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engineering
engineering mechanics dynamics

Questions and Answers of Engineering Mechanics Dynamics

The end of a chain of length \(L\) and mass \(ho\) per unit length which is piled on a platform is lifted vertically with a constant velocity \(v\) by a variable force \(P\). Find \(P\) as a function
A rocket of initial total mass \(m_{0}\) is fired vertically up from the north pole and accelerates until the fuel, which burns at a constant rate, is exhausted. The relative nozzle velocity of the
A 75-kg man stands on a spring scale in an elevator. During the first 3 seconds of motion from rest, the tension \(T\) in the hoisting cable is \(8300 \mathrm{~N}\). Find the reading \(R\) of the
A small inspection car with a mass of \(200 \mathrm{~kg}\) runs along the fixed overhead cable and is controlled by the attached cable at \(A\). Determine the acceleration of the car when the control
The 250-lb concrete block \(A\) is released from rest in the position shown and pulls the \(400-\mathrm{lb} \log\) up the \(30^{\circ} \mathrm{ramp}\). If the coefficient of kinetic friction between
The design model for a new ship has a mass of \(10 \mathrm{~kg}\) and is tested in an experimental towing tank to determine its resistance to motion through the water at various speeds. The test
The collar of mass \(m\) slides up the vertical shaft under the action of a force \(F\) of constant magnitude but variable direction. If \(\theta=k t\) where \(k\) is a constant and if the collar
Determine the maximum speed \(v\) which the sliding block may have as it passes the topmost point \(A\) without losing contact with the lower surface. Assume a slightly loose fit between the slider
Small objects are released from rest at \(A\) and slide down the smooth circular surface of radius \(R\) to a conveyor \(B\). Determine the expression for the normal contact force \(N\) between the
A \(1500-\mathrm{kg}\) car enters a section of curved road in the horizontal plane and slows down at a uniform rate from a speed of \(100 \mathrm{~km} / \mathrm{h}\) at \(A\) to a speed of \(50
Compute the magnitude \(v\) of the velocity required for the spacecraft \(S\) to maintain a circular orbit of altitude \(200 \mathrm{mi}\) above the surface of the earth. h R S n t' S F= G mme (R+ h)
Tube \(A\) rotates about the vertical \(O\)-axis with a constant angular rate \(\dot{\theta}=\omega\) and contains a small cylindrical plug \(B\) of mass \(m\) whose radial position is controlled by
Calculate the velocity \(v\) of the \(50 \mathrm{~kg}\) crate when it reaches the bottom of the chute at \(B\) if it is given an initial velocity of \(4 \mathrm{~m} / \mathrm{s}\) down the chute at
The flatbed truck, which carries an 80-kg crate, starts from rest and attains a speed of \(72 \mathrm{~km} / \mathrm{h}\) in a distance of \(75 \mathrm{~m}\) on a level road with constant
The 50-kg block at \(A\) is mounted on rollers so that it moves along the fixed horizontal rail with negligible friction under the action of the constant 300-N force in the cable. The block is
The power winch \(A\) hoists the \(800-\mathrm{lb}\) log up the \(30^{\circ}\) incline at a constant speed of \(4 \mathrm{ft} / \mathrm{sec}\). If the power output of the winch is \(6 \mathrm{hp}\),
A satellite of mass \(m\) is put into an elliptical orbit around the earth. At point \(A\), its distance from the earth is \(h_{1}=500 \mathrm{~km}\) and it has a velocity \(v_{1}=30000 \mathrm{~km}
The 6-lb slider is released from rest at position 1 and slides with negligible friction in a vertical plane along the circular rod. The attached spring has a stiffness of \(2 \mathrm{lb} /
The 10-kg slider moves with negligible friction up the inclined guide. The attached spring has a stiffness of \(60 \mathrm{~N} / \mathrm{m}\) and is stretched \(0.6 \mathrm{~m}\) in position \(A\),
The system shown is released from rest with the lightweight slender bar \(O A\) in the vertical position shown. The torsional spring at \(O\) is undeflected in the initial position and exerts a
