Solved: Figure 5-55 gives, as a function of time t, the

Only two horizontal forces act on a 3.0 kg body that can move over a frictionless floor. One force is 9.0 N, acting due east, and the other is 8.0 N, acting 62 north of west. What is the magnitude of the body's acceleration?

Two horizontal forces act on a 2.0 kg chopping block that can slide over a frictionless kitchen counter, which lies in an xy plane. One force is FI = (3.0 N)i + (4.0 N)]. Find the acceleration of the chopping block in unit-vector notation when the other force is (a) F2 = (-3.0 N)i + (-4.0 N)], (b) F2 = (-3.0 N)i + (4.0 N)], and (c) F2 = (3.0 N)i + (-4.0 N)].

If the 1 kg standard body has an acceleration of 2.00 m/s2 at 20.0 to the positive direction of an x axis, what are (a) the x component and (b) the y component of the net force acting on the body, and (c) what is the net force in unit-vector notation?

While two forces act on it, a particle is to move at the constant velocity v = (3 mls)i - (4 mls)]. One of the forces is ~ = (2 N)i + ( -6 N)]. What is the other force?

Three astronauts, propelled by jet backpacks, push and guide a 120 kg asteroid toward a processing dock, exerting the forces shown in Fig. 5-29, with FI = 32 N, F2 = 55 N, F3 = 41 N, 81 = 30, and 83 = 60. What is the asteroid's acceleration (a) in unit-vector notation and as (b) a magnitude and ( c) a direction relative to the positive direction of the x axis?

In a two-dimensional tug-ofwar, Alex, Betty, and Charles pull horizontally on an automobile tire at the angles shown in the overhead view of Fig. 5-30. The tire remains stationary in spite of the three pulls. Alex pulls with force ~ of magnitude 220 N, and Charles pulls with force Fc of magnitude 170 N. Note that the direction of Fc is not given. What is the magnitude of Betty's force Fs?

There are two forces on the 2.00 kg box in the overhead view of Fig. 5-31, but only one is shown. For FI = 20.0 N, a = 12.0 mls2, and 8 = 30.0, find the second force (a) in unit -vector notation and as (b) a magnitude and (c) an angle relative to the positive direction of the x axis.

A 2.00 kg object is subjected to three forces that give it an acceleration a = -(8.00 mls2)i + (6.00 mls2)J, If two of the three forces are ~ = (30.0 N)i + (16.0 N)] and lS = -(12.0 N)i + (8.00 N)I, find the third force.

A 0.340 kg particle moves in an xy plane according to x(t) = -15.00 + 2.00t - 4.00t3 and yet) = 25.00 + 7.00t - 9.00t2, with x and y in meters and t in seconds. At t = 0.700 s, what are (a) the magnitude and (b) the angle (relative to the positive direction of the x axis) of the net force on the particle, and (c) what is the angle of the particle's direction of travel?

A 0.150 kg particle moves along an x axis according to x(t) = -13.00 + 2.00t + 4.00t2 - 3.00t3, with x in meters and tin seconds. In unit-vector notation, what is the net force acting on the particle at t = 3.40 s?

A 2.0 kg particle moves along an x axis, being propelled by a variable force directed along that axis. Its position is given by x = 3.0 m + (4.0 mls)t + ct2 - (2.0 m/s3 )t3, with x in meters and tin seconds. The factor c is a constant. At t = 3.0 s, the force on the particle has a magnitUde of 36 N and is in the negative direction of the axis. What is c?

Two horizontal forces FI and F2 act on a 4.0 kg disk that slides over frictionless ice, on which an xy coordinate system l'x is laid out. Force FI is in the positive direction of the x axis 2 and has a magnitude of 7.0 N. Force F2 has a magnitUde of 9.0 f----f---7tc---If-----I t (s) N. Figure 5-32 gives the x com- -2 ponent v of the velocity of the disk as a function of time t dur- -4 ing the sliding. What is the an- Fig. 5-32 Problem 12. gle between the constant directions of forces FI and F2

Figure 5-33 shows an arrangement in which four disks are suspended by cords. The longer, top cord loops over a frictionless pulley and pulls with a force of magnitude 98 N on the wall to which it is attached. The tensions in the three shorter cords are TI = 58.8 N, T2 = 49.0 N, and T3 = 9.8 N. What are the masses of (a) disk A, (b) disk B, (c) disk C, and (d) disk D?

