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engineering
engineering mechanics dynamics
Questions and Answers of
Engineering Mechanics Dynamics
A 60-g bullet is fired horizontally with a velocity v1 = 600 m/s into the 3-kg block of soft wood initially at rest on the horizontal surface. The bullet emerges from the block with the velocity v2 =
A 75-g projectile traveling at 600 m/s strikes and becomes embedded in the 40-kg block, which is initially stationary. Compute the energy lost during the impact. Express your answer as an absolute
The velocity of a 1.2-kg particle is given by v = 1.5t3i + (2.4 − 3t2)j + 5k, where v is in meters per second and the time t is in seconds. Determine the linear momentum G of the particle, its
A jet-propelled airplane with a mass of 10 Mg is flying horizontally at a constant speed of 1000 km/h under the action of the engine thrust T and the equal and opposite air resistance R. The pilot
The two orbital maneuvering engines of the space shuttle develop 26 kN of thrust each. If the shuttle is traveling in orbit at a speed of 28 000 km/h, how long would it take to reach a speed of 28
A 0.2-kg wad of clay is released from rest and drops 2 m to a concrete floor. The clay does not rebound, and the collision lasts 0.04 s. Determine the time average of the force which the floor exerts
The two particles of mass m and 2m, respectively, are connected by a rigid rod of negligible mass and slide with negligible friction in a circular path of radius r on the inside of the vertical
The 0.6-kg slider is released from rest at A and slides down the smooth parabolic guide (which lies in a vertical plane) under the influence of its own weight and of the spring of constant 120 N/m.
The system is released from rest with the angle θ = 90°. Determine θ˙ when θ reaches 60°. Use the values m1 = 1 kg, m2 = 1.25 kg, and b = 0.40 m. Neglect friction and the mass of bar OB, and
When the 10-lb plunger is released from rest in its vertical guide at θ = 0, each spring of stiffness k = 20 lb /in. is uncompressed. The links are free to slide through their pivoted collars and
A spacecraft m is heading toward the center of the moon with a velocity of 2000 mi/hr at a distance from the moon’s surface equal to the radius R of the moon. Compute the impact velocity v with the
The system is initially moving with the cable taut, the 10-kg block moving down the rough incline with a speed of 0.3 m/s, and the spring stretched 25 mm. By the method of this article, (a)
Calculate the maximum velocity of slider B if the system is released from rest with x = y. Motion is in the vertical plane. Assume that friction is negligible. The sliders have equal masses, and the
A satellite is put into an elliptical orbit around the earth and has a velocity vP at the perigee position P. Determine the expression for the velocity vA at the apogee position A. The radii to A and
The cars of an amusement-park ride have a speed v1 = 90 km/h at the lowest part of the track. Determine their speed v2 at the highest part of the track. Neglect energy loss due to friction. (Caution:
Upon its return voyage from a space mission, the spacecraft has a velocity of 24 000 km /h at point A, which is 7000 km from the center of the earth. Determine the velocity of the spacecraft when it
A rocket launches an unpowered space capsule at point A with an absolute velocity vA = 8000 mi/hr at an altitude of 25 mi. After the capsule has traveled a distance of 250 mi measured along its
In the design of an inside loop for an amusementpark ride, it is desired to maintain the same centripetal acceleration throughout the loop. Assume negligible loss of energy during the motion and
The two 1.5-kg spheres are released from rest and gently nudged outward from the position θ = 0 and then rotate in a vertical plane about the fixed centers of their attached gears, thus maintaining
The slider of mass m is released from rest in position A and slides without friction along the vertical-plane guide shown. Determine the height h such that the normal force exerted by the guide on
The spring has an unstretched length of 25 in. If the system is released from rest in the position shown, determine the speed v of the ball (a) When it has dropped a vertical distance of 10
The system is released from rest with the spring initially stretched 2 in. Calculate the velocity of the 100-lb cylinder after it has dropped 6 in. Also determine the maximum drop distance of the
The particle of mass m = 1.2 kg is attached to the end of the light rigid bar of length L = 0.6 m. The system is released from rest while in the horizontal position shown, at which the torsional
The two springs, each of stiffness k = 1.2 kN/m, are of equal length and undeformed when θ = 0. If the mechanism is released from rest in the position θ = 20°, determine its angular velocity θ˙
The 0.8-kg particle is attached to the system of two light rigid bars, all of which move in a vertical plane. The spring is compressed an amount b/2 when θ = 0, and the length b = 0.30 m. The system
The system is released from rest with the spring initially stretched 3 in. Calculate the velocity v of the cylinder after it has dropped 0.5 in. The spring has a stiffness of 6 lb /in. Neglect the
The 3-lb collar is released from rest at A and slides freely down the inclined rod. If the spring constant k = 4 lb/ft and the unstretched length of the spring is 50 in., determine the speed of the
The 2-kg plunger is released from rest in the position shown where the spring of stiffness k = 500 N /m has been compressed to one-half its uncompressed length of 200 mm. Calculate the maximum height
The 1.2-kg slider is released from rest in position A and slides without friction along the vertical-plane guide shown. Determine (a) the speed vB of the slider as it passes position B and (b) the
