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physics
mechanics
Vector Mechanics for Engineers Statics and Dynamics 11th edition Ferdinand Beer, E. Russell Johnston Jr., David Mazurek, Phillip Cornwell, Brian Self - Solutions
Show that the radius r of the moon's orbit can be determined from the radius R of the earth, the acceleration of gravity g at the surface of the earth, and the time ( required for the moon to complete one full revolution about the earth. Compute r knowing that ( = 27.3 days, giving the answer in
Determine the maximum theoretical speed that may be achieved over a distance of 60 m by a car starting from rest, knowing that the coefficient of static friction is 0.80 between the tires and the pavement and that 60 percent of the weight of the car is distributed over its front wheels and 40
A satellite is placed into a circular orbit about the planet Saturn at an altitude of 2100 mi. The satellite describes its orbit with a velocity of 54.7 × 103 mi/h. Knowing that the radius of the orbit about Saturn and the periodic time of Atlas, one of Saturn's moons, are 85.54 × 103 mi and
A 500 kg spacecraft first is placed into a circular orbit about the earth at an altitude of 4500 km and then is transferred to a circular orbit about the moon. Knowing that the mass of the moon is 0.01230 times the mass of the earth and that the radius of the moon is 1737 km, determine(a) The
A space vehicle is in a circular orbit of 2200-km radius around the moon. To transfer it to a smaller circular orbit of 2080-km radius, the vehicle is first placed on an elliptic path AB by reducing its speed by 26.3 m/s as it passes through A. Knowing that the mass of the moon is 73.49 × 1021
To place a communications satellite into a geosynchronous orbit (see Problem 12.80) at an altitude of 22,240 mi above the surface of the earth, the satellite first is released from a space shuttle, which is in a circular orbit at an altitude of 185 mi, and then is propelled by an upper stage
If an automobile's braking distance from 90 km/h is 45 m on level pavement, determine the automobile's braking distance from 90 km/h when it is(a) Going up a 5° incline,(b) Going down a 3-percent incline. Assume the braking force is independent of grade?
A small ball swings in a horizontal circle at the end of a cord of length l1, which forms an angle (1 with the vertical. The cord is then slowly drawn through the support at O until the length of the free end is l2.(a) Derive a relation among l1, l2, (1, and (2.(b) If the ball is set in motion so
Marble A is placed in a hollow tube, and the tube is swung in a horizontal plane causing the marble to be thrown out. As viewed from the top, which of the following choices best describes the path of the marble after leaving the tube?(a) 1(b) 2(c) 3(d) 4(e) 5
The two systems shown start from rest. On the left, two 40 lb weights are connected by an inextensible cord, and on the right, a constant 40 lb force pulls on the cord. Neglecting all frictional forces, which of the following statements is true?(a) Blocks A and C will have the same acceleration(b)
The system shown is released from rest in the position shown. Neglecting friction, the normal force between block A and the ground is(a) Less than the weight of A plus the weight of B(b) Equal to the weight of A plus the weight of B(c) Greater than the weight of A plus the weight of B
People sit on a Ferris wheel at Points A, B, C and D. The Ferris wheel travels at a constant angular velocity. At the instant shown, which person experiences the largest force from his or her chair (back and seat)? Assume you can neglect the size of the chairs, that is, the people are located the
At the instant shown, the length of the boom AB is being decreased at the constant rate of 0.2 m/s, and the boom is being lowered at the constant rate of 0.08 rad/s. If the mass of the men and lift connected to the boom at Point B is m, draw the FBD and KD that could be used to determine the
Disk A rotates in a horizontal plane about a vertical axis at the constant rate 0. Slider B has a mass m and moves in a frictionless slot cut in the disk. The slider is attached to a spring of constant k, which is un-deformed when r = 0. Knowing that the slider is released with no radial velocity
Pin B has a mass m and slides along the slot in the rotating arm OC and along the slot DE which is cut in a fixed horizontal plate. Neglecting friction and knowing that rod OC rotates at the constant rate 0, draw a FBD and KD that can be used to determine the forces P and Q exerted on pin B by rod
Two blocks weighing WA and WB are at rest on a conveyor that is initially at rest. The belt is suddenly started in an upward direction so that slipping occurs between the belt and the boxes. Assuming the coefficient of friction between the boxes and the belt is μk, draw the FBDs and KDs for
Objects A, B, and C have masses mA, mB, and mC respectively. The coefficient of kinetic friction between A and B is μk, and the friction between A and the ground is negligible and the pulleys are mass-less and frictionless. Assuming B slides on A draw the FBD and KD for each of the three masses
Blocks A and B have masses mA and mB respectively. Neglecting friction between all surfaces, draw the FBD and KD for each mass?