A block with a weight of 3.0 N is at rest on a horizontal surface. A 1.0 N upward force is applied to the block by means of an attached vertical string. What are the (a) magnitude and (b) direction of the force of the block on the horizontal surface?

(a) An 11.0 kg salami is supported by a cord that runs to a spring scale,which is upported by a cord hung from the ceiling (Fig. 5-34a). What is the reading on the scale, which is marked in weight units? (b) In Fig. 5-34b the salami is supported by a cord that runs around a pulley and to a scale. The opposite end of the scale is attached by a cord to a wall. What is the reading on the scale? (c) In Fig. 5-34c the wall has been replaced with a second 11.0 kg salami, and the assembly is stationary. What is the reading on the scale?

Some insects can walk below a thin rod (such as a twig) by hanging from it. Suppose that such an in- ~~~t sect has mass m and hangs from a horizontal rod as shown in Fig. 5-35, with angle () = 40. Its six legs are all ~ i ' - under the same tension, and the leg sections nearest the body are hori- Fig. 5-35 Problem 16. zontal. (a) What is the ratio of the tension in each tibia (forepart of a leg) to the insect's weight? (b) If the insect straightens out its legs somewhat, does the tension in each tibia increase, decrease, or stay the same?

In Fig. 5-36, let the mass of the block be 8.5 kg and the angle () be 30. Find (a) the tension in the cord and (b) the normal force acting on the block. (c) If the cord is cut, find the magnitude of the resulting acceleration of the block.

n April 1974, John Massis of Belgium managed to move two passenger railroad Fig.5-36 Problem 17. cars. He did so by clamping his teeth down on a bit that was attached to the cars with a rope and then leaning backward while pressing his feet against the railway ties. The cars together weighed 700 kN (about 80 tons). Assume that he pulled with a constant force that was 2.5 times his body weight, at an upward angle () of 30 from the horizontal. His mass was 80 kg, and he moved the cars by 1.0 m. Neglecting any retarding force from the wheel rotation, find the speed of the cars at the end of the pull.

A 500 kg rocket sled can be accelerated at a constant rate from rest to 1600 km/h in 1.8 s. What is the magnitude of the required net force?

A car traveling at 53 km/h hits a bridge abutment. A passenger in the car moves forward a distance of 65 cm (with respect to the rend) while being brought to rest by an inflated air bag. What magnitude of force (assumed constant) a

A constant horizontal force Fa pushes a 2.00 kg FedEx package across a frictionless floor on which an xy coordinate system has been drawn. Figure 5-37 gives the package's x and y velocity components versus time t. What are the (a) magnitude and (b) direction of Fa?

A customer sits in an amusement park ride in which the compartment is to be pulled downward in the negative direction of a y axis with an acceleration magnitude of 1.24g, with g = 9.80 mls2 A 0.567 g coin rests on the customer's knee. Once the motion begins and in unit-vector notation, what is the coin's acceleration relative to (a) the ground and (b) the customer? (c) How long does the coin take to reach the compartment ceiling, 2.20 m above the knee? In unit-vector notation, what are (d) the actual force on the coin and (e) the apparent force according to the customer's measure of the coin's acceleration?

Tarzan, who weighs 820 N, swings from a cliff at the end of a 20.0 m vine that hangs from a high tree limb and initially makes an angle of 22.0 with the vertical. Assume that an x axis extends horizontally away from the cliff edge and a y axis extends upward. Immediately after Tarzan steps off the cliff, the tension in the vine is 760 N. Just then, what are (a) the force on him from the vine in unit-vector notation and the net force on him (b) in unit-vector notation and as (c) a magnitude and (d) an angle relative to the positive direction of the x axis? What are the (e) magnitude and (f) angle of Tarzan's acceleration just then?