A tennis player strikes the tennis ball with her racket when the ball is at the uppermost point of its trajectory as shown. The horizontal velocity of the ball just before impact with the racket is
A 2-lb particle moves in the vertical \(y\) - \(z\) plane ( \(z\) up, \(y\) horizontal) under the action of its weight and a force \(\mathbf{F}\) which varies with time. The linear momentum of the
A particle with a mass of \(0.5 \mathrm{~kg}\) has a velocity of \(10 \mathrm{~m} / \mathrm{s}\) in the \(x\)-direction at time \(t=0\). Forces \(\mathbf{F}_{1}\) and \(\mathbf{F}_{2}\) act on the
The loaded \(150-\mathrm{kg}\) skip is rolling down the incline at \(4 \mathrm{~m} / \mathrm{s}\) when a force \(P\) is applied to the cable as shown at time \(t=0\). The force \(P\) is increased
The \(50-\mathrm{g}\) bullet traveling at \(600 \mathrm{~m} / \mathrm{s}\) strikes the 4 - \(\mathrm{kg}\) block centrally and is embedded within it. If the block slides on a smooth horizontal plane
A small sphere has the position and velocity indicated in the figure and is acted upon by the force \(F\). Determine the angular momentum \(\mathbf{H}_{O}\) about point \(O\) and the time derivative
A comet is in the highly eccentric orbit shown in the figure. Its speed at the most distant point \(A\), which is at the outer edge of the solar system, is \(v_{A}=740 \mathrm{~m} / \mathrm{s}\).
The assembly of the light rod and two end masses is at rest when it is struck by the falling wad of putty traveling with speed \(v_{1}\) as shown. The putty adheres to and travels with the right-hand
A small mass particle is given an initial velocity \(\mathbf{v}_{0}\) tangent to the horizontal rim of a smooth hemispherical bowl at a radius \(r_{0}\) from the vertical centerline, as shown at
The ram of a pile driver has a mass of \(800 \mathrm{~kg}\) and is released from rest \(2 \mathrm{~m}\) above the top of the \(2400-\mathrm{kg}\) pile. If the ram rebounds to a height of \(0.1
A ball is projected onto the heavy plate with a velocity of \(50 \mathrm{ft} / \mathrm{sec}\) at the \(30^{\circ}\) angle shown. If the effective coefficient of restitution is 0.5 , compute the
Spherical particle 1 has a velocity \(v_{1}=6 \mathrm{~m} / \mathrm{s}\) in the direction shown and collides with spherical particle 2 of equal mass and diameter and initially at rest. If the
An artificial satellite is launched from point \(B\) on the equator by its carrier rocket and inserted into an elliptical orbit with a perigee altitude of \(2000 \mathrm{~km}\). If the apogee
A simple pendulum of mass \(m\) and length \(r\) is mounted on the flatcar, which has a constant horizontal acceleration \(a_{0}\) as shown. If the pendulum is released from rest relative to the
The flatcar moves with a constant speed \(v_{0}\) and carries a winch which produces a constant tension \(P\) in the cable attached to the small carriage. The carriage has a mass \(m\) and rolls
A ball is thrown vertically upward with an initial speed of \(80 \mathrm{ft} / \mathrm{sec}\) from the base \(A\) of a \(50-\mathrm{ft}\) cliff. Determine the distance \(h\) by which the ball clears
The car is traveling at a constant speed \(v_{0}=100\) \(\mathrm{km} / \mathrm{h}\) on the level portion of the road. When the 6-percent \((\tan \theta=6 / 100)\) incline is encountered, the driver
In the final stages of a moon landing, the lunar module descends under retrothrust of its descent engine to within \(h=5 \mathrm{~m}\) of the lunar surface where it has a downward velocity of \(2
A girl rolls a ball up an incline and allows it to return to her. For the angle \(\theta\) and ball involved, the acceleration of the ball along the incline is constant at \(0.25 \mathrm{~g}\),
A motorcycle starts from rest with an initial acceleration of \(3 \mathrm{~m} / \mathrm{s}^{2}\), and the acceleration then changes with distance \(s\) as shown. Determine the velocity \(v\) of the