Once under way at a steady speed, the 1000-kg elevator A rises at the rate of 1 story (3 m) per second. Determine the power input Pin into the motor unit M if the combined mechanical and electrical
The two particles of equal mass are joined by a rod of negligible mass. If they are released from rest in the position shown and slide on the smooth guide in the vertical plane, calculate their
The vertical motion of the 50-lb block is controlled by the two forces P applied to the ends A and B of the linkage, where A and B are constrained to move in the horizontal guide. If forces P = 250
Extensive testing of an experimental 2000-lb automobile reveals the aerodynamic drag force FD and the total nonaerodynamic rolling-resistance force FR to be as shown in the plot.
The nest of two springs is used to bring the 0.5-kg plunger A to a stop from a speed of 5 m/s and reverse its direction of motion. The inner spring increases the deceleration, and the adjustment of
The 6-kg cylinder is released from rest in the position shown and falls on the spring, which has been initially precompressed 50 mm by the light strap and restraining wires. If the stiffness of the
Calculate the horizontal velocity v with which the 48-lb carriage must strike the spring in order to compress it a maximum of 4 in. The spring is known as a “hardening” spring, since its
It is experimentally determined that the drive wheels of a car must exert a tractive force of 560 N on the road surface in order to maintain a steady vehicle speed of 90 km/h on a horizontal road. If
The system is released from rest with no slack in the cable and with the spring stretched 200 mm. Determine the distance s traveled by the 4-kg cart before it comes to rest (a) If m approaches
The system is released from rest with no slack in the cable and with the spring unstretched. Determine the distance s traveled by the 4-kg cart before it comes to rest (a) If m approaches
In a railroad classification yard, a 68-Mg freight car moving at 0.5 m/s at A encounters a retarder section of track at B which exerts a retarding force of 32 kN on the car in the direction opposite
The small slider of mass m is released from rest while in position A and then slides along the vertical-plane track. The track is smooth from A to D and rough (coefficient of kinetic friction μk)
The third stage of a rocket fired vertically up over the north pole coasts to a maximum altitude of 500 km following burnout of its rocket motor. Calculate the downward velocity v of the rocket when
A car with a mass of 1500 kg starts from rest at the bottom of a 10-percent grade and acquires a speed of 50 km/h in a distance of 100 m with constant acceleration up the grade. What is the power P
Two 425,000-lb locomotives pull fifty 200,000-lb coal hoppers. The train starts from rest and accelerates uniformly to a speed of 40 mi/hr over a distance of 8000 ft on a level track. The constant
A projectile is launched from the north pole with an initial vertical velocity v0. What value of v0 will result in a maximum altitude of R/3? Neglect aerodynamic drag and use g = 9.825 m/s2 as the
A 90-lb boy starts from rest at the bottom A of a 10-percent incline and increases his speed at a constant rate to 5 mi / hr as he passes B, 50 ft along the incline from A. Determine his power output
The motor unit A is used to elevate the 300-kg cylinder at a constant rate of 2 m/s. If the power meter B registers an electrical input of 2.20 kW, calculate the combined electrical and mechanical
The collar of mass m is released from rest while in position A and subsequently travels with negligible friction along the vertical-plane circular guide. Determine the normal force (magnitude
In the design of a conveyor-belt system, small metal blocks are discharged with a velocity of 0.4 m/s onto a ramp by the upper conveyor belt shown. If the coefficient of kinetic friction between the
The 15-lb cylindrical collar is released from rest in the position shown and drops onto the spring. Calculate the velocity v of the cylinder when the spring has been compressed 2 in. B | | A 15 lb
A 3600-lb car travels up the 6-percent incline shown. The car is subjected to a 60-lb aerodynamic drag force and a 50-lb force due to all other factors such as rolling resistance. Determine the power
An escalator handles a steady load of 30 people per minute in elevating them from the first to the second floor through a vertical rise of 24 ft. The average person weighs 140 lb. If the motor which
The position vector of a particle is given by r = 8ti + 1.2t2j − 0.5(t3 − 1)k, where t is the time in seconds from the start of the motion and where r is expressed in meters. For the condition
The 4-kg ball and the attached light rod rotate in the vertical plane about the fixed axis at O. If the assembly is released from rest at θ = 0 and moves under the action of the 60-N force, which is
The 0.8-kg collar slides freely on the fixed circular rod. Calculate the velocity v of the collar as it hits the stop at B if it is elevated from rest at A by the action of the constant 40-N force in
The 120-lb woman jogs up the flight of stairs in 5 seconds. Determine her average power output. Convert all given information to SI units and repeat your calculation. 9'
The system of the previous problem is rearranged as shown. For what constant force P will the 0.8-kg collar just reach position B with no speed after beginning from rest at position A? Friction is
The 0.8-kg collar travels with negligible friction on the vertical rod under the action of the constant force P = 20 N. If the collar starts from rest at A, determine its speed as it passes point B.