There are two horizontal forces on the 2.0 kg box in the overhead view of Fig. 5-38 but only one (of magnitude FI = 20 N) is shown. Fig. 5-38 Problem 24. The box moves along the x axis. For each of the following values for the acceleration a, of the box, find the second force in unit-vector notation: (a) 10 m/s2, (b) 20 m/s2, (c) 0, (d) -10 mls2, and (e) -20 mls2

Sunjamming. A "sun yacht" is a spacecraft with a large sail that is pushed by sunlight. Although such a push is tiny in everyday circumstances, it can be large enough to send the spacecraft outward from the Sun on a cost-free but slow trip. Suppose that the spacecraft has a mass of 900 kg and receives a push of 20 N. (a) What is the magnitude of the resulting acceleration? If the craft starts from rest, (b) how far will it travel in 1 day and (c) how fast will it then be moving?

The tension at which a fishing line snaps is commonly called the line's "strength." What minimum strength is needed for a line that is to stop a salmon of weight 85 N in 11 cm if the fish is initially drifting at 2.8 mls? Assume a constant deceleration.

An electron with a speed of 1.2 X 107 mls moves horizontally into a region where a constant vertical force of 4.5 X 10- 16 N acts on it. The mass of the electron is 9.11 X 10-31 kg. Determine the vertical distance the electron is deflected during the time it has moved 30 mm horizontally.

A car that weighs 1.30 X 104 N is initially moving at 40 km/h when the brakes are applied and the car is brought to a stop in 15 m. Assuming the force that stops the car is constant, find (a) the magnitude of that force and (b) the time required for the change in speed. If the initial speed is doubled, and the car experiences the same force during the braking, by what factors are (c) the stopping distance and (d) the stopping time multiplied? (There could be a lesson here about the danger of driving at high speeds.)

A firefighter who weighs 712 N slides down a vertical pole with an acceleration of 3.00 m/s2, directed downward. What are the (a) magnitude and (b) direction (up or down) of the vertical force on the firefighter from the pole and the (c) magnitude and (d) direction of the vertical force on the pole from the firefighter?

The high-speed winds around a tornado can drive projectiles into trees, building walls, and even metal traffic signs. In a laboratory simulation, a standard wood toothpick was shot by pneumatic gun into an oak branch. The toothpick's mass was 0.13 g, its speed before entering the branch was 220 mis, and its penetration depth was 15 mm. If its speed was decreased at a uniform rate, what was the magnitude of the force of the branch on the toothpick?

A block is projected up a frictionless inclined plane with initial speed Vo = 3.50 m/s. The angle of incline is () = 32.00 (a) How far up the plane does the block go? (b) How long does it take to get there? (c) What is its speed when it gets back to the bottom?

Figure 5-39 shows an overhead view of a 0.0250 kg lemon half and two of the three horizontal forces that act on it as it is on a frictionless table. Force ~ has a magnitude of 6.00 N and is at (}j = 30.00 Force IS has a magnitude of 7.00 N and is at (}2 = 30.00 In unit-vector notation, what is )' )-----.\' the third force if the lemon half (a) Fig.5-39 Problem 32. is stationary, (b) has the constant velocity v = (13.01 - 14.0]) mis, and (c) has the varying velocity v = (13.0ti 14.0tD mls2 , where tis time?

An elevator cab and its load have a combined mass of 1600 kg. Find the tension in the supporting cable when the cab, originally moving downward at 12 mis, is brought to rest with constant acceleration in a distance of 42 m.

In Fig. 5-40, a crate of mass 111 = 100 kg is pushed at constant speed up a frictionless ramo -4 III () = 30.00 ) by a horizontal force F. What are the magnitudes of (a) F and (b) the force on the crate from the ramp?

The velocity of a 3.00 kg particle is given by v = (8.00ti + 3.00t2J) mis, with time t in seconds. At the instant the net force on the particle has a magnitude of 35.0 N, what are Fig. 5-40 Problem 34. the direction (relative to the positive direction of the x axis) of (a) the net force and (b) the particle's direction of travel?

Holding on to a towrope moving parallel to a frictionless ski slope, a 50 kg skier is pulled up the slope, which is at an angle of 8.00 with the horizontal. What is the magnitude Frope of the force on the skier from the rope when (a) the magnitude v of the skier's velocity is constant at 2.0 m/s and (b) v = 2.0 m/s as v increases at a rate of 0.10 m/s2?

A 40 kg girl and an 8.4 kg sled are on the frictionless ice of a frozen lake, 15 m apart but connected by a rope of negligible mass. The girl exerts a horizontal 5.2 N force on the rope. What are the acceleration magnitudes of (a) the sled and (b) the girl? (c) How far from the girl's initial position do they meet?

