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engineering
engineering mechanics dynamics

Questions and Answers of Engineering Mechanics Dynamics

When the skier of weight W is at point A he has a speed vA. Determine his speed when he reaches point B on the smooth slope. For this distance the slope follows the cosine curve shown. Also, what is
Cylinder A has weight WA and block B has weight WB. Determine the distance A must descend from rest before it obtains speed vA. Also, what is the tension in the cord supporting block A? Neglect the
The cyclist travels to point A, pedaling until he reaches speed vA. He then coasts freely up the curved surface. Determine the normal force he exerts on the surface when he reaches point B. The total
The collar has mass M and slides along the smooth rod. Two springs are attached to it and the ends of the rod as shown. If each spring has an uncompressed length L and the collar has speed v0 when s
The catapulting mechanism is used to propel slider A of mass M to the right along the smooth track. The propelling action is obtained by drawing the pulley attached to rod BC rapidly to the left by
The cyclist travels to point A, pedaling until he reaches speed vA. He then coasts freely up the curved surface. Determine how high he reaches up the surface before he comes to a stop. Also, what are
The man at the window A wishes to throw a sack of mass M onto the ground. To do this he allows it to swing from rest at B to point C, when he releases the cord at θ = θ1. Determine the speed at
A block of weight W rests on the smooth semicylindrical surface. An elastic cord having a stiffness k is attached to the block at B and to the base of the semicylinder at point C. If the block is
The block of weight W is pressed against the spring so as to compress it a distance δ when it is at A. If the plane is smooth, determine the distance d, measured from the wall, to where the block
The spring has a stiffness k and an unstretched length l0. As shown, it is confined by the plate and wall using cables so that its length is l. A block of weight W is given a speed vA when it is at
The skier starts from rest at A and travels down the ramp. If friction and air resistance can be neglected, determine his speed vB when he reaches B. Also, find the distance d to where he strikes the
A spring having a stiffness k is compressed a distance δ. The stored energy in the spring is used to drive a machine which requires power P. Determine how long the spring can supply energy at the
Determine the power input for a motor necessary to lift a weight W at a constant rate v. The efficiency of the motor is ε. Given: W 300 lbf v = 5 = ft - S ε = 0.65
The escalator steps move with a constant speed v. If the steps are of height h and length l, determine the power of a motor needed to lift an average mass M per step. There are n steps. Given: M =
An electrically powered train car draws a power P. If the car has weight W and starts from rest, determine the maximum speed it attains in time t. The mechanical efficiency is ε. Given: P = 30 kW W
If the escalator in Prob. 14−46 is not moving, determine the constant speed at which a man having a mass M must walk up the steps to generate power P—the same amount that is needed to power a
The crate of weight W is given speed v in time t1 starting from rest. If the acceleration is constant, determine the power that must be supplied to the motor when t = t2. The motor has an efficiency
An electric streetcar has a weight W and accelerates along a horizontal straight road from rest such that the power is always P. Determine how far it must travel to reach a speed of v. Given: W =
The elevator of mass mel starts from rest and travels upward with a constant acceleration ac. Determine the power output of the motor M when t = t1. Neglect the mass of the pulleys and cable.
To dramatize the loss of energy in an automobile, consider a car having a weight Wcar that is traveling at velocity v. If the car is brought to a stop, determine how long a light bulb with power
Determine the power output of the draw-works motor M necessary to lift the drill pipe of weight W upward with a constant speed v. The cable is tied to the top of the oil rig, wraps around the lower
The crate has mass mc and rests on a surface for which the coefficients of static and kinetic friction are μs and μk respectively. If the motor M supplies a cable force of F = at2 + b, determine
The crate of mass mc is hoisted up the incline of angle θ by the pulley system and motor M. If the crate starts from rest and by constant acceleration attains speed v after traveling a distance d
The load of weight W is hoisted by the pulley system and motor M. If the crate starts from rest and by constant acceleration attains a speed v after rising a distance s = s1, determine the power that
The collar of weight W starts from rest at A and is lifted by applying a constant vertical force F to the cord. If the rod is smooth, determine the power developed by the force at the instant θ =
An athlete pushes against an exercise machine with a force that varies with time as shown in the first graph. Also, the velocity of the athlete’s arm acting in the same direction as the force
An athlete pushes against an exercise machine with a force that varies with time as shown in the first graph. Also, the velocity of the athlete’s arm acting in the same direction as the force
Block A has weight WA and block B has weight WB. Determine the speed of block A after it moves a distance d down the plane, starting from rest. Neglect friction and the mass of the cord and pulleys.
