moves along a straight line is given by a = bt + c. If s = s0 and v = v0 when t = 0, determine the particle’s velocity and position when t = t1. Also, determine
A car starts from rest and reaches a speed v after traveling a distance d along a straight road. Determine its constant acceleration and the time of travel. Given: V = 80 ft S d = 500 ft
A particle moves along a straight line such that its position is defined by sp = at3 + bt2 + c. Determine the average velocity, the average speed, and the acceleration of the particle at time t1.
The velocity of a particle traveling in a straight line is given v = bt + ct2. If s = 0 when t = 0, determine the particle’s deceleration and position when t = t1. How far has the particle traveled
A particle is moving along a straight line such that its acceleration is defined as a = −kv. If v = v0 when d = 0 and t = 0, determine the particle’s velocity as a function of position and the
Traveling with an initial speed v0 a car accelerates at rate a along a straight road. How long will it take to reach a speed vf ? Also, through what distance does the car travel during this time? VO
The acceleration of a rocket traveling upward is given by ap = b + c sp. Determine the time needed for the rocket to reach an altitute sp1. Initially, vp = 0 and sp = 0 when t = 0. Given: b =
The elevator starts from rest at the first floor of the building. It can accelerate at rate a1 and then decelerate at rate a2. Determine the shortest time it takes to reach a floor a distance d above
A freight train travels at v = v0 (1− e−bt) where t is the elapsed time. Determine the distance traveled in time t1, and the acceleration at this time. Given: VO = 60 = S t1 = 3 s S
From approximately what floor of a building must a car be dropped from an at-rest position so that it reaches a speed vf when it hits the ground? Each floor is a distance h higher than the one below
A car is to be hoisted by elevator to the fourth floor of a parking garage, which is at a height h above the ground. If the elevator can accelerate at a1, decelerate at a2, and reach a maximum speed
A particle moves along a straight line such that its position is defined by s = bt2 + ct + d. Determine the average velocity, the average speed, and the acceleration of the particlewhen t = t1.
A particle is moving along a straight line such that when it is at the origin it has a velocity v0. If it begins to decelerate at the rate a = bv1/2 determine the particle’s position and velocity
A particle, initially at the origin, moves along a straight line through a fluid medium such that its velocity is defined as v = b(1− e−ct). Determine the displacement of the particle during the
A stone A is dropped from rest down a well, and at time t1 another stone B is dropped from rest. Determine the distance between the stones at a later time t2. Given: d = 80 ft t₁ = 1 s t2 = 2 s 8 =
A particle travels to the right along a straight line with a velocity vp = a / (b + sp). Determine its deceleration when sp = sp1. Given: a = 5 m S b = 4 m Spl = 2 m
Two particles A and B start from rest at the origin s = 0 and move along a straight line such that aA = (at − b) and aB = (ct2 − d), where t is in seconds. Determine the distance between them at
A car can have an acceleration and a deceleration a. If it starts from rest, and can have a maximum speed v, determine the shortest time it can travel a distance d at which point it stops. Given: a =
An airplane starts from rest, travels a distance d down a runway, and after uniform acceleration, takes off with a speed vr It then climbs in a straight line with a uniform acceleration aa until it
A particle has an initial speed v0. If it experiences a deceleration a = bt, determine the distance traveled before it stops. Given: v0 = 27 Vo m S b = -6 m 3 S
The acceleration of a particle along a straight line is defined by ap = b t + c. At t = 0, sp = sp0 and vp = vp0. When t = t1 determine(a) The particle's position,(b) The total distance traveled,(c)
The v-t graph for a particle moving through an electric field from one plate to another has the shape shown in the figure, where tf and vmax are given. Draw the s-t and a-t graphs for the particle.