A 40 kg skier skis directly down a frictionless slope angled at 100 to the horizontal. Assume the skier moves in the negative direction of an x axis along the slope. A wind force with component Fr acts on the skier. What is F, if the magnitude of the skier's velocity is (a) constant, (b) increasing at a rate of 1.0 mls2, and (c) increasing at a rate of2.0 mls2?

A sphere of mass 3.0 X 10-4 kg is suspended from a cord. A steady horizontal breeze pushes the sphere so Vx (m/s) that the cord makes a con- 4 stant angle of 370 with the vertical. Find (a) the push magnitude and (b) the tension in the cord.

A dated box of dates, of mass 5.00 kg, is sent sliding up a frictionless ramp at an angle of () to the horizontal.Figure 5-41 gives, as a function of time t, the component vr of the box's velocity along an x axis that extends directly up the ramp. What is the magnitude of the normal force on the box from the ramp?

Using a rope that will snap if the tension in it exceeds 387 N, you need to lower a bundle of old roofing material weighing 449 N from a point 6.1 m above the ground. (a) What magnitude of the bundle's acceleration will put the rope on the verge of snapping? (b) At that acceleration, with what speed would the bundle hit the ground?

In earlier days, horses pulled barges down canals in the manner shown in Fig. 5-42. Suppose the horse pulls on the rope with a force of 7900 N at an angle of 8 = 18 to the direction of motion of the barge, which is headed straight along the positive direction of an x axis. The mass of the barge is 9500 kg, and the magnitude of its acceleration is 0.12 m/s2 What are the (a) magnitude and (b) direction (relative to positive x) of the force on the barge from the water?

In Fig. 5-43, a chain consisting of five links, each of mass 0.100 kg, is lifted vertically with constant acceleration of magnitude a = 2.50 m/s2 Find the magnitudes of (a) the force on link 1 from link 2, (b) the force on link 2 from link 3, (c) the force on link 3 from link 4, and (d) the force on link 4 from link 5. Then find the magnitudes of (e) the force F on the top link from the person lifting the chain and (f) the net force accelerating each link.

A lamp hangs vertically from a cord in a de- Fig. 5-43 scending elevator that decelerates at 2.4 mls2 (a) If Problem 43. the tension in the cord is 89 N, what is the lamp's mass? (b) What is the cord's tension when the elevator ascends with an upward acceleration of 2.4 m/s2 ?

An elevator cab that weighs 27.8 kN moves upward. What is the tension in the cable if the cab's speed is (a) increasing at a rate of 1.22 mls2 and (b) decreasing at a rate of 1.22 mls2?

An elevator cab is pulled upward by a cable. The cab and its single occupant have a combined mass of 2000 kg. When that occupant drops a coin, its acceleration relative to the cab is 8.00 m/s2 downward. What is the tension in the cable?

The Zacchini family was renowned for their humancannonball act in which a family member was shot from a cannon using either elastic bands or compressed air. In one version of the act, Emanuel Zacchini was shot over three Ferris wheels to land in a net at the same height as the open end of the cannon and at a range of 69 m. He was propelled inside the barrel for 5.2 m and launched at an angle of 53. If his mass was 85 kg and he underwent constant acceleration inside the barrel, what was the magnitude of the force propelling him? (Hint: Treat the launch as though it were along a ramp at 53. Neglect air drag.)

In Fig. 5-44, elevator cabs A and B are connected by a short cable and can be pulled upward or lowered by the cable above cab A. Cab A has mass 1700 kg; cab B has mass1300 kg. A 12.0 kg box of catnip lies on the floor of cab A. The tension in the cable connecting the cabs is 1.91 X 104 N. What is the magnitude of the normal force on the box from the floor?

In Fig. 5-45, a block of mass m = 5.00 kg is pulled along a horizontal frictionless floor by a cord that exerts a force of magnitude F = 12.0 N at an angle 8 = 25.0. (a) What is the magnitude of the block's acceleration? (b) The force magnitude F is slowly increased. What is its value just before the block is lifted (completely) off the floor? (c) What is the magnitude of the block's acceleration just before it is lifted (completely) off the floor?