Blocks A and B have masses mA and mB respectively. Neglecting friction between all surfaces, draw the FBD and KD for the two systems shown?
Wires AC and BC are attached to a sphere which revolves at a constant speed v in the horizontal circle of radius r as shown. Draw a FBD and KD of C?
A collar of mass m is attached to a spring and slides without friction along a circular rod in a vertical plane. The spring has an un-deformed length of 5 in. and a constant k. Knowing that the collar has a speed v at Point C, draw the FBD and KD of the collar at this point?
A 400-kg satellite is placed in a circular orbit 6394 km above the surface of the earth. At this elevation the acceleration of gravity is 4.09m/s2. Knowing that its orbital speed is 20 000 km/h, determine the kinetic energy of the satellite.
A 1.4 kg model rocket is launched vertically from rest with a constant thrust of 25 N until the rocket reaches an altitude of 15 m and the thrust ends. Neglecting air resistance, determine(a) The speed of the rocket when the thrust ends,(b) The maximum height reached by the rocket,(c) The speed of
A spacecraft is describing an elliptic orbit of minimum altitude hA = 2400 km and maximum altitude hB = 9600 km above the surface of the earth. Determine the speed of the spacecraft at A.
While describing a circular orbit, 185 mi 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 geosynchronous orbit at an altitude of 22,230 mi above the surface of the earth.Determine(a) The velocity of
A spacecraft approaching the planet Saturn reaches Point A with a velocity vA of magnitude 68.8 x 103 ft/s It is to be placed in an elliptic orbit about Saturn so that it will be able to periodically examine Tethys, one of Saturn's moons. Tethys is in a circular orbit of radius 183 x 103 mi about
A spacecraft traveling along a parabolic path toward the planet Jupiter is expected to reach Point A with a velocity vA of magnitude 26.9 km/s. Its engines will then be fired to slow it down, placing it into an elliptic orbit which will bring it to within 100 x 103 km of Jupiter. Determine the
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 the earth and to Mars are 149.6 x 106km and 227.8 x 106 km, respectively. To place the spacecraft into
The optimal way of transferring a space vehicle from an inner circular orbit to an outer coplanar circular orbit is to fire its engines as it passes through A to increase its speed and place it in an elliptic transfer orbit. Another increase in speed as it passes through B will place it in the
During a flyby of the earth, the velocity of a spacecraft is 10.4 km/s as it reaches its minimum altitude of 990 km above the surface at Point A. At Point B the spacecraft is observed to have an altitude of 8350 km.Determine(a) The magnitude of the velocity at Point B,(b) The angle Ï•B.
A space platform is in a circular orbit about the earth at an altitude of 300 km. As the platform passes through A, a rocket carrying a communications satellite is launched from the platform with a relative velocity of magnitude 3.44 km/s in a direction tangent to the orbit of the platform. This
Packages are thrown down an incline at A with a velocity of 1 m/s. The packages slide along the surface ABC to a conveyor belt which moves with a velocity of 2 m/s. Knowing that 0.25µk = 0.25 between the packages and the surface ABC, determine the distance d if the packages are to arrive at C
A space vehicle is in a circular orbit at an altitude of 225 mi 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 a direction opposite to the direction of its motion. Knowing that the velocity of the space vehicle
A space probe describes a circular orbit of radius nR with a velocity v0 about a planet of radius R and center O.Show that(a) In order for the probe to leave its orbit and hit the planet at an angle θ with the vertical, its velocity must be reduced to αv0, where(b) The probe will not hit the
(a) Express in terms of rmin and vmax the angular momentum per unit mass, h, and the total energy per unit mass, E/m, of a space vehicle moving under the gravitational attraction of a planet of mass M.(b) Eliminating vmax between the equations obtained, derive the formula.(c) Show that the
A 35,000 Mg ocean liner has an initial velocity of 4 km/h. Neglecting the frictional resistance of the water, determine the time required to bring the liner to rest by using a single tugboat which exerts a constant force of 150 kN.