The cone falling with a speed \(v_{0}\) strikes and penetrates the block of packing material. The acceleration of the cone after impact is \(a=g-c y^{2}\), where \(c\) is a positive constant and
The \(x\) - and \(y\)-motions of guides \(A\) and \(B\) with rightangle slots control the curvilinear motion of the connecting pin \(P\), which slides in both slots. For a short interval, the motions
A rocket runs out of fuel in the position shown and continues in unpowered flight above the atmosphere. If its velocity in this position was \(600 \mathrm{mi} / \mathrm{hr}\), calculate the maximum
Calculate the minimum possible magnitude \(u\) of the muzzle velocity which a projectile must have when fired from point \(A\) to reach a target \(B\) on the same horizontal plane \(12 \mathrm{~km}\)
The water nozzle ejects water at a speed \(v_{0}=45\) \(\mathrm{ft} / \mathrm{sec}\) at the angle \(\theta=40^{\circ}\). Determine where, relative to the wall base point \(B\), the water lands.
A football player attempts a 30-yd field goal. If he is able to impart a velocity \(u\) of \(100 \mathrm{ft} / \mathrm{sec}\) to the ball, compute the minimum angle \(\theta\) for which the ball will
An experimental fireworks shell is launched vertically from point \(A\) with an initial velocity of magnitude \(v_{0}=100 \mathrm{ft} / \mathrm{sec}\). In addition to the acceleration due to gravity,
A bicycle is placed on a service rack with its wheels hanging free. As part of a bearing test, the front wheel is spun at the rate \(N=45 \mathrm{rev} / \mathrm{min}\). Assume that this rate is
Six acceleration vectors are shown for the car whose velocity vector is directed forward. For each acceleration vector describe in words the instantaneous motion of the car. 04 az a2 a5 an V
The design of a camshaft-drive system of a fourcylinder automobile engine is shown. As the engine is revved up, the belt speed \(v\) changes uniformly from \(3 \mathrm{~m} / \mathrm{s}\) to \(6
The direction of motion of a flat tape in a numericalcontrol device is changed by the two pulleys \(A\) and \(B\) shown. If the speed of the tape increases uniformly from \(2 \mathrm{~m} /
The sphere \(P\) travels in a straight line with speed \(v=10 \mathrm{~m} / \mathrm{s}\). For the instant depicted, determine the corresponding values of \(\dot{r}\) and \(\dot{\theta}\) as measured
The racing airplane is beginning an inside loop in the vertical plane. The tracking station at \(O\) records the following data for a particular instant: \(r=90 \mathrm{~m}\), \(\dot{r}=15.5
An industrial robot is being used to position a small part \(P\). Calculate the magnitude of the acceleration \(\mathbf{a}\) of \(P\) for the instant when \(\beta=30^{\circ}\) if \(\dot{\beta}=10
The car \(A\) is ascending a parking-garage ramp in the form of a cylindrical helix of 24 - \(\mathrm{ft}\) radius rising \(10 \mathrm{ft}\) for each half turn. At the position shown the car has a
In a design test of the actuating mechanism for a telescoping antenna on a spacecraft, the supporting shaft rotates about the fixed \(z\)-axis with an angular rate \(\dot{\theta}\). Determine the
Car \(A\) rounds a curve of \(150-\mathrm{m}\) radius at a constant speed of \(54 \mathrm{~km} / \mathrm{h}\). At the instant represented, car \(B\) is moving at \(81 \mathrm{~km} / \mathrm{h}\) but
A marathon participant \(R\) is running north at a speed \(v_{R}=10 \mathrm{mi} / \mathrm{hr}\). A wind is blowing in the direction shown at a speed \(v_{W}=15 \mathrm{mi} / \mathrm{hr}\).(a)
A ferry is moving due east and encounters a southwest wind of speed \(v_{W}=10 \mathrm{~m} / \mathrm{s}\) as shown. The experienced ferry captain wishes to minimize the effects of the wind on the
Starting from the relative position shown, aircraft \(B\) is to rendezvous with the refueling tanker \(A\). If \(B\) is to arrive in close proximity to \(A\) in a two-minute time interval, what
The aircraft \(A\) with radar detection equipment is flying horizontally at an altitude of \(12 \mathrm{~km}\) and is increasing its speed at the rate of \(1.2 \mathrm{~m} / \mathrm{s}\) each second.