In Fig. 5-46, three ballot boxes are connected by cords, one of which wraps over a pulley having negligible friction on its axle and negligible mass. The three masses are A B Fig. 5-44 Problem 48. B C mA = 30.0 kg, mB = 40.0 kg, and Fig. 5-46 Problem 50. me = 10.0 kg. When the assembly is released from rest, (a) what is the tension in the cord connecting Band C, and (b) how far does A move in the first 0.250 s (assuming it does not reach the pulley)?

Figure 5-47 shows two blocks connected by a cord (of negligible mass) that passes over a frictionless pulley (also of negligible mass). The arrangement is known as Atwoods l11achine. One block has mass m1 = 1.30 kg; the other has mass m2 = 2.80 kg. What are (a) the magnitude of the blocks' acceleration and (b) the tension in the cord?

An 85 kg man lowers himself to the ground from a height of 10.0 m by holding onto a rope that runs over a frictionless pulley to a 65 kg sandbag. With what speed does the man hit the ground if he started from rest?

In Fig. 5-48, three connected blocks are pulled to the right on a horizontal frictionless table by a force of magnitude 73 = 65.0 N. If 1111 = 12.0 kg, /112 = 24.0 kg, and 1113 = 31.0 kg, calculate (a) the magnitude of the system's acceleration, (b) the tension Tb and ( c) the tension T2

Figure 5-49 shows four penguins that are being playfully pulled along very slippery (frictionless) ice by a curator. The masses of three penguins and the tension in two of the cords are 111] = 12 kg, 1113 = 15 kg, 1114 = 20 kg, T2 = 111 N, and T4 = 222 N. Find the penguin mass 1112 that is not given.

Two blocks are in contact on a frictionless table. A horizontal force is applied to the larger block, as shown in Fig. 5-50. (a) If 1111 = 2.3 kg, 1112 = 1.2 kg, and F = 3.2 N, find the magnitude of the force between the two blocks. (b) Show that if a force of the same magnitude F is applied to the smaller Fig. 5-50 Problem 55. block but in the opposite direction, the magnitude of the force between the blocks is 2.1 N, which is not the same value calculated in (a). (c) Explain the difference.

In Fig. 5-51a, a constant horizontal force 1;, is applied to block A, which pushes against block B with a 20.0 N force directed horizontally to the right. In Fig. 5-51b, the same force 1;, is applied to block B; now block A pushes on block B with a 10.0 N force directed horizontally to the left. The blocks have a combined mass of 12.0 kg. What are the magnitudes of (a) their acceleration in Fig. 5-51a and (b) force 1;,

A block of mass 111] = 3.70 kg on a frictionless plane inclined at angle fJ = 30.0 is connected by a cord over a massless, frictionless pulley to a second block of mass 1112 = 2.30 kg (Fig. 5-52). What are (a) the magnitude of the accelera- Fig.5-52 Problem 57. tion of each block, (b) the direction of the acceleration of the hanging block, and (c) the tension in the cord?

Figure 5-53 shows a man sitting in a bosun's chair that dangles from a massless rope, which runs over a massless, frictionless pulley and back down to the man's hand. The combined mass of man and chair is 95.0 kg. With what force magnitude must the man pull on the rope if he is to rise (a) with a constant velocity and (b) with an upward acceleration of 1.30 mls2? (Hint: A free-body diagram can really help.) If the rope on the right extends to the ground and is pulled by a coworker, with what force magnitude must the co-worker pull for the man to rise (c) with a constant velocity and (d) with an upward acceleration of 1.30 m/s2 ? What is the magnitude of the force on the ceiling from the pulley system in (e) part a, (f) part b, (g) part c, and (h) part d?

A 10 kg monkey climbs up a massless rope that runs over a frictionless tree limb and back down to a 15 kg package on the ground (Fig. 5-54). (a) What is the magnitude of the least acceleration the monkey must have if it is to lift the package off the ground? If, after the package has been lifted, the monkey stops its climb and holds onto the rope, what are the (b) magnitude and (c) direction of the monkey's acceleration and (d) the tension in the rope?

Figure 5-45 shows a 5.00 kg block being pulled along a frictionless floor by a cord that applies a force of constant magnitude 20.0 N but with an angle fJ(t) that varies with time. When angle fJ = 25.0, at what rate is the acceleration of the block changing if (a) fJ(t) = (2.00 X 10-2 deg/s)t and (b) fJ(t) = -(2.00 X 10-2 deg/s)t? (Hint: The angle should be in radians.)

