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engineering
mechanical engineering

Questions and Answers of Mechanical Engineering

A tennis player serves the ball at a height h with an initial velocity of 40 m/s at an angle of 4? with the horizontal. Knowing that the ball clears the 0.914 m net by 152 mm, determine(a) The height
The conveyor belt, which forms an angle of 20? with the horizontal, is used to load an airplane. Knowing that a worker tosses a package with an initial velocity v0 at an angle of 45? so that its
A golfer hits a ball with an initial velocity of magnitude v0 at an angle ? with the horizontal. Knowing that the ball must clear the tops of two trees and land as close as possible to the flag,
A homeowner uses a snow blower to clear his driveway. Knowing that the snow is discharged at an average angle of 40? with the horizontal, determine the initial speed d v0 of thesnow.
A basketball player shoots when she is 5 m from the backboard. Knowing that the ball has an initial velocity v0 at an angle of 30? with the horizontal, determine the value of v0 when d is equal to(a)
A ball is projected from point A with a velocity v0 which is perpendicular to the incline shown. Knowing that the ball strikes the incline at B, determine the initial speed v0 in terms of the range R
An outfielder throws a ball with an initial velocity of magnitude v0 at an angle of 10? with the horizontal to the catcher 50 m away. Knowing that the ball is to arrive at a height between 0.5 m and
A model rocket is launched from point A with an initial velocity v0 of 86 m/s. If the rocket??s descent parachute does not deploy and the rocket lands 104 m from A, determine(a) The angle ? that v0
An outfielder throws a ball with an initial velocity of magnitude v0 at an angle of 10? with the horizontal to the catcher 50 m away. Knowing that the ball is to arrive at a height between 0.5 m and
The pitcher in a softball game throws a ball with an initial velocity v0 of 40 mi/h at an angle ? with the horizontal. If the height of the ball at point B is 2.2 ft, determine(a) The angle ? ,(b)
An outfielder throws a ball with an initial velocity of magnitude v0 at an angle of 10? with the horizontal to the catcher 50 m away. Knowing that the ball is to arrive at a height between 0.5 m and
A nozzle at A discharges water with an initial velocity of 36 ft/s at an angle α with the horizontal. Determine (a) The distance d to the farthest point B on the roof that the water can reach, (b)
A projectile is launched from point A with an initial velocity v0 of 120 ft/s at an angle ? with the vertical. Determine? (a) The distance d to the farthest point B on the hill that the projectile
Airplane A is flying due east at 700 km/h, while airplane B is flying at 500 km/h at the same altitude and in a direction to the west of south. Knowing that the speed of B with respect to A is 1125
Instruments in an airplane which is in level flight indicate that the velocity relative to the air (airspeed) is 120 km/h and the direction of the relative velocity vector (heading) is 70? east of
At an intersection car A is traveling south with a velocity of 25 mi/h when it is struck by car B traveling 30? north of east with a velocity of 30 mi/h. Determine the relative velocity of car B with
Small wheels attached to the ends of rod AB roll along two surfaces. Knowing that at the instant shown the velocity vA of wheel A is 4.5 ft/s to the right and the relative velocity vB/A of wheel B
The velocities of commuter trains A and B are as shown. Knowing that the speed of each train is constant and that B reaches the crossing 10 min after A passed through the same crossing, determine (a)
Airplanes A and B are flying at the same altitude and are tracking the eye of hurricane C. The relative velocity of C with respect to A is vC/A = 470 km/h A 75?, and the relative velocity of C with
Slider block B starts from rest and moves to the right with a constant acceleration on of 1ft/s2. Determine (a) the relative acceleration of portion C of the cable with respect to slider block A, (b)
Slider block B starts from rest and moves to the right with a constant acceleration on of 1ft/s2. Determine(a) the relative acceleration of portion C of the cable with respect to slider block A,(b)
At t = 0, wedge A starts moving to the left with a constant acceleration of 80 mm/s2 and block B starts moving along the wedge toward the right with a constant acceleration of 120 mm/s2 relative to
A boat is moving to the right with a constant deceleration of 0.3 m/s2 when a boy standing on the deck D throws a ball with an initial velocity relative to the deck which is vertical. The ball rises
The conveyor belt A moves with a constant velocity and discharges sand onto belt B as shown. Knowing that the velocity of belt B is 8 ft/s, determine the velocity of the sand relative to belt B as it