A particle is moving along a straight line such that its acceleration is defined as a = k s2. If v = v0 when s = sp0 and t = 0, determine the particle’s velocity as a function of position. Given: k
If the position of a particle is defined as s = bt + ct2, construct the s–t, v–t, and a–t graphs for 0 ≤ t ≤ T. Given: b = 5 ft c = -3 ft T = 10 s t = 0,0.017.. T
Determine the time required for a car to travel a distance d along a road if the car starts from rest, reaches a maximum speed at some intermediate point, and then stops at the end of the road. The
The v-t graph for a particle moving through an electric field from one plate to another has the shape shown in the figure. The acceleration and deceleration that occur are constant and both have a
When two cars A and B are next to one another, they are traveling in the same direction with speeds vA0 and vB0 respectively. If B maintains its constant speed, while A begins to decelerate at the
A car travels along a straight road with the speed shown by the v–t graph. Determine the total distance the car travels until it stops at t2. Also plot the s–t and a–t graphs. Given: t₁ = 30
If the effects of atmospheric resistance are accounted for, a freely falling body has an acceleration defined by the equation a = g(1− cv2), where the positive direction is downward. If the body is
A motorcycle starts from rest at s = 0 and travels along a straight road with the speed shown by the v-t graph. Determine the motorcycle's acceleration and position when t = t4 and t = t5. Given: v0
From experimental data, the motion of a jet plane while traveling along a runway is defined by the v–t graph shown. Construct the s-t and a-t graphs for the motion. Given: VI = 80 El t1 = 10 s 12 =
A car starting from rest moves along a straight track with an acceleration as shown. Determine the time t for the car to reach speed v. Given: v = 50 a1 = 8 a] m S m 2 S t1 = 10 s
If the position of a particle is defined by sp = b sin(ct) + d, construct the s-t, v-t, and a-t graphs for 0 ≤ t ≤ T. Given: b = 2 m 1 5 S C =- d = 4 m T = 10 s t = 0,0.017..T
Accounting for the variation of gravitational acceleration a with respect to altitude y (see Prob. 12-34), derive an equation that relates the velocity of a freely falling particle to its altitude.
As a body is projected to a high altitude above the earth ’s surface, the variation of the acceleration of gravity with respect to altitude y must be taken into account. Neglecting air resistance,
When a particle falls through the air, its initial acceleration a = g diminishes until it is zero, and thereafter it falls at a constant or terminal velocity vf. If this variation of the acceleration
The v–t graph for the motion of a train as it moves from station A to station B is shown. Draw the a–t graph and determine the average speed and the distance between the stations. Given: t1 = 30
The a–t graph for a motorcycle traveling along a straight road has been estimated as shown. Determine the time needed for the motorcycle to reach a maximum speed vmax and the distance traveled in
The v-t graph for the motion of a car as if moves along a straight road is shown. Draw the a-t graph and determine the maximum acceleration during the time interval 0 2. The car starts from rest at s
Two cars start from rest side by side and travel along a straight road. Car A accelerates at the rate aA for a time t1, and then maintains a constant speed. Car B accelerates at the rate aB until
The a–s graph for a boat moving along a straight path is given. If the boat starts at s = 0 when v = 0, determine its speed when it is at s = s2, and s3, respectively. Use Simpson’s rule with n
The s–t graph for a train has been experimentally determined. From the data, construct the v–t and a–t graphs for the motion; 0 ≤ t ≤ t2. For 0 ≤ t ≤ t1, the curve is a parabola, and
A two-stage rocket is fired vertically from rest at s = 0 with an acceleration as shown. After time t1 the first stage A burns out and the second stage B ignites. Plot the v-t and s-t graphs which
The v-t graph for the motion of a car as it moves along a straight road is shown. Draw the s-t graph and determine the average speed and the distance traveled for the time interval 0 2. The car
A motorcyclist at A is traveling at speed v1 when he wishes to pass the truck T which is traveling at a constant speed v2. To do so the motorcyclist accelerates at rate a until reaching a maximum
The v-s graph for a go-cart traveling on a straight road is shown. Determine the acceleration of the go-cart at s3 and s4. Draw the a-s graph. Given: VI = 8 m S $1 = 100 m $2 = 200 m $3 = 50 m $4 =
The a–t graph for a car is shown. Construct the v–t and s–t graphs if the car starts from rest at t = 0. At what time t' does the car stop? Given: aj || a2 = จ Ele t] = 10 s