If block \(A\) has a velocity of \(3.6 \mathrm{ft} / \mathrm{sec}\) to the right, determine the velocity of cylinder \(B\). A B
A truck equipped with a power winch on its front end pulls itself up a steep incline with the cable and pulley arrangement shown. If the cable is wound up on the drum at the constant rate of \(40
The position coordinate of a particle which is confined to move along a straight line is given by \(s=2 t^{3}-24 t+6\), where \(s\) is measured in meters from a convenient origin and \(t\) is in
A particle moves along the \(x\)-axis with an initial velocity \(v_{x}=50 \mathrm{ft} / \mathrm{sec}\) at the origin when \(t=0\). For the first 4 seconds it has no acceleration, and thereafter it is
The spring-mounted slider moves in the horizontal guide with negligible friction and has a velocity \(v_{0}\) in the \(s\)-direction as it crosses the mid-position where \(s=0\) and \(t=0\). The two
A freighter is moving at a speed of 8 knots when its engines are suddenly stopped. (1) If it takes 10 minutes for the freighter to reduce its speed to 4 knots, determine and plot the distance \(s\)
The curvilinear motion of a particle is defined by \(v_{x}=50-16 t\) and \(y=100-4 t^{2}\), where \(v_{x}\) is in meters per second, \(y\) is in meters, and \(t\) is in seconds. It is also known that
To anticipate the dip and hump in the road, the driver of a car applies her brakes to produce a uniform deceleration. Her speed is \(100 \mathrm{~km} / \mathrm{h}\) at the bottom \(A\) of the dip and
A certain rocket maintains a horizontal attitude of its axis during the powered phase of its flight at high altitude. The thrust imparts a horizontal component of acceleration of \(20 \mathrm{ft} /
Rotation of the radially slotted arm is governed by \(\theta=0.2 t+0.02 t^{3}\), where \(\theta\) is in radians and \(t\) is in seconds. Simultaneously, the power screw in the arm engages the slider
A tracking radar lies in the vertical plane of the path of a rocket which is coasting in unpowered flight above the atmosphere. For the instant when \(\theta=30^{\circ}\), the tracking data give
The power screw starts from rest and is given a rotational speed \(\dot{\theta}\) which increases uniformly with time \(t\) according to \(\dot{\theta}=k t\), where \(k\) is a constant. Determine the
An aircraft \(P\) takes off at \(A\) with a velocity \(v_{0}\) of \(250 \mathrm{~km} / \mathrm{h}\) and climbs in the vertical \(y^{\prime}-z^{\prime}\) plane at the constant \(15^{\circ}\) angle
Passengers in the jet transport \(A\) flying east at a speed of \(800 \mathrm{~km} / \mathrm{h}\) observe a second jet plane \(B\) that passes under the transport in horizontal flight. Although the
Car \(A\) is accelerating in the direction of its motion at the rate of \(3 \mathrm{ft} / \mathrm{sec}^{2}\). Car \(B\) is rounding a curve of \(440-\mathrm{ft}\) radius at a constant speed of \(30
The pipe has a mass M and is held in place on the truck bed using the two boards A and B. Determine the acceleration of the truck so that the pipe begins to lose contact at A and the bed of the truck
The drop gate at the end of the trailer has mass M and mass center at G. If it is supported by the cable AB and hinge at C, determine the tension in the cable when the truck begins to accelerate at
The sports car has mass M and a center of mass at G. Determine the shortest time it takes for it to reach speed v, starting from rest, if the engine only drives the rear wheels, whereas the front
Angular motion is transmitted from a driver wheel A to the driven wheel B by friction between the wheels at C. If A always rotates at constant rate ωA and the coefficient of kinetic friction between
The conical spool rolls on the plane without slipping. If the axle has an angular velocity ω1 and an angular acceleration α1 at the instant shown, determine the angular velocity and angular