A hot-air balloon of mass M is descending vertically with downward acceleration of magnitude a. How much mass (ballast) must be thrown out to give the balloon an upward acceleration of magnitude a? Assume that the upward force from the air (the lift) does not change because of the decrease in mass.

In shot putting, many athletes elect to launch the shot at an angle that is smaller than the theoretical one (about 42) at which the distance of a projected ball at the same speed and height is greatest. One reason has to do with the speed the athlete can give the shot during the acceleration phase of the throw. Assume that a 7.260 kg shot is accelerated along a straight path of length 1.650 m by a constant applied force of magnitude 380.0 N, starting with an initial speed of 2.500 mls (due to the athlete's preliminary motion). What is the shot's speed at the end of the acceleration phase if the angle between the path and the horizontal is (a) 30.00 and (b) 42.000? (Hint: Treat the motion as though it were along a ramp at the given angle.) (c) By what percent is the launch speed decreased if the athlete increases the angle from 30.00 to 42.000?

Figure 5-55 gives, as a function of time t, the force component Fr that acts on a 3.00 kg ice block that can move only along the x axis. At t = 0, the block is moving in the positive direction of the axis, with a speed of 3.0 mls. What are its (a) speed and (b) direction of travel at t = 11 s?

Figure 5-56 shows a box of mass /112 = 1.0 kg on a frictionless plane inclined at angle 8 = 30. It is connected by a cord of negligible mass to a box of mass 1111 = 3.0 kg on a horizontal frictionless surface. The pulley is frictionless and massless. (a) If the magnitude of horizontal force F is 2.3 N, what is the tension in the connecting cord? (b) What is the largest value the magnitude of F may have without the cord becoming slack?

Figure 5-47 shows Atwood's l11achine, in which two containers are connected by a cord (of negligible mass) passing over a frictionless pulley (also of negligible mass). At time t = 0, container 1 has mass 1.30 kg and container 2 has mass 2.80 kg, but container 1 is losing mass (through a leak) at the constant rate of 0.200 kg/so At what rate is the acceleration magnitude of the containers changing at (a) t = 0 and (b) t = 3.00 s? ( c) When does the acceleration reach its maximum value?

Figure 5-57 shows a section of a cable-car system. The maximum permissible mass of each car with occupants is 2800 kg. The cars, riding on a support cable, are pulled by a second cable attached to the support tower on each car. Assume that the cables are taut and inclined at angle 8 = 35. What is the difference in tension between adjacent sections of pull cable if the cars are at the maximum permissible mass and are being accelerated up the incline at 0.81 m/s2?

Figure 5-58 shows three blocks attached by cords that loop over frictionless pulleys. Block B lies on a frictionless table; the masses are I11A = 6.00 kg, 1118 = 8.00 kg, and l11e = 10.0 kg. When the blocks are released, what is the tension in the cord at the right?

A shot putter launches a 7.260 kg shot by pushing it along a straight line of length 1.650 m and at an angle of 34.10 from the horizontal, accelerating the shot to the launch speed from its initial speed of 2.500 m/s (which is due to the athlete's preliminary motion). The shot leaves the hand at a height of 2.110 m and at an angle of 34.10, and it lands at a horizontal distance of 15.90 m. What is the magnitude of the athlete's average force on the shot during the acceleration phase? (Hint: Treat the motion during the acceleration phase as though it were along a ramp at the given angle.)

In Fig. 5-59,4.0 kg block A and 6.0 kg block B are connected by a string of negligible mass. Force ~ = (12 N)i acts on block A; force Fs = (24 N)i acts on block B. What is the tension in the string?

An 80 kg man drops to a concrete patio from a window 0.50 m above the patio. He neglects to bend his knees on landing, taking 2.0 cm to stop. (a) What is his average acceleration from when his feet first touch the patio to when he stops? (b) What is the magnitude of the average stopping force exerted on him by the patio?