The a-s graph for a train traveling along a straight track is given for 0 ≤ s ≤ s2. Plot the v-s graph. v = 0 at s = 0.Given: $1 = 200 m $2 = 400 m a₁ = 2 m 2 S
The v-s graph for an airplane traveling on a straight runway is shown. Determine the acceleration of the plane at s = s3 and s = s4. Draw the a-s graph. Given: s] = 100 m s4 = 150 m $2 = 200 m vj $3
The jet plane starts from rest at s = 0 and is subjected to the acceleration shown. Determine the speed of the plane when it has traveled a distance d. Also, how much time is required for it to
The jet car is originally traveling at speed v0 when it is subjected to the acceleration shown in the graph. Determine the car’s maximum speed and the time t when it stops. Given: Vo = 20 ao
The v–s graph was determined experimentally to describe the straight-line motion of a rocket sled. Determine the acceleration of the sled at s = s3 and s = s4. Given: VI = 20 v2 = 60 EI S E S $3 =
The v–s graph for a test vehicle is shown. Determine its acceleration at s = s3 and s4. Given: VI = 50 m S s] = 150 m $3 = 100 m $2 = 200 m s4 = 175 m
A particle travels along the curve from A to B in time t1. If it takes time t2 for it to go from A to C, determine its average velocity when it goes from B to C. Given: t₁ = 1 s t1 12 = 3 s r = 20 m
Starting from rest at s = 0, a boat travels in a straight line with an acceleration as shown by the a-s graph. Determine the boat’s speed when s = s4, s5, and s6. Given: $1 = 50 ft $2 = 150 ft $3 =
The velocity of a particle is given by v = [at2i + bt3j + (ct + d)k]. If the particle is at the origin when t = 0, determine the magnitude of the particle's acceleration when t = t1. Also, what is
A particle travels along the curve from A to B in time t1. It takes time t2 for it to go from B to C and then time t3 to go from C to D. Determine its average speed when it goes from A to D. Given:
A particle is traveling with a velocity ofDetermine the magnitude of the particle’s displacement from t = 0 to t1. Use Simpson’s rule with n steps to evaluate the integrals. What is the magnitude
The position of a particle is defined by r = {a cos(bt) i + c sin(bt) j}. Determine the magnitudes of the velocity and acceleration of the particle when t = t1. Also, prove that the path of the
A car traveling along the straight portions of the road has the velocities indicated in the figure when it arrives at points A, B, and C. If it takes time tAB to go from A to B, and then time tBC to
When a rocket reaches altitude h1 it begins to travel along the parabolic path (y − h1)2 = b x. If the component of velocity in the vertical direction is constant at vy = v0, determine the
A particle, originally at rest and located at point (a, b, c), is subjected to an acceleration ac = {d t i + e t2 k}. Determine the particle's position (x, y, z) at time t1. Given: a = 3 ft b = 2
The balloon A is ascending at rate vA and is being carried horizontally by the wind at vw. If a ballast bag is dropped from the balloon when the balloon is at height h, determine the time needed for
A car travels east a distance d1 for time t1, then north a distance d2 for time t2 and then west a distance d3 for time t3. Determine the total distance traveled and the magnitude of displacement of
A particle moves along the curve y = aebx such that its velocity has a constant magnitude of v = v0. Determine the x and y components of velocity when the particle is at y = y1. Given: a = 1 ft b
Determine the minimum speed of the stunt rider, so that when he leaves the ramp at A he passes through the center of the hoop at B. Also, how far h should the landing ramp be from the hoop so that he
The man stands a distance d from the wall and throws a ball at it with a speed v0. Determine the angle θ at which he should release the ball so that it strikes the wall at the highest point
At the instant shown particle A is traveling to the right at speed v1 and has an acceleration a1. Determine the initial speed v0 of particle B so that when it is fired at the same instant from the
Determine the height h on the wall to which the firefighter can project water from the hose, if the angle θ is as specified and the speed of the water at the nozzle is vC. Given: VC = 48 h1 = 3
The flight path of the helicopter as it takes off from A is defined by the parametric equations x = bt2 and y = ct3. Determine the distance the helicopter is from point A and the magnitudes of its
The stones are thrown off the conveyor with a horizontal velocity v = v0 as shown. Determine the speed at which the stones hit the ground at B. Given: Vo = 10 ft S h = 100 ft

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