Packages are thrown down an incline at A with a velocity of 1 m/s. The packages slide along the surface ABC to a conveyor belt which moves with a velocity of 2 m/s. Knowing that d = 7.5m and µk = 0.25 between the packages and all surfaces,Determine(a) The speed of the package at C,(b) The
A 2500-lb automobile is moving at a speed of 60 mi/h when the brakes are fully applied, causing all four wheels to skid.Determine the time required to stop the automobile(a) On dry pavement,(b) On an icy road.
A sailboat weighing 980 lb with its occupants is running down wind at 8 mi/h when its spinnaker is raised to increase its speed. Determine the net force provided by the spinnaker over the 10-s interval that it takes for the boat to reach a speed of 12 mi/h.
A truck is hauling a 300-kg log out of a ditch using a winch attached to the back of the truck. Knowing the winch applies a constant force of 2500 N and the coefficient of kinetic friction between the ground and the log is 0.45, determine the time for the log to reach a speed of 0.5m/s.
Baggage on the floor of the baggage car of a high-speed train is not prevented from moving other than by friction. The train is travelling down a 5 percent grade when it decreases its speed at a constant rate from 120 mi/h to 60 mi/h in a time interval of 12 s. Determine the smallest allowable
The 18000-kg F-35B uses thrust vectoring to allow it to take off vertically. In one maneuver, the pilot reaches the top of her static hover at 200 m. The combined thrust and lift force on the airplane applied at the end of the static hover can be expressed as F = (44t + 2500t2)i + (250t2 + t +
A light train made of two cars travels at 45 mi/h. Car A weighs 18 tons, and car B weighs 13 tons. When the brakes are applied, a constant braking force of 4300 lb is applied to each car.Determine(a) The time required for the train to stop after the brakes are applied,(b) The force in the coupling
Boxes are transported by a conveyor belt with a velocity v0 to a fixed incline at A where they slide and eventually fall off at B. Knowing that 0.40,µk = determine the velocity of the conveyor belt if the boxes leave the incline at B with a velocity of 8 ft/s.
The system shown is at rest when a constant 150-N force is applied to collar B. Neglecting the effect of friction,Determine(a) The time at which the velocity of collar B will be 2.5 m/s to the left,(b) The corresponding tension in the cable.
An 8-kg cylinder C rests on a 4-kg platform A supported by a cord which passes over the pulleys D and E and is attached to a 4-kg block B. Knowing that the system is released from rest,Determine(a) The velocity of block B after 0.8 s,(b) The force exerted by the cylinder on the platform.
A 60-g model rocket is fired vertically. The engine applies a thrust P which varies in magnitude as shown. Neglecting air resistance and the change in mass of the rocket,Determine(a) The maximum speed of the rocket as it goes up,(b) The time for the rocket to reach its maximum elevation.
A crash test is performed between an SUV A and a 2500 lb compact car B. The compact car is stationary before the impact and has its brakes applied. A transducer measures the force during the impact, and the force P varies as shown. Knowing that the coefficients of friction between the tires and
A crash test is performed between a 4500 lb SUV A and a compact car B. A transducer measures the force during the impact, and the force P varies as shown. Knowing that the SUV is travelling 30 mph when it hits the car, determine the speed of the SUV immediately after the impact.
Boxes are transported by a conveyor belt with a velocity v0 to a fixed incline at A where they slide and eventually fall off at B. Knowing that 0.40,µk = determine the velocity of the conveyor belt if the boxes are to have zero velocity at B.
