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engineering
mechanical engineering
Questions and Answers of
Mechanical Engineering
A 70-kg skier starts from rest at point A and skis down the slope shown. Neglecting friction, determine the force exerted on the skier by the snow (a) Just before the skier reaches B, (b) Immediately
Prove that a force rce F(x, y, z)is conservative if, and only if, the following relations are satisfied:
The force F = (yzi + zxj + xyk)/ xyz acts on the particle P(x,y,z) which moves in space.(a) Using the relation derived in Prob. 13.77, show that this force is a conservative force.(b) Determine the
The force F = (xi + yj + zk) / (x2 + y2 + z2)3/2 acts on the particle P(x,y,z) which moves in space.(a) Using the relation derived in Prob. 13.77, prove that F is a conservative force.(b) Determine
A force F acts on a particle P(x, y) which moves in the xy plane. Determine whether F is a conservative force and compute the work of F when P describes the path ABCA knowing that (a) F = (kx + y)i +
Certain springs are characterized by increasing stiffness with increasing deformation according to the relation F = k1x + k2x3 , where F is the force exerted by the spring, k1 and k2 are positive
Certain springs are characterized by decreasing stiffness with increasing deformation according to the relation F = k1x ?? k2x3 , where F is the force exerted by the spring, 1 k and 2 k are positive
A spacecraft is describing a circular orbit at an altitude of 930 mi above the surface of the earth. As it passes through point A, its speed is reduced by 40 percent and it enters an elliptic crash
A satellite describes an elliptic orbit of minimum altitude 376 mi above the surface of the earth. The semimajor and semiminor axes are 10840 mi and 8670 mi, respectively. Knowing that the speed of
Knowing that the velocity of an experimental space probe fired from the earth has a magnitude vA = 32.5 Mm/h at point A, determine the velocity of the probe as it passes through point B.
A lunar excursion module (LEM) was used in the Apollo moon-landing missions to save fuel by making it unnecessary to launch the entire Apollo spacecraft from the moon’s surface on its return trip
A satellite is placed into an elliptic orbit about the earth. Knowing that the ratio vA/vP of the velocity at the apogee A to the velocity at the perigee P is equal to the ratio rP/rA of the distance
While describing a circular orbit 200 mi above the earth a space vehicle launches a 6000-lb communications satellite. Determine(a) the additional energy required to place the satellite in a
A space shuttle ejects two communication satellites while describing a circular orbit, 296 km above the surface of the earth. Knowing that one of these satellites had a mass of 3600 kg, determine(a)
A satellite of mass m describes a circular orbit of radius r about the earth. Express as a function of r(a) The potential energy of the satellite,(b) Its kinetic energy,(c) Its total energy. Denote
The orbit of the planet Venus is nearly circular with an orbital velocity of 78.3 × 103 mi/h. Knowing that the mean distance from the center of the sun to the center of Venus is 67.2 × 106 mi and
(a) Show that, by setting r=R+y in the right-hand member of Eq. (13.17′) and expanding that member in a power series iny/R, the expression in Eq. (13.16) for the potential energy Vg due to gravity
Collar B has a mass of 4 kg and is attached to a spring of constant 1500 N/m and of undeformed length of 0.4 m. The system is set in motion with r = 0.2 m, vθ = 6 m/s, and vr = 0. Neglecting the
For the motion described in Prob. 13.93, determine(a) The maximum distance between the origin and the collar,(b) The corresponding velocity.