Gear A is fixed while gear B is free to rotate on the shaft S. If the shaft is turning about the z axis with angular velocity ωz, while increasing at rate αz, determine the velocity and
If the hoop has a weight W and radius r and is thrown onto a rough surface with a velocity vG parallel to the surface, determine the amount of backspin, ω0, it must be given so that it stops
If the collar at A is moving downward with an acceleration aA, at the instant its speed is vA, determine the acceleration of the collar at B at this instant. Given: VA = 8 ft S a = 3 ft c = 2 ft
Gear A is fixed to the crankshaft S, while gear C is fixed and gear B and the propeller are free to rotate. The crankshaft is turning with angular velocity ωs about its axis. Determine the
The cone rolls without slipping such that at the instant shown ωz and ω'z are given. Determine the velocity and acceleration of point B at this instant. Given: (0₂ = 4 00₂ = 3 rad S rad 2 S
If the plate gears A and B are rotating with the angular velocities shown, determine the angular velocity of gear C about the shaft DE. What is the angular velocity of DE about the y axis? Given: A =
The right circular cone rotates about the z axis at a constant rate ω1 without slipping on the horizontal plane. Determine the magnitudes of the velocity and acceleration of points B and C.
Rod AB is attached to a disk and a collar by ball and-socket joints. If the disk is rotating with an angular acceleration α, and at the instant shown has an angular velocity ω, determine the
Rod AB is attached to a disk and a collar by ball-and-socket joints. If the disk is rotating at a constant angular velocity ω, determine the velocity and acceleration of the collar at A at the
The rod BC is attached to collars at its ends by ball-and-socket joints. If disk A has angular velocity ωA, determine the angular velocity of the rod and the velocity of collar B at the instant
The rod AB is attached to collars at its ends by ball-and-socket joints. If collar A has a speed vA, determine the speed of collar B at the instant shown. Given: VA 20 = a = 2 ft b = 6 ft ft S 8 = 45
The rod is attached to smooth collars A and B at its ends using ball-and-socket joints. At the instant shown, A is moving with speed vA and is decelerating at the rate aA. Determine the acceleration
Rod AB is attached to collars at its ends by using ball-and-socket joints. If collar A moves along the fixed rod with a velocity vA and has an acceleration aA at the instant shown, determine the
The rod is attached to smooth collars A and B at its ends using ball-and-socket joints. Determine the speed of B at the instant shown if A is moving with speed vA. Also, determine the angular
Rod AB is attached to collars at its ends by using ball-and-socket joints. If collar A moves along the fixed rod with speed vA, determine the angular velocity of the rod and the velocity of collar B
The pendulum consists of two rods: AB is pin supported at A and swings only in the y-z plane, whereas a bearing at B allows the attached rod BD to spin about rod AB. At a given instant, the rods have
The pendulum consists of two rods: AB is pin supported at A and swings only in the y-z plane, whereas a bearing at B allows the attached rod BD to spin about rod AB. At a given instant, the rods have
At a given instant, rod BD is rotating about the y axis with angular velocity ωBD and angular acceleration ω'BD. Also, when θ = θ1, link AC is rotating downward such that θ' = ω2 and θ'' =
During the instant shown the frame of the X-ray camera is rotating about the vertical axis at ωz and ω'z. Relative to the frame the arm is rotating at ωrel and ω'rel. Determine the velocity and

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