A suitcase can slide down a conveyor belt on a truck that has no brakes. When t = 0 the suitcase is at point A and the velocities of both the truck and suitcase are zero. When the suitcase reaches
As the driver of an automobile travels north at 20 km/h in a parking lot, he observes a truck approaching from the northwest. After he reduces his speed to 12 km/h and turns so that he is traveling
Instruments in airplane A indicate that with respect to the air the plane is headed 30? north of east with an airspeed of 480 km/h. At the same time radar on ship B indicates that the relative
When a small boat travels north at 3 mi/h, a flag mounted on its stern forms s an angle θ = 50? with the centerline of the boat as shown. A short time later, when the boat travels east at 12 mi/h,
As observed from a ship moving due east at 6 mi/h, the wind appears to blow from the south. After the ship has changed course and speed, and as it is moving due north at 4 mi/h, the wind appears to
The diameter of the eye of a stationary hurricane is 32 km and the maximum wind speed is 160 km/h at the eye wall, r = 16 km. Assuming that the wind speed is constant for constant r and decreases
At the instant shown, race car A is passing race car B with a relative velocity of 1 m/s. Knowing that the speeds of both cars are constant and that the relative acceleration of car A with respect to
Determine the maximum speed that the cars of the roller-coaster can reach along the circular portion AB of the track if the normal component of their acceleration cannot exceed3g.
As cam A rotates, follower wheel B rolls without slipping on the face of the cam. Knowing that the normal components of the acceleration of the points of contact at C of the cam A and the wheel B are
A motorist is traveling on a curved portion of highway of radius 350 m at a speed of 72 km/h. The brakes are suddenly applied, causing the speed to decrease at a constant rate of 1.25 m/s2. Determine
An outdoor track is a full circle of diameter 130 m. A runner starts from rest and reaches her maximum speed in 4 s with constant tangential acceleration and then maintains that speed until she
The peripheral speed of the tooth of a 10-in.-diameter circular saw blade is 150 ft/s when the power to the saw is turned off. The speed of the tooth decreases at a constant rate, and the blade comes
A motorist starts from rest at point A on a circular entrance ramp when t = 0, increases the speed of her automobile at a constant rate and enters the highway at point B. Knowing that her speed
At a given instant in an airplane race, airplane A is flying horizontally in a straight line, and its speed is being increased at a rate of 6 m/s2. Airplane B is flying at the same altitude as
Racing cars A and B are traveling on circular portions of a race track. At the instant shown, the speed of A is decreasing at the e rate of 8m/s2, and the speed of B is increasing at the rate of
A nozzle discharges a stream of water in the direction shown with an initial velocity of 8 m/s. Determine the radius of curvature of the stream (a) As it leaves the nozzle, (b) At the maximum height
A child throws a ball from point A with an initial velocity v0 at an angle of 3? with the horizontal. Knowing that the ball hits a wall at point B, determine(a) The magnitude of the initial
A projectile is launched from point A with an initial velocity v0 of 120 ft/s at an angle of 30? with the vertical. Determine the radius of curvature of the trajectory described by the projectile(a)
The motion of particle P on the elliptical path shown is defined by the equations x = (2 cos πt ?? 1) / (2 ??cos πt) and y = 1.5 sin πt/(2 ?? cos πt), where x and y are expressed in feet and t is
The motion of a particle is defined by the equations x = [(t ? 4)3/6] + t2 and y = (t3 / 6) ? (t ? 1)2 / 4, where x and y are expressed in meters and t is expressed in seconds. Determine the
A horizontal pipe discharges at point A a stream of water into a reservoir. Express the radius of curvature of the stream at point B in terms of the magnitudes of the velocities vA andvB.
A projectile is fired from point A with an initial velocity v0. (a) Show that the radius of curvature of the trajectory of the projectile reaches its minimum value at the highest point B of the
A projectile is fired from point A with an initial velocity v0 which forms an angle ? with the horizontal. Express the radius of curvature of the trajectory of the projectile at point C in terms of
Determine the radius of curvature of the path described by the particle of Prob. 11.97 when t = 0.
Determine the radius of curvature of the path described by the particle of Prob. 11.98 when t = 0, A = 3, and B = 1.