Two identical 4-lb collars, A and B, are attached to a spring of constant 7 lb/ft and can slide on a horizontal rod which is free to rotate about a vertical shaft. Collar B is initially prevented
Two identical 4-lb collars, A and B, are attached to a spring of constant 7 lb/ft and can slide on a horizontal rod which is free to rotate about a vertical shaft. Collar B is initially prevented
A 0.7-kg ball that can slide on a horizontal frictionless surface is attached to a fixed point O by means of an elastic cord of constant nt k = 150 N/m and un-deformed length 600 mm. The ball is
A 0.7-kg ball that can slide on a horizontal frictionless surface is attached to a fixed point O by means of an elastic cord of constant nt k = 150 N/m and un-deformed length 600 mm. The ball is
After completing their moon-exploration mission, the two astronauts forming the crew of an Apollo lunar excursion module (LEM) would prepare to rejoin the command module which was orbiting the moon
While describing a circular orbit, 264 km above the surface of the earth, a space shuttle ejects at point A an inertial upper stage (IUS) carrying a communication satellite to be placed in a
As a first approximation to the analysis of a space flight from the earth to Mars, it is assumed that the orbits of the earth and Mars are circular and coplanar. The mean distances from the sun to
A spacecraft describing an elliptic orbit about a planet has a maximum speed d vA =5mi/s at its minimum altitude hA = 1200 mi above the surface of the planet and a minimum speed vB = 1.2 mi/s at its
The optimal way of transferring a space vehicle from an inner circular orbit to an outer coplanar orbit is to fire its engines as it passes through A to increase its speed and place it in an elliptic
A spacecraft approaching the planet Saturn reaches point A with a velocity vA of magnitude 21 km/s. It is placed in an elliptic orbit about Saturn so that it will be able to periodically examine
A space shuttle is to rendezvous with an orbiting laboratory which circles the earth at a constant altitude of 360 km. The shuttle has reached an altitude of 60 km when its engine is shut off, and
An experimental space probe is launched from the earth and enters a highly eccentric elliptic orbit as it reaches point A. Knowing that its velocity there is observed to be vA = 30,000 km/h at an
An experimental space probe is launched from the earth and enters a highly eccentric elliptic orbit as it reaches point A. Knowing that its velocity there is observed to be vA = 30,000 km/h at an
A satellite describes an elliptic orbit of minimum altitude 377 mi above the surface of the earth and semi major axis 10,840 mi, knowing that the speed of the satellite at point C is 2.97 mi/s, apply
When the lunar excursion module (LEM) was set adrift after returning two of the Apollo astronauts to the command module, which was orbiting the moon at an altitude of 87 mi, its speed was reduced to
A satellite is projected into space with a velocity v0 at a distance r0 from the center of the earth by the last stage of its launching rocket. The velocity v0 was designed to send the satellite into
A space vehicle is in a circular orbit at an altitude of 362 km above the earth. To return to earth, it decreases its speed as it passes through A by firing its engine for a short interval of time in
In Prob. 13.112, the speed of the space vehicle was decreased as it passed through A by firing its engine in a direction opposite to the direction of motion. An alternative strategy for taking the
Show that the values vA and vP of the speed of an earth satellite at the apogee A and perigee P of an elliptic orbit are defined by the relations where M is the mass of the earth, and rA and rP
Show that the total energy E of an earth satellite of mass m describing an elliptic orbit is E= ?? GMm/(rA + rP), where M is the mass of the earth, and rA and rP represent, respectively, the maximum
A spacecraft of mass m describes a circular orbit of radius us r1around the earth. (a) Show that the additional energy ΔE which must be imparted to the spacecraft to transfer it to a circular orbit
Using the answers obtained in Prob. 13.111, show that the intended circular orbit and the resulting elliptic orbit intersect at the ends of the minor axis of the elliptic orbit.
A missile is fired from the ground with an initial velocity v0 forming an angle ? 0 with the vertical. If the missile is to reach a maximum altitude equal to ? R, where R is the radius of the
A 3-lb particle is acted upon by a force F = (20 sin 2t)i + (24 cos 2t)j, where F is expressed in pounds and t in seconds. Determine the magnitude and direction of the velocity of the particle at t =
A 4-kg particle is acted upon by a force F = (4t – 8)i – 2j where F is expressed in newtons and t in seconds. Knowing that the velocity of the particle is zero at t = 0, determine its maximum
A 440-kg sailboat with its occupants is running downwind at 12 km/h when its spinnaker is raised to increase its speed. Determine the net force provided by the spinnaker over the 10-s interval that
The initial velocity of the block in position A is 9 m/s. Knowing that the coefficient of kinetic friction between the block and the plane is μk = 0.30, determine the time it takes for the block to
Steep safety ramps are built beside mountain highways to enable vehicles with defective brakes to stop. A 10-ton truck enters a 15? ramp at a high speed v0 = 108 ft/s and travels for 6 s before its
A 10-ton truck enters a 15? safety ramp at a high speed v0 and travels 540 ft in 5.5 s before its speed is reduced to v0/2. Assuming constant deceleration determine (a) The initial speed v0, (b) The
In anticipation of a long 6° upgrade, a bus driver accelerates at a constant rate from 80 km/h to 100 km/h in 8 s while still on a level section of the highway. Knowing that the speed of the bus is
A 20-kg block is at rest on an incline when a constant horizontal force P is applied to it. The static and kinetic coefficients of friction between the block and the incline are 0.4 and 0.3,
The coefficients of friction between the load and the flatbed trailer shown are μs = 0.40 and μk = 0.35. Knowing that the speed of the rig is 55 mi/h, determine the shortest time in which the rig
The 40-lb block is moving downward with a speed of 3 ft/s at t = 0 when constant forces P and 2P are applied through the ropes. Knowing that the block is moving upward with a speed of 2 ft/s when t =
A tractor-trailer rig with a 2000-kg tractor, a 4500-kg trailer, and a 3600-kg trailer is traveling on a level road at 90 km/h. The brakes on the rear trailer fail and the antiskid system of the
A light train made of two cars travels at 72 km/h. The mass of car A is 18 Mg and the mass of car B is 13 Mg. When the brakes are suddenly applied, a constant braking force of 19 kN is applied to
Solve Prob. 13.130, assuming that a constant braking force of 19 kN is applied to car B but the brakes on car A are not applied.