Figure 5-60 shows a box of dirty money (mass /111 = 3.0 kg) on a frictionless plane inclined at angle 81 = 30. The box is connected via a cord of negligible mass to a box 81 of laundered money (mass /112 = 2.0 kg) on a frictionless Fig. 5-60 Problem 71. plane inclined at angle 82 = 60. The pulley is frictionless and has negligible mass. What is the tension in the cord?

Three forces act on a particle that moves with unchanging velocity~v = (2 m/s)i (~m/s)]. Two?f the for~es are F; =~ (2 N)i + (3 N)j + (-2 N)k and F2 = (-5 N)i + (8 N)j + (-2 N)k. What is the third force?

In Fig. 5-61, a tin of antioxidants (1111 = 1.0 kg) on a frictionless inclined surface is connected to a tin of corned beef (1112 = 2.0 kg). The pulley is massless and frictionless. An upward force of magnitude F = 6.0 N acts on the corned beef tin, which has a downward acceleration of 5.5 m/s2 What are (a) the tension in the connecting cord and (b) angle ?

The only two forces acting on a body have magnitudes of 20 Nand 35 N and directions that differ by 80. The resulting acceleration has a magnitude of 20 m/s2 What is the mass of the body?

Figure 5-62 is an overhead view of a 12 kg tire that is to be pulled by three horizontal ropes. One rope's force (F1 = 50 N) is indicated. The forces from the other ropes are to be oriented such that the tire's acceleration magnitude a is least. What is that least a if (a) F2 = 30 N, F3 = 20 N; (b) F2 = 30 N, F3 = 10 N;and (c) F2 = F3 = 30 N?

A block of mass M is pulled along a horizontal frictionless surface by a rope of mass In, as shown Fig. 5-62 Problem 75. in Fig. 5-63. A horizontal force J! Fig. 5-63 Problem 76. acts on one end of the rope. (a) Show that the rope must sag, even if only by an imperceptible amount. Then, assuming that the sag is negligible, find (b) the acceleration of rope and block, (c) the force on the block from the rope, and (d) the tension in the rope at its midpoint.

A worker drags a crate across a factory floor by pulling on a rope tied to the crate. The worker exerts a force of magnitUde F = 450 N on the rope, which is inclined at an upward angle 8 = 38 to the horizontal, and the floor exerts a horizontal force of magnitUde f = 125 N that opposes the motion. Calculate the magnitude of the acceleration of the crate if (a) its mass is 310 kg and (b) its weight is 310 N.

In Fig. 5-64, a force J! of magnitude 12 N is applied to a FedEx box of mass 1112 = 1.0 kg. The force is directed up a plane tilted by 8 = 37. The box is connected by a cord to a UPS box of mass m1 = 3.0 kg Fig. 5-64 Problem 78. on the floor. The floor, plane, and pulley are frictionless, and the masses of the pulley and cord are negligible. What is the tension in the cord?

A certain particle has a weight of 22 N at a point where g = 9.8 m/s2 What are its (a) weight and (b) mass at a point where g = 4.9 rnJs2 ? What are its (c) weight and (d) mass if it is moved to a point in space where g = O?

An 80 kg person is parachuting and experiencing a downward acceleration of 2.5 m/s2. The mass of the parachute is 5.0 kg. (a) What is the upward force on the open parachute from the air? (b) What is the downward force on the parachute from the person?

A spaceship lifts off vertically from the Moon, where g = 1.6 rnJs2 . If the ship has an upward acceleration of 1.0 rnJs2 as it lifts off, what is the magnitUde of the force exerted by the ship on its pilot, who weighs 735 N on Earth?

In the overhead view of Fig. 5-65, five forces pull on a box of mass /11 = 4.0 kg. The force magnitudes are F1 = 11 N, F2 = 17 N, F3 = 3.0 N, F4 = 14 N, and Fs = 5.0 N, and angle 84 is 30. Find the box's acceleration (a) in unit-vector notation and as (b) a magnitude and ( c) an angle relative to the positive direction of the x axis.

A certain force gives an object of mass 1111 an acceleration of 12.0 rnJs2 and an object of mass /112 an acceleration of 3.30 m/s2. What acceleration would the force give to an object of mass (a) 1112 - 1111 and (b) 1112 + 1111?

You pull a short refrigerator with a constant force J! across a greased (frictionless) floor, either with J! horizontal (case 1) or with J! tilted upward at an angle 8 (case 2). (a) What is the ratio of the refrigerator's speed in case 2 to its speed in case 1 if you pull for a certain time t? (b) What is this ratio if you pull for a certain distance d?