The collar has mass M and rests on the smooth rod. Two springs are attached to it and the ends of the rod as shown. Each spring has an uncompressed length l. If the collar is displaced a distance s =
A suitcase of weight W slides from rest a distance d down the smooth ramp. Determine the point where it strikes the ground at C. How long does it take to go from A to C? Given: W = 40 lb = 30 deg d =
A suitcase of weight W slides from rest a distance d down the rough ramp. The coefficient of kinetic friction along ramp AB is μk. The suitcase has an initial velocity down the ramp v0. Determine
The winding drum D is drawing in the cable at an accelerated rate a. Determine the cable tension if the suspended crate has mass M. Units Used:Given: kN = 1000 N
At a given instant block A of weight WA is moving downward with a speed v1. Determine its speed at the later time t. Block B has weight WB, and the coefficient of kinetic friction between it and the
A force F is applied to the cord. Determine how high the block A of weight W rises in time t starting from rest. Neglect the weight of the pulleys and cord. Given: F = 15 lb t = 2 s W = 30 lb g 8 =
At a given instant block A of weight WA is moving downward with speed vA0. Determine its speed at a later time t. Block B has a weight WB and the coefficient of kinetic friction between it and the
A freight elevator, including its load, has mass Me. It is prevented from rotating due to the track and wheels mounted along its sides. If the motor M develops a constant tension T in its attached
At the instant shown the block A of weight WA is moving down the plane at v0 while being attached to the block B of weight WB. If the coefficient of kinetic friction is μk, determine the
A woman having a mass M stands in an elevator which has a downward acceleration a starting from rest. Determine the work done by her weight and the work of the normal force which the floor exerts on
The crate of weight W has a velocity vA when it is at A. Determine its velocity after it slides down the plane to s = s'. The coefficient of kinetic friction between the crate and the plane is μk.
The crate of mass M is subjected to a force having a constant direction and a magnitude F, where s is measured in meters. When s = s1, the crate is moving to the right with a speed v1. Determine its
The “air spring” A is used to protect the support structure B and prevent damage to the conveyor-belt tensioning weight C in the event of a belt failure D. The force developed by the spring as a
The block has a mass M and moves within the smooth vertical slot. If it starts from rest when the attached spring is in the unstretched position at A, determine the constant vertical force F which
The collar has mass M and slides along the smooth rod. Two springs are attached to it and the ends of the rod as shown. If each spring has an uncompressed length L and the collar has speed v0 when s
Two equal-length springs are “nested” together in order to form a shock absorber. If it is designed to arrest the motion of mass M that is dropped from a height s1 above the top of the springs
The ride at an amusement park consists of a gondola which is lifted to a height h at A. If it is released from rest and falls along the parabolic track, determine the speed at the instant y = d. Also
The double-spring bumper is used to stop the steel billet of weight W in the rolling mill. Determine the maximum deflection of the plate A caused by the billet if it strikes the plate with a speed v.