A 1.62 ounce golf ball is hit with a golf club and leaves it with a velocity of 100 mi/h. We assume that for 0 ≤ t ≤ t0, where t0 is the duration of the impact, the magnitude F of the force exerted on the ball can be expressed as F = Fmsin(πt/t0). Knowing that t0 = 0.5ms, determine the maximum
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 athlete. Assuming that he approaches the takeoff line from the left with a horizontal velocity of 10 m/s,
The last segment of the triple jump track-and-field event is the jump, in which the athlete makes a final leap, landing in a sand-filled pit. Assuming that the velocity of a 80-kg athlete just before landing is 9 m/s at an angle of 35° with the horizontal and that the athlete comes to a complete
The design for a new cementless hip implant is to be studied using an instrumented implant and a fixed simulated femur. Assuming the punch applies an average force of 2 kN over a time of 2 ms to the 200 g implant.Determine(a) The velocity of the implant immediately after impact,(b) The average
A 25-ton railroad car moving at 2.5 mi/h is to be coupled to a 50 ton car which is at rest with locked wheels.Determine(a) The Velocity of both cars after the coupling is completed,(b) The time it takes for both cars to come to rest.
At an intersection car B was traveling south and car A was traveling 30° north of east when they slammed into each other. Upon investigation it was found that after the crash the two cars got stuck and skidded off at an angle of 10° north of east. Each driver claimed that he was going at the
The 650-kg hammer of a drop-hammer pile driver falls from a height of 1.2 m onto the top of a 140-kg pile, driving it 110 mm into the ground. Assuming perfectly plastic impact (0),Determine the average resistance of the ground to penetration.
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 head of the hammer has a weight of 1.5 lbs and that it strikes the rivet with a velocity of 20 ft/s.
Bullet B weighs 0.5 oz and blocks A and C both weigh 3 lb. The coefficient of friction between the blocks and the plane is µk = 0.25, Initially the bullet is moving at v0 and blocks A and C are at rest (Figure 1). After the bullet passes through A it becomes embedded in block C and all three
A 1200-kg trailer is hitched to a 1400-kg car. The car and trailer are traveling at 72 km/h when the driver applies the brakes on both the car and the trailer. Knowing that the braking forces exerted on the car and the trailer are 5000 N and 4000 N, respectively,Determine(a) The distance traveled
A 75-g ball is projected from a height of 1.6 m with a horizontal velocity of 2 m/s and bounces from a 400-g smooth plate supported by springs. Knowing that the height of the rebound is 0.6 m,Determine(a) The velocity of the plate immediately after the impact,(b) The energy lost due to the impact.
A ballistic pendulum is used to measure the speed of high-speed projectiles. A 6-g bullet A is fired into a 1-kg wood block B suspended by a cord of length l = 2.2m. The block then swings through a maximum angle of θ = 60o.Determine(a) The initial speed of the bullet vo,(b) The impulse imparted
A 1-oz bullet is traveling with a velocity of 1400 ft/s when it impacts and becomes embedded in a 5-lb wooden block. The block can move vertically without friction.Determine(a) The velocity of the bullet and block immediately after the impact,(b) The horizontal and vertical components of the
In order to test the resistance of a chain to impact, the chain is suspended from a 240-lb rigid beam supported by two columns. A rod attached to the last link is then hit by a 60-lb block dropped from a 5-ft height. Determine the initial impulse exerted on the chain and the energy absorbed by the
One of the requirements for tennis balls to be used in official competition is that, when dropped onto a rigid surface from a height of 100 in., the height of the first bounce of the ball must be in the range 53 in. ≤ h ≤ 58 in. Determine the range of the coefficient of restitution of the
To apply shock loading to an artillery shell, a 20-kg pendulum A is released from a known height and strikes impactor B at a known velocity v0. Impactor B then strikes the 1-kg artillery shell C. Knowing the coefficient of restitution between all objects is e, determine the mass of B to maximize
A trailer truck enters a 2 percent uphill grade traveling at 72 km/h and reaches a speed of 108 km/h in 300 m. The cab has a mass of 1800 kg and the trailer 5400 kg.Determine(a) The average force at the wheels of the cab,(b) The average force in the coupling between the cab and the trailer.
At an amusement park there are 200-kg bumper cars A, B, and C that have riders with masses of 40 kg, 60 kg, and 35 kg respectively. Car A is moving to the right with a velocity vA = 2m/s and car C has a velocity vB = 1.5m/s to the left, but car B is initially at rest. The coefficient of restitution
At an amusement park there are 200-kg bumper cars A, B, and C that have riders with masses of 40 kg, 60 kg, and 35 kg respectively. Car A is moving to the right with a velocity vA = 2m/s when it hits stationary car B. The coefficient of restitution between each car is 0.8. Determine the velocity of
A 600-g ball A is moving with a velocity of magnitude 6 m/s when it is hit as shown by a 1-kg ball B which has a velocity of magnitude 4 m/s. Knowing that the coefficient of restitution is 0.8 and assuming no friction, determine the velocity of each ball after impact.
