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engineering
engineering mechanics dynamics

Questions and Answers of Engineering Mechanics Dynamics

A ship with a total displacement of 16 000 metric tons (1 metric ton = 1000 kg) starts from rest in still water under a constant propeller thrust T = 250 kN. The ship develops a total resistance to
At time t = 0, the 1.8-lb particle P is given an initial velocity v0 = 1 ft/sec at the position θ = 0 and subsequently slides along the circular path of radius r = 1.5 ft. Because of the viscous
A projectile is launched from point A with speed v0 = 30 m /s. Determine the value of the launch angle θ which maximizes the range R indicated in the figure. Determine the corresponding value of R.
A low-flying crop duster A is moving with a constant speed of 40 m /s in the horizontal circle of radius 300 m. As it passes the twelve-o’clock position shown at time t = 0, car B starts from rest
A particle P is launched from point A with the initial conditions shown. If the particle is subjected to aerodynamic drag, compute the range R of the particle and compare this with the case in which
By means of the control unit M, the pendulum OA is given an oscillatory motion about the vertical given by θ = θ0sin √g/l t, where θ0 is the maximum angular displacement in radians, g is the
The 50-kg crate is projected along the floor with an initial speed of 8 m /s at x = 0. The coefficient of kinetic friction is 0.40. Calculate the time required for the crate to come to rest and the
The 50-kg crate is stationary when the force P is applied. Determine the resulting acceleration of the crate if (a) P = 0, (b) P = 150 N, and (c) P = 300 N. 씨s = 0.20 %3D Hk = 0.15 50 kg P 15°
At a certain instant, the 80-lb crate has a velocity of 30 ft /sec up the 20° incline. Calculate the time t required for the crate to come to rest and the corresponding distance d traveled. Also,
A man pulls himself up the 15° incline by the method shown. If the combined mass of the man and cart is 100 kg, determine the acceleration of the cart if the man exerts a pull of 175 N on the rope.
For a given value of y, determine the upward velocity of A in terms of the downward velocity of B. Neglect the diameters of the pulleys. 2b y A B Problem 2/219
The small sliders A and B are connected by the rigid slender rod. If the velocity of slider B is 2 m/s to the right and is constant over a certain interval of time, determine the speed of slider A
At the instant represented, vB/A = 3.5j m/s. Determine the velocity of each body at this instant. Assume that the upper surface of A remains horizontal. y L--x A B Problem 2/208
If the velocity x˙ of block A up the incline is increasing at the rate of 0.044 m/s each second, determine the acceleration of B. В Problem 2/207
At a certain instant after jumping from the airplane A, a skydiver B is in the position shown and has reached a terminal (constant) speed vB = 50 m/s. The airplane has the same constant speed vA = 50
A place kicker A executes a “pooch” kick, which is designed to eliminate a potential return by the receiving team. The “pooch” kick features a high trajectory and short range, thereby
A batter hits the baseball A with an initial velocity of v0 = 100 ft/sec directly toward fi elder B at an angle of 30° to the horizontal; the initial position of the ball is 3 ft above ground level.
For the conditions of Prob. 2/201, determine the values of r¨ and θ¨ as measured by an observer in car B at the instant represented. Use the results for r˙ and θ˙ cited in the answers for that
Car A is traveling at the constant speed of 60 km/h as it rounds the circular curve of 300-m radius and at the instant represented is at the position θ = 45°. Car B is traveling at the constant
After starting from the position marked with the “x”, a football receiver B runs the slant-in pattern shown, making a cut at P and thereafter running with a constant speed vB = 7 yd/sec in the
The shuttle orbiter A is in a circular orbit of altitude 200 mi, while spacecraft B is in a geosynchronous circular orbit of altitude 22,300 mi. Determine the acceleration of B relative to a