A satellite will travel indefinitely in a circular orbit around a planet if the normal component of the acceleration of the satellite is equal to g(R/r)2 , where g is the acceleration of gravity at
A satellite will travel indefinitely in a circular orbit around a planet if the normal component of the acceleration of the satellite is equal to g(R/r)2, where g is the acceleration of gravity at
Determine the speed of a satellite relative to the indicated planet if the satellite is to travel indefinitely in a circular orbit 100 mi above the surface of the planet. (See information given in
Determine the speed of a satellite relative to the indicated planet if the satellite is to travel indefinitely in a circular orbit 100 mi above the surface of the planet. (See information given in
Determine the speed of a satellite relative to the indicated planet if the satellite is to travel indefinitely in a circular orbit 100 mi above the surface of the planet. (See information given in
A Global Positioning System (GPS) satellite is in a circular orbit 10,900 mi above the surface of the earth. Knowing that the radius of the earth is 3960 mi, determine the time of one orbit of the
A satellite will travel indefinitely in a circular orbit around the earth if the normal component of its acceleration is equal to g(R / r)2 , where g = 9.81 m/s2 , R = radius of the earth = 6370 km,
Satellites A and B are traveling in the same plane in circular orbits around the earth at altitudes of 190 and 320 km, respectively. If at t = 0 the satellites are aligned as shown and knowing that
The rotation of rod OA about O is defined by the relation ? = 0.5e?0.8t sin 3?t, where ? and t are expressed in radians and seconds, respectively. Collar B slides along the rod so that its distance
The oscillation of rod OA about O is defined by the relation (θ = 4/π)(sin πt), where θ and t are expressed in radians and seconds, respectively. Collar B slides along the rod so that its
The two-dimensional motion of a particle is defined by the relations r = 2 B cos(At/2B) and θ = At/ 2B, where r is expressed in meters, t in seconds, and θ in radians. Knowing that A and B are
The path of a particle P is a limaçon. The motion of the particle is defined by the relations ons r=b(2+cos?t) and ? = ? t, where t and ? are expressed in seconds and radians, respectively.
The motion of particle P on the parabolic path shown is defined by the equations ons r = 6t??1 + 4t2 and θ = tan??1 2t, where r is expressed in feet, θ in radians, and t in seconds. Determine the
The two-dimensional motion of a particle is defined by the relations r = 3 / sin θ – cos θ and 2 tan θ = 1 + 1/t2, where r and θ are expressed in feet and radians, respectively, and t is
To study the performance of a race car, a high-speed motion-picture camera is positioned at point A. The camera is mounted on a mechanism which permits it to record the motion of the car as the car
Determine the magnitude of the acceleration of the race car of Prob. 11.169 in terms of b, , , and d.
After taking off, a helicopter climbs in a straight line at a constant angle β . Its flight is tracted by radar from point A. Determine the speed of the helicopter in terms of d, β , θ, and θ
Pin C is attached to rod BC and slides freely in the slot of rod OA which rotates at the constant rate Ï‰ . At the instant when Î² = 60°, determine(a) r and Î¸(b)
A test rocket is fired vertically from a launching pad at B. When the rocket is at P the angle of elevation ion is ? =47.0?, and 0.5 s later it is ? = 48.0? . Knowing that b = 4 km, determine
An airplane passes over a radar tracking station at A and continues to fly due east. When the plane is at P, the distance and angle of elevation of the plane are, respectively, r = 12,600 ft and θ =
A particle moves along the spiral shown. Determine the magnitude of the velocity of the particle in terms of b, θ, and d θ.
A particle moves along the spiral shown. Determine the magnitude of the velocity of the particle in terms of b,θ, and θ.
A particle moves along the spiral shown. Knowing that θ is constant and denoting this constant by ω , determine the magnitude of the acceleration of the particle in terms of b, θ , and ω .
A particle moves along the spiral shown. Knowing that θ is constant and denoting this constant by ω , determine the magnitude of the acceleration of the particle in terms of b, θ , and ω
Show that r = hφ sin θ knowing that at the instant shown, step AB of the step exerciser is rotating counterclockwise at a constant rate φ.
The three-dimensional motion of a particle is defined by the cylindrical coordinates (see Fig. 11.26) ( R = A / t + 1), θ = Bt, and z = Ct / (t + 1). Determine the magnitudes of the velocity and
The motion of a particle on the surface of a right circular cylinder is defined by the relations, R = A θ = 2πt, and z = At2 / 4, where A is a constant. Determine the magnitudes of the velocity and
For the conic helix of Prob. 11.97, determine the angle that the oscillating plane forms with the y axis.