A 52 kg circus performer is to slide down a rope that will break if the tension exceeds 425 N. (a) What happens if the performer hangs stationary on the rope? (b) At what magnitude of acceleration does the performer just avoid breaking the rope?

Compute the weight of a 75 kg space ranger (a) on Earth, (b) on Mars, where g = 3.7 m/s2, and (c) in interplanetary space, where g = O. (d) What is the ranger's mass at each location?

An object is hung from a spring balance attached to the ceiling of an elevator cab. The balance reads 65 N when the cab is standing still. What is the reading when the cab is moving upward (a) with a constant speed of 7.6 rnJs and (b) with a speed of 7.6 m/s while decelerating at a rate of 2.4 rnJs2?

Imagine a landing craft approaching the surface of Callisto, one of Jupiter's moons. If the engine provides an upward force (thrust) of 3260 N, the craft descends at constant speed; if the engine provides only 2200 N, the craft accelerates downward at 0.39 m/s2 (a) What is the weight of the landing craft in the vicinity of Callisto's surface? (b) What is the mass of the craft? (c) What is the magnitUde of the free-fall acceleration near the surface of Callisto?

A 1400 kg jet engine is fastened to the fuselage of a passenger jet by just three bolts (this is the usual practice). Assume that each bolt supports one-third of the load. (a) Calculate the force on each bolt as the plane waits in line for clearance to take off. (b) During flight, the plane encounters turbulence, which suddenly imparts an upward vertical acceleration of 2.6 rnJs2 to the plane. Calculate the force on each bolt now

An interstellar ship has a mass of 1.20 X 106 kg and is initially at rest relative to a star system. (a) What constant acceleration is needed to bring the ship up to a speed of O.lOe (where e is the speed of light, 3.0 X 108 rnJs) relative to the star system in 3.0 days? (b) What is that acceleration in g units? (c) What force is required for the acceleration? (d) If the engines are shut down when 0.10e is reached (the speed then remains constant), how long does the ship take (start to finish) to journey 5.0 light-months, the distance that light travels in 5.0 months?

A motorcycle and 60.0 kg rider accelerate at 3.0 rnJs2 up a ramp inclined 10 above the horizontal. What are the magnitudes of (a) the net force on the rider and (b) the force on the rider from the motorcycle?

Compute the initial upward acceleration of a rocket of mass 1.3 X 104 kg if the initial upward force produced by its engine (the thrust) is 2.6 X 105 N. Do not neglect the gravitational force on the rocket.

Figure 5-66a shows a mobile hanging from a ceiling; it consists of two metal pieces (1111 = 3.5 kg and 1n2 = 4.5 kg) that are strung together by cords of negligible mass. What is the tension in (a) the bottom cord and (b) the top cord? Figure 5-66b shows a mobile consisting of three metal pieces. Two of the masses are 1113 = 4.8 kg and 1115 = 5.5 kg. The tension in the top cord is 199 N. What is the tension in (c) the lowest cord and (d) the middle cord?

For sport, a 12 kg armadillo runs onto a large pond of level, frictionless ice. The armadillo's initial velocity is 5.0 mls along the positive direction of an x axis. Take its initial position on the ice as being the origin. It slips over the ice while being pushed by a wind with a force of 17 N in the positive direction of the y axis. In unit-vector notation, what are the animal's (a) velocity and (b) position vector when it has slid for 3.0 s?

Suppose that in Fig. 5-12, the masses of the blocks are 2.0 kg and 4.0 kg. (a) Which mass should the hanging block have if the magnitude of the acceleration is to be as large as possible? What then are (b) the magnitude of the acceleration and (c) the tension in the cord?

A nucleus that captures a stray neutron must bring the neutron to a stop within the diameter of the nucleus by means of the strong force. That force, which "glues" the nucleus together, is approximately zero outside the nucleus. Suppose that a stray neutron with an initial speed of 1.4 X 107 m/s is just barely captured by a nucleus with diameter d = 1.0 X 10-14 m. Assuming the strong force on the neutron is constant, find the magnitude of that force. The neutron's mass is 1.67 X 10-27 kg.