As part of an unmanned-autonomous-vehicle (UAV) demonstration, an unmanned vehicle B launches a projectile A from the position shown while traveling at a constant speed of 30 km/h. The projectile is
Car A is traveling at 25 mi/hr and applies the brakes at the position shown so as to arrive at the intersection C at a complete stop with a constant deceleration. Car B has a speed of 40 mi/hr at the
For the cars of Prob. 2 /195, determine the instantaneous values of r¨ and θ¨ if car A is slowing down at a rate of 1.25 m/s2 and car B is speeding up at a rate of 2.5 m/s2. Refer to the printed
At the instant illustrated, car B has a speed of 30 km/h and car A has a speed of 40 km/h. Determine the values of r˙ and θ˙ for this instant where r and θ are measured relative to a longitudinal
A sailboat moving in the direction shown is tacking to windward against a north wind. The log registers a hull speed of 6.5 knots. A “telltale” (light string tied to the rigging) indicates that
For the planes of Prob. 2/192, beginning at the position shown, plane A increases its speed at a constant rate and acquires a speed of 415 km/h by the time it reaches position E, while plane B
Plane A travels along the indicated path with a constant speed vA = 285 km/h. Relative to the pilot in plane B, which is flying at a constant speed vB = 350 km/h, what are the velocities which plane
A drop of water falls with no initial speed from point A of a highway overpass. After dropping 6 m, it strikes the windshield at point B of a car which is traveling at a speed of 100 km/h on the
The jet transport B is flying north with a velocity vB = 600 km /h when a smaller aircraft A passes underneath the transport headed in the 60° direction shown. To passengers in B, however, A appears
Train A is traveling at a constant speed vA = 35 mi/hr while car B travels in a straight line along the road as shown at a constant speed vB. A conductor C in the train begins to walk to the rear of
For the instant represented, car A has an acceleration in the direction of its motion, and car B has a speed of 45 mi/hr which is increasing. If the acceleration of B as observed from A is zero for
The car A has a forward speed of 18 km/h and is accelerating at 3 m/s2. Determine the velocity and acceleration of the car relative to observer B, who rides in a nonrotating chair on the Ferris
Train A travels with a constant speed vA = 120 km /h along the straight and level track. The driver of car B, anticipating the railway grade crossing C, decreases the car speed of 90 km/h at the rate
A ship capable of making a speed of 16 knots through still water is to maintain a true course due west while encountering a 3-knot current running from north to south. What should be the heading of
A helicopter approaches a rescue scene. A victim P is drifting along with the river current of speed vC = 2 m/s. The wind is blowing at a speed vW = 3 m/s as indicated. Determine the velocity
Rapid-transit trains A and B travel on parallel tracks. Train A has a speed of 80 km/h and is slowing at the rate of 2 m/s2, while train B has a constant speed of 40 km/h. Determine the velocity and
The disk A rotates about the vertical z-axis with a constant speed ω = θ˙ = π/3 rad/s. Simultaneously, the hinged arm OB is elevated at the constant rate Φ˙ = 2π/3 rad /s. At time t = 0, both
The particle P moves down the spiral path which is wrapped around the surface of a right circular cone of base radius b and altitude h. The angle γ between the tangent to the curve at any point and
In the design of an amusement-park ride, the cars are attached to arms of length R which are hinged to a central rotating collar which drives the assembly about the vertical axis with a constant
Beginning with Eq. 2 /18, the expression for particle velocity in spherical coordinates, derive the acceleration components in Eq. 2 /19. Start by writing the unit vectors for the R-, θ-, and
The rod OA is held at the constant angle β = 30° while it rotates about the vertical with a constant angular rate θ˙= 120 rev/min. Simultaneously, the sliding ball P oscillates along the rod with
The vertical shaft of the industrial robot rotates at the constant rate ω. The length h of the vertical shaft has a known time history, and this is true of its time derivatives h˙ and h¨ as well.