The two blocks shown are released from rest at time t = 0. Neglecting the masses of the pulleys and the effect of friction in the pulleys and between the blocks and the incline, determine(a) The
The coefficients of friction between the three blocks and the horizontal surfaces are ?s = 0.25 and ?k = 0.20. The weights of the blocks are WA = WC = 20 lb, and WB = 10 lb. The velocities of blocks
The system shown is released from rest. Determine the time it takes for the velocity of A to reach 0.6 m/s. Neglect friction and the mass of the pulleys.
Two packages are placed on an incline as shown. The coefficients of friction are μs = 0.30 and μk = 0.25 between the incline and package A, and μs = 0.20 and μk = 0.15 between the incline and
A 2-kg collar which can slide on a frictionless vertical rod is acted upon by a force P which varies in magnitude as shown. Knowing that the collar is initially at rest, determine its velocity at(a)
A 2-kg collar which can slide on a frictionless vertical rod is acted upon by a force P which varies in magnitude as shown. Knowing that the collar is initially at rest, determine (a) The maximum
A 12-lb block which can slide on a frictionless inclined surface is acted upon by a force P which varies in magnitude as shown. Knowing that the block is initially at rest, determine (a) The velocity
A simplified model consisting of a single straight line is to be obtained for the variation of pressure inside the 0.4-in.-diameter barrel of a rifle as a 0.7-oz bullet is fired. Knowing that it
A player hits a 2-oz tennis ball with a horizontal initial velocity of 54 ft/s at a height of 4.5 ft. The ball bounces at point A and rises to a maximum height of 3 ft where the velocity is 30 ft/s,
The triple jump is a track-and-field event in which an athlete gets a running start and tries to leap as far as he can with a hop, step, and jump. Shown in the figure is the initial hop of the
A 28-g steel-jacketed bullet is fired with a velocity of 650 m/s toward a steel plate and ricochets along path CD with a velocity 500 m/s. Knowing that the bullet leaves a 50-mm scratch on the
A 1.5-kg collar can slide on a horizontal rod which is free to rotate about a vertical shaft. The collar is initially held at A by a cord attached to the shaft. As the rod rotates at a rate θ = 18
A 45-g golf ball is hit with a golf club and leaves it with a velocity of 38 m/s. Assume that for 0≤t ≤t0, where t0 is the duration of the impact, the magnitude F of the force exerted on the ball
An estimate of the expected load on over-the-shoulder seat belts is made before designing prototype belts that will be evaluated in automobile crash tests. Assuming that an automobile traveling at 72
A 120-ton tugboat is moving at 6 ft/s with a slack towing cable attached to a 100-ton barge which is at rest. The cable is being unwound from a drum on the tugboat at a constant rate of 5.4 ft/s and
A 1-oz bullet is fired into an 8-lb wooden block and becomes embedded in it. Knowing that the block and bullet then move up the smooth incline for 1.2 s before they come to a stop, determine (a) The
A 2-kg block A can slide without friction down a slot in a 10-kg block B which can slide without friction on a horizontal surface. Both blocks are at rest when block A is released in the position
Two swimmers A and B, of mass 75 kg and 50 kg, respectively, dive off the end of a 200-kg boat. Each swimmer has a relative horizontal velocity of 3 m/s when leaving the boat. If the boat is
A 3-oz ball is projected from a height of 4.8 ft with a horizontal velocity of 6 ft/s and bounces from a 14-oz smooth plate supported by springs. Knowing that the height of the rebound is 1.8 ft,
In order to test the resistance of a chain to impact, the chain is suspended from a 120-kg rigid beam supported by two columns. A rod attached to the last link is then hit by a 30-kg block dropped
A small rivet connecting two pieces of sheet metal is being clinched by hammering. Determine the impulse exerted on the rivet and the energy absorbed by the rivet under each blow, knowing that the
A baseball player catching a ball can soften the impact by pulling his hand back. Assuming that a 5-oz ball reaches his glove at 96 mi/h and that the player pulls his hand back during the impact at