The collar of weight W has a speed v at A. The attached spring has an unstretched length δ and a stiffness k. If the collar moves over the smooth rod, determine its speed when it reaches point B,
The spring mechanism is used as a shock absorber for railroad cars. Determine the maximum compression of spring HI if the fixed bumper R of a railroad car of mass M, rolling freely at speed v strikes
The safe S has weight Ws and is supported by the rope and pulley arrangement shown. If the end of the rope is given to a boy B of weight Wb, determine his acceleration if in the confusion he
The mine car of mass mcar is hoisted up the incline using the cable and motor M. For a short time, the force in the cable is F = bt2. If the car has an initial velocity v0 when t = 0, determine its
The mine car of mass mcar is hoisted up the incline using the cable and motor M. For a short time, the force in the cable is F = bt2. If the car has an initial velocity v0 when t = 0, determine the
The tanker has a weight W and is traveling forward at speed v0 in still water when the engines are shut off. If the drag resistance of the water is proportional to the speed of the tanker at any
The block A of mass mA rests on the plate B of mass mB in the position shown. Neglecting the mass of the rope and pulley, and using the coefficients of kinetic friction indicated, determine the time
The collar C of mass mc is free to slide along the smooth shaft AB. Determine the acceleration of collar C if collar A is subjected to an upward acceleration a. The collar moves in the plane. Given:
The collar C of mass mc is free to slide along the smooth shaft AB. Determine the acceleration of collar C if(a) The shaft is fixed from moving,(b) Collar A, which is fixed to shaft AB, moves
Determine the acceleration of block A when the system is released from rest. The coefficient of kinetic friction and the weight of each block are indicated. Neglect the mass of the pulleys and cord.
Block B rests on a smooth surface. If the coefficients of static and kinetic friction between A and B are μs and μk respectively, determine the acceleration of each block if someone pushes
The conveyor belt is moving at speed v. If the coefficient of static friction between the conveyor and the package B of mass M is μs, determine the shortest time the belt can stop so that the
Blocks A and B each have mass m. Determine the largest horizontal force P which can be applied to B so that A will not slip up B. The coefficient of static friction between A and B is μs. Neglect
The conveyor belt delivers each crate of mass M to the ramp at A such that the crate’s speed is vA directed down along the ramp. If the coefficient of kinetic friction between each crate and the
Each of the three plates has mass M. If the coefficients of static and kinetic friction at each surface of contact are μs and μk respectively, determine the acceleration of each plate when the
The tractor is used to lift load B of mass M with the rope of length 2h, and the boom, and pulley system. If the tractor is traveling to the right at constant speed v, determine the tension in the
Crate B has a mass m and is released from rest when it is on top of cart A, which has a mass 3m. Determine the tension in cord CD needed to hold the cart from moving while B is sliding down A.
The tractor is used to lift load B of mass M with the rope of length 2h, and the boom, and pulley system. If the tractor is traveling to the right with an acceleration a and has speed v at the
Block B has a mass m and is hoisted using the cord and pulley system shown. Determine the magnitude of force F as a function of the block’s vertical position y so that when F is applied the block
Block A has mass mA and is attached to a spring having a stiffness k and unstretched length l0. If another block B, having mass mB is pressed against A so that the spring deforms a distance d,
Block A has a mass mA and is attached to a spring having a stiffness k and unstretched length l0. If another block B, having a mass mB is pressed against A so that the spring deforms a distance d,
The helicopter of mass M is traveling at a constant speed v along the horizontal curved path while banking at angle θ. Determine the force acting normal to the blade, i.e., in the y' direction, and
The plane is traveling at a constant speed v along the curve y = bx2 + c. If the pilot has weight W, determine the normal and tangential components of the force the seat exerts on the pilot when the
The helicopter of mass M is traveling at a constant speed v along the horizontal curved path having a radius of curvature ρ. Determine the force the blade exerts on the frame and the bank angle θ.
The sled and rider have a total mass M and start from rest at A(b, 0). If the sled descends the smooth slope, which may be approximated by a parabola, determine the normal force that the ground
If the crest of the hill has a radius of curvature ρ, determine the maximum constant speed at which the car can travel over it without leaving the surface of the road. Neglect the size of the car in
The sled and rider have a total mass M and start from rest at A(b, 0). If the sled descends the smooth slope which may be approximated by a parabola, determine the normal force that the ground exerts
The snowmobile of mass M with passenger is traveling down the hill at a constant speed v. Determine the resultant normal force and the resultant frictional force exerted on the tracks at the instant
Determine the constant speed of the passengers on the amusement-park ride if it is observed that the supporting cables are directed at angle q from the vertical. Each chair including its passenger
The snowmobile of mass M with passenger is traveling down the hill such that when it is at point A, it is traveling at speed v and increasing its speed at v'. Determine the resultant normal force and
A collar having a mass M and negligible size slides over the surface of a horizontal circular rod for which the coefficient of kinetic friction is μk. If the collar is given a speed v1 and then
The roller coaster car and passenger have a total weight W and starting from rest at A travel down the track that has the shape shown. Determine the normal force of the tracks on the car when the car
The pendulum bob B of mass M is released from rest when θ = 0°. Determine the initial tension in the cord and also at the instant the bob reaches point D, θ = θ1. Neglect the size of the bob.