For the helicopter of Prob. 2/172, fi nd the values of R¨ , θ¨, and Φ¨ for the radar tracking device at O at the instant when h = 100 m. Refer to the printed answers for Prob. 2 /172 as
A helicopter starts from rest at point A and travels along the indicated path with a constant acceleration a. If the helicopter has a speed of 60 m/s when it reaches B, determine the values of R˙ ,
The rotating element in a mixing chamber is given a periodic axial movement z = z0 sin 2πnt while it is rotating at the constant angular velocity θ˙ = ω. Determine the expression for the maximum
The radar antenna at P tracks the jet aircraft A, which is flying horizontally at a speed u and an altitude h above the level of P. Determine the expressions for the components of the velocity in the
A projectile is launched from point O at a speed v0 = 80 m/s with the goal of hitting the target A. At the launch instant, a strong horizontal wind begins blowing and imparts a constant acceleration
If the launch speed of the projectile in Prob. 2/167 remains unchanged, what values of θ and Φ (positive and less than 90°) will ensure that the projectile impacts the target at A if the wind
An amusement ride called the “corkscrew” takes the passengers through the upside-down curve of a horizontal cylindrical helix. The velocity of the cars as they pass position A is 15 m/s, and the
A projectile is launched from point O with an initial velocity of magnitude v0 = 600 ft/sec, directed as shown in the figure. Compute the x-, y-, and z-components of position, velocity, and
The rectangular coordinates of a particle are given in millimeters as functions of time t in seconds by x = 30 cos 2t, y = 40 sin 2t, and z = 20t + 3t2. Determine the angle θ1 between the position
A golf ball is driven with the initial conditions shown in the figure. If the wind imparts a constant horizontal deceleration of 4 ft/sec2, determine the values of r, r˙, r¨, θ, θ˙ , and θ¨
At time t = 0, the baseball player releases a ball with the initial conditions shown in the figure. Determine the quantities r, r˙, r¨, θ, θ˙, and θ¨, all relative to the x-y coordinate system
The low-flying aircraft P is traveling at a constant speed of 360 km/h in the holding circle of radius 3 km. For the instant shown, determine the quantities r, r˙, r¨, θ, θ˙ , and θ¨ relative
A meteor P is tracked by a radar observatory on the earth at O. When the meteor is directly overhead (θ = 90°), the following observations are recorded: r = 80 km, r˙ = −20 km/s, and θ˙ = 0.4
An earth satellite traveling in the elliptical orbit shown has a velocity v = 12,149 mi/hr as it passes the end of the semi minor axis at A. The acceleration of the satellite at A is due to
For the conditions of Prob. 2/157, determine θ˙ as a function of time.Data from Prob. 2/157The small block P starts from rest at time t = 0 at point A and moves up the incline with constant
The small block P starts from rest at time t = 0 at point A and moves up the incline with constant acceleration a. Determine r˙ as a function of time. of A А — х -R- Problem 2/157
A locomotive is traveling on the straight and level track with a speed v = 90 km/h and a deceleration a = 0.5 m/s2 as shown. Relative to the fixed observer at O, determine the quantities r˙, r¨,
At the instant depicted in the figure, the radar station at O measures the range rate of the space shuttle P to be r˙ = −12,272 ft/sec, with O considered fixed. If it is known that the shuttle is
The member OA of the industrial robot telescopes and pivots about the fixed axis at point O. At the instant shown, θ = 60°, θ˙ = 1.2 rad/s, θ¨ = 0.8 rad/s2, O̅A̅ = 0.9 m, O̅A̅˙ = 0.5
At the bottom of a loop in the vertical (r-θ) plane at an altitude of 400 m, the airplane P has a horizontal velocity of 600 km / h and no horizontal acceleration. The radius of curvature of the
In addition to the information supplied in the previous problem, the sensors at O indicate that r¨ = 14 ft/sec2. Determine the corresponding acceleration a of the aircraft and the value of θ¨.
Instruments located at O are part of the ground traffic control system for a major airport. At a certain instant during the takeoff roll of the aircraft P, the sensors indicate the angle θ = 50°
The diver leaves the platform with an initial upward speed of 2.5 m /s. A stationary camera on the ground is programmed to track the diver throughout the dive by rotating the lens to keep the diver
Repeat Prob. 2/148, but now the speed of the particle P is decreasing at the rate of 20 m/s2 as it moves along the indicated straight path.Data from Prob. 2/148As it passes the position shown, the
A football player releases a ball with the initial conditions shown in the figure. Determine the radius of curvature ρ of the path and the time rate of change v˙ of the speed at times t = 1 sec and
The figure shows a portion of a plate cam used in the design of a control mechanism. The motion of pin P in the fixed slot of the plate cam is controlled by the vertical guide A, which travels
The preliminary design for a “small” space station to orbit the earth in a circular path consists of a ring (torus) with a circular cross section as shown. The living space within the torus is
As it passes the position shown, the particle P has a constant speed v = 100 m/s along the straight line shown. Determine the corresponding values of r˙, θ˙, r¨, and θ¨. y v = 100 m/s P 30° 80
The rocket is fi red vertically and tracked by the radar station shown. When θ reaches 60°, other corresponding measurements give the values r = 9 km, r¨ = 21m/s2, and θ˙ = 0.02 rad/s. Calculate