Determine the direction of the binormal of the path described by the particle of Prob. 11.98 when (a) t = 0, (b) t = π /2 s.
The acceleration of a particle is directly proportional to the square of the time t. When t = 0, the particle is at x = 36 ft. Knowing that at t = 9 s, x = 144 ft and v = 27 ft/s, express x and v in
The acceleration of a particle is defined by the relation a=0.6(1 − kv), where k is a constant. Knowing that at t = 0 the particle starts from rest at x = 6 m and that v = 6 m/s when t = 20 s,
A motorist enters a freeway at 25 mi/h and accelerates uniformly to 65 mi/h. From the odometer in the car, the motorist knows that she traveled 0.1 mi while accelerating. Determine (a) The
Block C starts from rest and moves downward with a constant acceleration. Knowing that after 12 s the velocity of block A is 456 mm/s, determine (a) The accelerations of A, B, and C, (b) The velocity
A particle moves in a straight line with the velocity shown in the figure. Knowing that x = ?540 m at t = 0,(a) construct the a ? t and x ? t curves for 0 (b) The total distance traveled by the
Car A is traveling on a highway at a constant speed (vA)0 = 100km/h and is 120 m from the entrance of an access ramp when car B enters the acceleration lane at that point at a speed (vB)0 = 25km/h.
A baseball pitching machine ??throws?? baseballs with a horizontal velocity v0 . Knowing that height h varies between 788 mm and 1068 mm, determine (a) The range of values of v0, (b) The values of α
A ball is dropped onto a step at point A and rebounds with a velocity v0 at an angle of 15? with the vertical. Determine the value of v0 knowing that just before the ball bounces at point B its
Coal discharged from a dump truck with an initial velocity (vC) 0 = 1.8 m/s A 50? falls onto conveyor belt B. Determine the required velocity B v of the belt if the relative velocity with which the
Pin A, which is attached to link AB, is constrained to move in the circular slot CD. Knowing that at at t = 0 the pin starts from rest and moves so that its speed increases at a constant rate of 0.8
Coal is discharged from the tailgate of a dump truck with an initial velocity vA = 2 m/s A 50?. Determine the radius of curvature of the trajectory described by the coal (a) At point A, (b) At the
The two-dimensional motion of a particle is defined by the relations r = 6 (4 − 2e− t) and θ = 2(2t + 4e− 2t), where r is expressed in feet, t in seconds, and θ in radians. Determine the
The acceleration due to gravity on Mars is 3.75 m/s2. Knowing that the mass of a silver bar has been officially designated as 20 kg, determine, on Mars, its weight in newtons.
The value of the acceleration of gravity at any latitude φ is given by g = 9.7087(1 + 0.0053 sin2 φ) m/s2, where the effect of the rotation of tbhye earth as well as the fact that the earth is not
A spring scale A and a lever scale B having equal lever arms are fastened to the roof on an elevator, and identical packages are attached to the scales as shown. Knowing that when the elevator moves
A Global Positioning System (GPS) satellite is in a circular orbit 12,580 mi above the surface of the earth and completes one orbit every 12 h. Knowing that the magnitude of the linear momentum of
The 40-lb block starts from rest and moves upward when constant forces of 10 lb and 20 lb are applied to supporting ropes. Neglecting the masses of the pulleys and the effect of friction, determine
A motorist traveling at a speed of 108 km/h suddenly applies the brakes and comes to a stop after skidding 75 m. Determine(a) The time required for the car to stop,(b) The coefficient of friction
A 1400-kg automobile is driven down a 4° incline at a speed of 88 km/h when the brakes are applied, causing a total braking force of 7500 N to be applied to the automobile. Determine the distance
In the braking test of a sports car its velocity is reduced from 70 mi/h to zero in a distance of 170 ft with slipping impending. Knowing that the coefficient of kinetic friction is 80 percent of the
A 0.2-lb model rocket is launched vertically from rest at time t = 0 with a constant thrust of 2 lb for one second and no thrust for t > 1 s. Neglecting air resistance and the decrease in mass of
A 40-kg package is at rest on an incline when a force P is applied to it. Determine the magnitude of P if 4 s is required for the package to travel 10 m up the incline. The static and kinetic

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