The smooth block B, having mass M, is attached to the vertex A of the right circular cone using a light cord. The cone is rotating at a constant angular rate about the z axis such that the block
A ball having a mass M and negligible size moves within a smooth vertical circular slot. If it is released from rest at θ1, determine the force of the slot on the ball when the ball arrives at
The box of mass M has a speed v0 when it is at A on the smooth ramp. If the surface is in the shape of a parabola, determine the normal force on the box at the instant x = x1. Also, what is the rate
The man has mass M and sits a distance d from the center of the rotating platform. Due to the rotation his speed is increased from rest by the rate v'. If the coefficient of static friction between
The collar A, having a mass M, is attached to a spring having a stiffness k. When rod BC rotates about the vertical axis, the collar slides outward along the smooth rod DE. If the spring is
The block has weight W and it is free to move along the smooth slot in the rotating disk. The spring has stiffness k and an unstretched length δ. Determine the force of the spring on the block and
A particle having mass M moves along a path defined by the equations r = a + bt, θ = ct2 + d and z = e + ft3. Determine the r, θ, and z components of force which the path exerts on the particle
The boy has weight W and hangs uniformly from the bar. Determine the force in each of his arms at time t = t1 if the bar is moving upward with(a) A constant velocity v0(b) A speed v = bt2 Given: W =
The path of motion of a particle of weight W in the horizontal plane is described in terms of polar coordinates as r = at + b and θ = ct2 + dt. Determine the magnitude of the unbalanced force acting
A satellite S travels in a circular orbit around the earth. A rocket is located at the apogee of its elliptical orbit for which the eccentricity is e. Determine the sudden change in speed that must
The rocket is traveling in free flight along an elliptical trajectory A'A .The planet has no atmosphere, and its mass is k times that of the earth’s. The rocket has an apoapsis and periapsis as
An asteroid is in an elliptical orbit about the sun such that its perihelion distance is d. If the eccentricity of the orbit is e, determine the aphelion distance of the orbit. Given: d = 9.30 x 10
A rocket is in free-flight elliptical orbit around the planet Venus. Knowing that the periapsis and apoapsis of the orbit are rp and ap, respectively, determine(a) The speed of the rocket at point
The rocket is traveling in a free-flight elliptical orbit about the earth such that the eccentricity is e and its perigee is a distanced d as shown. Determine its speed when it is at point B. Also
A satellite is in an elliptical orbit around the earth with eccentricity e. If its perigee is hp, determine its velocity at this point and also the distance OB when it is at point B, located at angle
The rocket is traveling in free flight along an elliptical trajectory A'A. The planet has no atmosphere, and its mass is k times that of the earth’s. If the rocket has an apoapsis and periapsis as
The speed of a satellite launched into a circular orbit about the earth is given by Eq. 13-25. Determine the speed of a satellite launched parallel to the surface of the earth so that it travels in a
A communications satellite is to be placed into an equatorial circular orbit around the earth so that it always remains directly over a point on the earth’s surface. If this requires the period T
An elliptical path of a satellite has an eccentricity e. If it has speed vp when it is at perigee, P, determine its speed when it arrives at apogee, A. Also, how far is it from the earth's surface
The rocket is in circular orbit about the earth at altitude h. Determine the minimum increment in speed it must have in order to escape the earth's gravitational field. Given: h = 4106 m G = 66.73 x
Using air pressure, the ball of mass M is forced to move through the tube lying in the vertical plane and having the shape of a logarithmic spiral. If the tangential force exerted on the ball due to

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