For the fireworks shell of Prob. 2 /145, determine the values of r¨ and θ¨ when the shell reaches an altitude y = 175 ft. Refer to the printed answers for Prob. 2/145 as needed.Data from
A fi reworks shell P is launched upward from point A and explodes at its apex at an altitude of 275 ft. Relative to an observer at O, determine the values of r˙ and θ˙ when the shell reaches an
Cars A and B are both moving with constant speed v on the straight and level highway. They are side by- ide in adjacent lanes as shown. If the radar unit attached to the stationary police car P
The slider P can be moved inward by means of the string S, while the slotted arm rotates about point O. The angular position of the arm is given by θ = 0.8t − t2/20 , where θ is in radians and t
A helicopter starts from rest at point A and travels along the straight-line path with a constant acceleration a. If the speed v = 28 m/s when the altitude of the helicopter is h = 40 m, determine
The radial position of a fluid particle P in a certain centrifugal pump with radial vanes is approximated by r = r0 cosh Kt, where t is time and K = θ˙ is the constant angular rate at which the
The nozzle shown rotates with constant angular speed Ω about a fixed horizontal axis through point O. Because of the change in diameter by a factor of 2, the water speed relative to the nozzle at A
Consider the portion of an excavator shown. At the instant under consideration, the hydraulic cylinder is extending at a rate of 6 in. /sec, which is decreasing at the rate of 2 in. /sec every
A particle moving along a plane curve has a position vector r, a velocity v, and an acceleration a. Unit vectors in the r- and θ-directions are er and eθ, respectively, and both r and θ are
The boom OAB pivots about point O, while section AB simultaneously extends from within section OA. Determine the velocity and acceleration of the center B of the pulley for the following conditions:
For the bar of Prob. 2/135, determine the values of r¨ and θ¨ if the velocity of collar C is decreasing at a rate of 5 mm/s2 at the instant in question. Refer to the printed answers for Prob.
Rotation of bar OA is controlled by the lead screw which imparts a horizontal velocity v to collar C and causes pin P to travel along the smooth slot. Determine the values of r˙ and θ˙, where r =
Motion of the sliding block P in the rotating radial slot is controlled by the power screw as shown. For the instant represented, θ˙ = 0.1 rad/s, θ¨ = −0.04 rad /s2, and r = 300 mm. Also, the
A drone flies over an observer O with constant speed in a straight line as shown. Determine the signs (plus, minus, or zero) for r, r˙, r¨, θ, θ˙ , and θ¨ for each of the positions A, B,
The sprinter begins from rest at position A and accelerates along the track. If the stationary tracking camera at O is rotating counterclockwise at the rate of 12.5 deg/s when the sprinter passes the
A car P travels along a straight road with a constant speed v = 65 mi/ hr. At the instant when the angle θ = 60°, determine the values of r˙ in ft/sec and θ˙ in deg/sec. P 100' y Problem 2/131
A projectile is launched at time t = 0 with the initial conditions shown in the figure. If the wind imparts a constant leftward acceleration of 5 m/s2, plot the n- and t-components of acceleration
A particle which moves with curvilinear motion has coordinates in meters which vary with time t in seconds according to x = 2t2 + 3t − 1 and y = 5t − 2. Determine the coordinates of the center of
In a handling test, a car is driven through the slalom course shown. It is assumed that the car path is sinusoidal and that the maximum lateral acceleration is 0.7g. If the testers wish to design a
In the design of a control mechanism, the vertical slotted guide is moving with a constant velocity x˙ = 15 in. /sec during the interval of motion from x = −8 in. to x = +8 in. For the instant
An earth satellite which moves in the elliptical equatorial orbit shown has a velocity v in space of 17 970 km/h when it passes the end of the semi minor axis at A. The earth has an absolute surface
In the design of a timing mechanism, the motion of pin P in the fixed circular slot is controlled by the guide A, which is being elevated by its lead screw. Guide A starts from rest with pin P at the
The particle P starts from rest at point A at time t = 0 and changes its speed thereafter at a constant rate of 2g as it follows the horizontal path shown. Determine the magnitude and direction of
During a short interval the slotted guides are designed to move according to x = 16 − 12t + 4t2 and y = 2 + 15t − 3t2, where x and y are in millimeters and t is in seconds. At the instant when t
Two cars travel at constant speeds through a curved portion of highway. If the front ends of both cars cross line CC at the same instant, and each driver minimizes his or her time in the curve,
A spacecraft S is orbiting Jupiter in a circular path 1000 km above the surface with a constant speed. Using the gravitational law, calculate the magnitude v of its orbital velocity with respect to
If the golf ball of Prob. 2/116 is launched at time t = 0, determine the two times when the radius of curvature of the trajectory has a value of 1800 ft.Data from Prob. 2/116A golf ball is launched
A golf ball is launched with the initial conditions shown in the figure. Determine the radius of curvature of the trajectory and the time rate of change of the speed of the ball (a) just after launch

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