A 4-lb sphere A is connected to a fixed point O by an inextensible cord of length 3.6 ft. The sphere is resting on a frictionless horizontal surface at a distance of 1.5 ft from O when it is given
Collars A and B, of the same mass m, are moving toward each other with the velocities shown. Knowing that the coefficient of restitution between the collars is 0 (plastic impact), show that after
Collars A and B, of the same mass m, are moving in the same direction with vA > vB . Neglecting friction and knowing that the coefficient of restitution is 0.5, determine (a) The velocity of each
Two steel blocks slide without friction on a horizontal surface; immediately before impact their velocities are as shown. Knowing that e = 0.75, determine (a) Their velocities after impact, (b) The
The velocities of two steel blocks before impact are as shown. If after impact the velocity of block B is observed to be 2.5 m/s to the right, determine the coefficient of restitution between the two
A 1.2-lb ball A is moving with a velocity vA when it is struck by a 2.4-lb ball B which has a velocity vB of magnitude vB = 18 ft/s. Knowing that the velocity of ball B is zero after impact and that
A 1.2-lb ball A is moving with a velocity vA of magnitude vA = 24 ft/s when it is struck by a 2.4-lb ball B which has a velocity vB. Knowing that the velocity of ball A is zero after impact and that
Two disks sliding on a frictionless horizontal plane with opposite velocities of the same magnitude e v0 hit each other squarely. Disk A is known to have a mass of 6 kg and is observed to have zero
Three steel spheres of equal mass are suspended from the ceiling by cords of equal length which are spaced at a distance slightly greater than the diameter of the spheres. After being pulled back and
Packages in an automobile parts supply house are transported to the loading dock by pushing them along a roller track with very little friction. At the instant shown packages B and C are at rest and
A 1.1-kg ball A is falling vertically with a velocity of magnitude vA = 2.5 m/s when it is hit as shown by a 0.7-kg ball B which has a velocity of magnitude vB = 2 m/s. Knowing that the coefficient
Two identical billiard balls can move freely on a horizontal table. Ball A has a velocity v0 as shown and hits ball B, which is at rest, at a point C defined by θ = 45?. Knowing that the coefficient
A 17.5-lb sphere A of radius 4.5 in. moving with a velocity v0 of magnitude v0 = 6 ft/s strikes a 1.6-lb sphere B of radius 2 in. which was at rest. Both spheres are hanging from identical light
Solve Prob. 13.166, assuming that the flexible cords from which the spheres are hanging are replaced by light rigid rods.
A 58-lb sphere A of radius 4.5 in. moving with a velocity of magnitude v0 = 6 ft/s strikes a 5.3-lb sphere B of radius 2 in. which is initially at rest. All surfaces of contact are frictionless.
(a) Show that when two identical spheres A and B with coefficient of restitution e =1 collide while moving with velocities vA and vB which are perpendicular to each other they will rebound with
(a) Show that when two identical spheres A and B with coefficient of restitution e =1 collide while moving with velocities vA and vB which are perpendicular to each other they will rebound with
In Prob. 13.170, determine(a) The velocity of ball A after impact,(b) The fraction of the initial energy lost during impact.
A sphere rebounds as shown after striking an inclined plane with a vertical velocity v0 of magnitude v0 = 5 m/s. Knowing that α =30? and e = 0.8 between the sphere and the plane, determine the
A boy releases a ball with an initial horizontal velocity at a height of 0.6 m. The ball bounces off the ground at point A, bounces off the wall at point B, and hits the ground again at point C,
A girl throws a ball at an inclined wall from a height of 3 ft, hitting the wall at A with a horizontal velocity v0 of magnitude 25 ft/s. Knowing that the coefficient of restitution between the ball
A ball is thrown into a 90? corner with an initial velocity v. Denoting the coefficient of restitution by e, show that the final velocity is of magnitude and that the initial and final paths AB and
A 2.5-lb block B is moving with a velocity v0 of magnitude v0 = 6 ft/s as it hits the 1.5-lb sphere A, which is at rest and hanging from a cord attached at O. Knowing that μk = 0.6 between the block
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