Two identical hockey pucks are moving on a hockey rink at the same speed of 3 m/s and in perpendicular directions when they strike each other as shown. Assuming a coefficient of restitution e = 0.9, determine the magnitude and direction of the velocity of each puck after impact.
The coefficient of restitution is 0.9 between the two 60-mm-diameter billiard balls A and B. Ball A is moving in the direction shown with a velocity of 1 m/s when it strikes ball B, which is at rest. Knowing that after impact B is moving in the x direction, determine (a) the angle ,θ (b) the
A boy located at Point A halfway between the center O of a semicircular wall and the wall itself throws a ball at the wall in a direction forming an angle of 45° with OA. Knowing that after hitting the wall the ball rebounds in a direction parallel to OA, determine the coefficient of restitution
The subway train shown is traveling at a speed of 30 mi/h when the brakes are fully applied on the wheels of cars B and C, causing them to slide on the track, but are not applied on the wheels of car A. Knowing that the coefficient of kinetic friction is 0.35 between the wheels and the
The Mars Pathfinder spacecraft used large airbags to cushion its impact with the planet's surface when landing. Assuming the spacecraft had an impact velocity of 18 m/s at an angle of 45° with respect to the horizontal, the coefficient of restitution is 0.85 and neglecting friction, determine
Rockfalls can cause major damage to roads and infrastructure. To design mitigation bridges and barriers, engineers use the coefficient of restitution to model the behavior of the rocks. The rock A falls a distance of 20 m before striking an incline with slope α = 40°. Knowing that the
From experimental tests, smaller boulders tend to have a greater coefficient of restitution than larger boulders. The rock A falls a distance of 20 meters before striking an incline with slope α = 45°. Knowing that h= 30 m and d= 20 m, determine if a boulder will land on the road or beyond
A 1-kg block B is moving with a velocity v0 of magnitude v0 = 2m/s as it hits the 0.5-kg sphere A, which is at rest and hanging from a cord attached at O. Knowing that µk = 0.6 between the block and the horizontal surface and e = 0.8 between the block and the sphere, determine after impact (a)
A 0.25-lb ball thrown with a horizontal velocity v0 strikes a 1.5-lb plate attached to a vertical wall at a height of 36 in. above the ground. It is observed that after rebounding, the ball hits the ground at a distance of 24 in. from the wall when the plate is rigidly attached to the wall (Figure
After having been pushed by an airline employee, an empty 40-kg luggage carrier A hits with a velocity of 5 m/s an identical carrier B containing a 15-kg suitcase equipped with rollers. The impact causes the suitcase to roll into the left wall of carrier B. Knowing that the coefficient of
Blocks A and B each weigh 0.8 lb and block C weighs 2.4 lb. The coefficient of friction between the blocks and the plane is µk = 0.30 Initially block A is moving at a speed v0 = 15 ft/s and blocks B and C are at rest (Fig. 1). After A strikes B and B strikes C, all three blocks come to a stop in
A 5 kg sphere is dropped from a height y = 2 m to test newly designed spring floors used in gymnastics. The mass of the floor section is 10 kg, and the effective stiffness of the floor is k = 120kN/m. Knowing that the coefficient of restitution between the ball and the platform is 0.6,Determine(a)
The subway train shown is traveling at a speed of 30 mi/h when the brakes are fully applied on the wheels of cars A, causing it to slide on the track, but are not applied on the wheels of cars A or B. Knowing that the coefficient of kinetic friction is 0.35 between the wheels and the
A 5 kg sphere is dropped from a height y=3 m to test a new spring floor used in gymnastics. The mass of the floor section B is 12 kg, and the sphere bounces back upwards a distance of 44 mm. Knowing that the maximum deflection of the floor section is 33 mm from its equilibrium position, determine
The three blocks shown are identical. Blocks B and C are at rest when block B is hit by block A, which is moving with a velocity vA of 3 ft/s. After the impact, which is assumed to be perfectly plastic (0),e= the velocity of blocks A and B decreases due to friction, while block C picks up speed,
Block A is released from rest and slides down the frictionless surface of B until it hits a bumper on the right end of B. Block A has a mass of 10 kg and object B has a mass of 30 kg and B can roll freely on the ground. Determine the velocities of A and B immediately after impact when (a) e = 0,
A test machine that kicks soccer balls has a 5-lb simulated foot attached to the end of a 6-ft long pendulum arm of negligible mass. Knowing that the arm is released from the horizontal position and that the coefficient of restitution between the foot and the 1 lb ball is 0.8, determine the exit
Ball B is hanging from an inextensible cord. An identical ball A is released from rest when it is just touching the cord and drops through the vertical distance hA = 8 in. before striking ball B. Assuming e = 0.9 and no friction, determine the resulting maximum vertical displacement hB of ball B.