Each of the two systems is released from rest. Calculate the speed v of each 60-lb cylinder after the 40-lb cylinder has dropped 2 ft. The 30-lb cylinder of case (a) is replaced by a 30-lb force in
Each of the two systems is released from rest. Calculate the speed v of each 60-lb cylinder after the 40-lb cylinder has dropped 2 ft. The 30-lb cylinder of case (a) is replaced by a 30-lb force in
The 30-lb collar A is released from rest in the position shown and slides with negligible friction up the fixed rod inclined 30° from the horizontal under the action of a constant force P = 50 lb
The small 0.2-kg slider is known to move from position A to position B along the vertical-plane slot. Determine (a) The work done on the body by its weight (b) The work done on the body by
The car is moving with a speed v0 = 65 mi / hr up the 6-percent grade, and the driver applies the brakes at point A, causing all wheels to skid. The coefficient of kinetic friction for the
The man and his bicycle together weigh 200 lb. What power P is the man developing in riding up a 5-percent grade at a constant speed of 15 mi/hr? 15 mi/hr 5 100
The small 0.1-kg slider enters the “loop-the-loop” with a speed vA = 12 m /s as it passes point A, and it has a speed vB = 10 m /s as it exits at point B. Determine the work done by friction
The hollow tube assembly rotates about a vertical axis with angular velocity ω = θ˙ = 4 rad /s and ω˙ = θ¨ = −2 rad /s2. A small 0.2-kg slider P moves inside the horizontal tube portion
The 0.5-kg collar C starts from rest at A and slides with negligible friction on the fixed rod in the vertical plane. Determine the velocity v with which the collar strikes end B when acted upon by
The 2-kg collar is at rest in position A when the constant force P is applied as shown. Determine the speed of the collar as it passes position B if (a) P = 25 N (b) P = 40 N. The curved
In the design of a spring bumper for a 3500-lb car, it is desired to bring the car to a stop from a speed of 5 mi/hr in a distance equal to 6 in. of spring deformation. Specify the required stiffness
The small cart has a speed vA = 4 m /s as it passes point A. It moves without appreciable friction and passes over the top hump of the track. Determine the cart speed as it passes point B. Is
The spring is unstretched at the position x = 0. Under the action of a force P, the cart moves from the initial position x1 = −6 in. to the final position x2 = 3 in. Determine (a) The work
Each tire on the 1350-kg car can support a maximum friction force parallel to the road surface of 2500 N. This force limit is nearly constant over all possible rectilinear and curvilinear car motions
The slotted arm OB rotates in a horizontal plane about point O of the fixed circular cam with constant angular velocity θ˙ = 15 rad/s. The spring has a stiffness of 5 kN/m and is uncompressed when
A small object is released from rest at A and slides with friction down the circular path. If the coefficient of friction is 0.20, determine the velocity of the object as it passes B. Write the
The uniform slender rod of length L, mass m, and cross-sectional area A is rotating in a horizontal plane about the vertical central axis O-O at a constant high angular velocity ω. By analyzing the
The spacecraft P is in the elliptical orbit shown. At the instant represented, its speed is v = 13,244 ft /sec. Determine the corresponding values of r˙, θ˙, r¨, and θ¨. Use g = 32.23 ft /sec2
A small vehicle enters the top A of the circular path with a horizontal velocity v0 and gathers speed as it moves down the path. Determine an expression for the angle β which locates the point where
Remove the assumption of smooth surfaces as stated in Prob. 3 /88 and assume a coefficient of kinetic friction μk between the particle and rotating tube. Determine the radial position r of the
The particle P is released at time t = 0 from the position r = r0 inside the smooth tube with no velocity relative to the tube, which is driven at the constant angular velocity ω0 about a vertical