A 70 g ball B dropped from a height h0 = 1.5 reaches a height h2 = 0.25 m after bouncing twice from identical 210-g plates. Plate A rests directly on hard ground, while plate C rests on a foam-rubber mat. Determine (a) the coefficient of restitution between the ball and the plates, (b) the height
When the rope is at an angle of α =30° the 1-lb sphere A has a speed v0 = 4ft/s. The coefficient of restitution between A and the 2-lb wedge B is 0.7 and the length of rope l = 2.6 ft. The spring constant has a value of 2 lb/in. and θ = 20°. Determine (a) the velocities of A and B
When the rope is at an angle of α = 30° the 1-kg sphere A has a speed v = 0.6 m/s. The coefficient of restitution between A and the 2-kg wedge B is 0.8 and the length of rope l = 0.9 m The spring constant has a value of 1500 N/m and θ = 20°. Determine, (a) the velocities of A and B
Blocks A and B weigh 25 lbs and 10 lbs, respectively, and they are both at a height 6 ft above the ground when the system is released from rest. Just before hitting the ground block A is moving at a speed of 9 ft/s.Determine(a) The amount of energy dissipated in friction by the pulley,(b) The
A 32,000-lb airplane lands on an aircraft carrier and is caught by an arresting cable. The cable is inextensible and is paid out at A and B from mechanisms located below dock and consisting of pistons moving in long oil-filled cylinders. Knowing that the piston-cylinder system maintains a constant
A 2-oz pellet shot vertically from a spring-loaded pistol on the surface of the earth rises to a height of 300 ft. The same pellet shot from the same pistol on the surface of the moon rises to a height of 1900 ft. Determine the energy dissipated by aerodynamic drag when the pellet is shot on the
A 60-g steel sphere attached to a 200-mm cord can swing about Point O in a vertical plane. It is subjected to its own weight and to a force F exerted by a small magnet embedded in the ground. The magnitude of that force expressed in newtons is F = 3000/r2 where r is the distance from the magnet to
A 300-g block is released from rest after a spring of constant k = 600 N/m has been compressed 160 mm. Determine the force exerted by the loop ABCD on the block as the block passes through (a) Point A, (b) Point B, (c) Point C. Assume no friction.
A soccer kicking machine has a 5 lb "simulated foot" attached to A "kicking" attachment goes on the front of a wheelchair, allowing athletes with mobility impairments to play soccer. The athletes load up the spring shown through a ratchet mechanism that pulls the 2 kg "foot" back to the position 1.
A 300-g collar A is released from rest, slides down a frictionless rod, and strikes a 900-g collar B which is at rest and supported by a spring of constant 500 N/m. Knowing that the coefficient of restitution between the two collars is 0.9, determine (a) the maximum distance collar A moves up the
Blocks A and B are connected by a cord which passes over pulleys and through a collar C. The system is released from rest when x = 1.7m. As block A rises, it strikes collar C with perfectly plastic impact (e = 0). After impact, the two blocks and the collar keep moving until they come to a stop and
A 2-kg block A is pushed up against a spring compressing it a distance x. The block is then released from rest and slides down the 20° incline until it strikes a 1-kg sphere B which is suspended from a 1 m inextensible rope. The spring constant k = 800 N/m, the coefficient of friction between A
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