The disk spins about the fixed axis BB, which is inclined at the angle α to the vertical z-axis. A small block A is placed on the disk in its lowest position P at a distance r from the axis when the
The rotating drum of a clothes dryer is shown in the figure. Determine the angular velocity Ω of the drum which results in loss of contact between the clothes and the drum at θ = 50°. Assume that
A small coin is placed on the horizontal surface of the rotating disk. If the disk starts from rest and is given a constant angular acceleration θ¨ = α, determine an expression for the number of
Beginning from rest when θ = 20°, a 35-kg child slides with negligible friction down the sliding board which is in the shape of a 2.5-m circular arc. Determine the tangential acceleration and speed
The slotted arm revolves in the horizontal plane about the fixed vertical axis through point O. The 3-lb slider C is drawn toward O at the constant rate of 2 in. /sec by pulling the cord S. At the
The spring-mounted 0.8-kg collar A oscillates along the horizontal rod, which is rotating at the constant angular rate θ˙ = 6 rad /s. At a certain instant, r is increasing at the rate of 800 mm /s.
The small object of mass m is placed on the rotating conical surface at the radius shown. If the coefficient of static friction between the object and the rotating surface is 0.80, calculate the
The small object is placed on the inner surface of the conical dish at the radius shown. If the coefficient of static friction between the object and the conical surface is 0.30, for what range of
Determine the speed v at which the race car will have no tendency to slip sideways on the banked track, that is, the speed at which there is no reliance on friction. In addition, determine the
The 0.1-lb projectile A is subjected to a drag force of magnitude kv2, where the constant k = 0.0002 lb-sec2/ ft2. This drag force always opposes the velocity v. At the instant depicted, v = 100
The robot arm is elevating and extending simultaneously. At a given instant, θ = 30°, θ˙ = 40 deg /s, θ¨ = 120 deg /s2, l = 0.5 m, l˙ = 0.4 m /s, and l¨ = −0.3 m /s2. Compute the radial and
The rocket moves in a vertical plane and is being propelled by a thrust T of 32 kN. It is also subjected to an atmospheric resistance R of 9.6 kN. If the rocket has a velocity of 3 km/s and if the
The cars of an amusement park ride have a speed vA = 22 m/s at A and a speed vB = 12 m/s at B. If a 75-kg rider sits on a spring scale (which registers the normal force exerted on it), determine the
A 2-kg sphere S is being moved in a vertical plane by a robotic arm. When the angle θ is 30°, the angular velocity of the arm about a horizontal axis through O is 50 deg /s clockwise and its
The quarter-circular slotted arm OA is rotating about a horizontal axis through point O with a constant counterclockwise angular velocity Ω = 7 rad /sec. The 0.1-lb particle P is epoxied to the arm
Determine the altitude h (in kilometers) above the surface of the earth at which a satellite in a circular orbit has the same period, 23.9344 h, as the earth’s absolute rotation. If such an orbit
The configuration of Prob. 3/70 is now modified as shown in the figure. Use all the data of Prob. 3/70 and determine the forces applied to the slider B by both arm OA and the sides of the slot.
At the instant under consideration, the cable attached to the cart of mass m1 is tangent to the circular path of the cart. If the upward speed of the cylinder of mass m2 is v2 = 1.2 m/s, determine
Repeat the previous problem, only now the slotted arm is rotating with angular velocity Ω = 3 rad /s, and this rate is increasing at 5 rad /s2.
A 0.2-kg particle P is constrained to move along the vertical-plane circular slot of radius r = 0.5 m and is confined to the slot of arm OA, which rotates about a horizontal axis through O with a
Calculate the necessary rotational speed N for the aerial ride in an amusement park in order that the arms of the gondolas will assume an angle θ = 60° with the vertical. Neglect the mass of the
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