Question: A 12.0-kg box rests on

> Consider the system shown in Fig. P6.81. The rope and pulley have negligible mass, and the pulley is frictionless. Initially the 6.00-kg block is moving downward and the 8.00-kg block is moving to the right, both with a speed of 0.900 m/s. The blocks com

> A physics professor is pushed up a ramp inclined upward at 30.0° above the horizontal as she sits in her desk chair, which slides on frictionless rollers. The combined mass of the professor and chair is 85.0 kg. She is pushed 2.50 m along the incline by

> A 5.00-kg block is moving at v0 = 6.00 m/s along a frictionless, horizontal surface toward a spring with force constant k = 500 N/m that is attached to a wall (Fig. P6.79). The spring has negligible mass. (a) Find the maximum distance the spring will be

> When a car stops suddenly, the passengers tend to move forward relative to their seats. Why? When a car makes a sharp turn, the passengers tend to slide to one side of the car. Why?

> A crate slides up an inclined ramp and then slides down the ramp after momentarily stopping near the top. There is kinetic friction between the surface of the ramp and the crate. Which is greater? (i) The crate’s acceleration going up the ramp; (ii) the

> One end of a horizontal spring with force constant 76.0 N/m is attached to a vertical post. A 2.00-kg block of frictionless ice is attached to the other end and rests on the floor. The spring is initially neither stretched nor compressed. A constant hori

> One end of a horizontal spring with force constant 130.0 N/m is attached to a vertical wall. A 4.00-kg block sitting on the floor is placed against the spring. The coefficient of kinetic friction between the block and the floor is

> The spring of a spring gun has force constant k = 400 N/m and negligible mass. The spring is compressed 6.00 cm, and a ball with mass 0.0300 kg is placed in the horizontal barrel against the compressed spring. The spring is then released, and the ball is

> A 2.50-kg textbook is forced against a horizontal spring of negligible mass and force constant 250 N/m, compressing the spring a distance of 0.250 m. When released, the textbook slides on a horizontal tabletop with coefficient of kinetic friction

> You and your bicycle have combined mass 80.0 kg. When you reach the base of a bridge, you are traveling along the road at 5.00 m/s (Fig. P6.74). At the top of the bridge, you have climbed a vertical distance of 5.20 m and slowed to 1.50 m>s. Ignore wo

> You are asked to design spring bumpers for the walls of a parking garage. A freely rolling 1200-kg car moving at 0.65 m/s is to compress the spring no more than 0.090 m before stopping. What should be the force constant of the spring? Assume that the spr

> A proton with mass 1.67 × 10-27 kg is propelled at an initial speed of 3.00 × 105 m/s directly toward a uranium nucleus 5.00 m away. The proton is repelled by the uranium nucleus with a force of magnitude F = a/x2, where x is the separation between the t

> A small block with a mass of 0.0600 kg is attached to a cord passing through a hole in a frictionless, horizontal surface (Fig. P6.71). The block is originally revolving at a distance of 0.40 m from the hole with a speed of 0.70 m>s. The cord is then

> Consider a spring that does not obey Hooke’s law very faithfully. One end of the spring is fixed. To keep the spring stretched or compressed an amount x, a force along the x-axis with x-component Fx = kx - bx2 + cx3 must be applied to the free end. Here

> A box is sliding with a speed of 4.50 m/s on a horizontal surface when, at point P, it encounters a rough section. The coefficient of friction there is not constant; it starts at 0.100 at P and increases linearly with distance past P, reaching a value of

> When a car is hit from behind, the occupants may experience whiplash. Use Newton’s laws of motion to explain what causes this result.

> A net force along the x-axis that has x-component Fx = -12.0 N + (0.300 N/m2)x2 is applied to a 5.00-kg object that is initially at the origin and moving in the -x-direction with a speed of 6.00 m/s. What is the speed of the object when it reaches the po

> When a car is hit from behind, its passengers undergo sudden forward acceleration, which can cause a severe neck injury known as whiplash. During normal acceleration, the neck muscles play a large role in accelerating the head so that the bones are not i

> A 5.00-kg package slides 2.80 m down a long ramp that is inclined at 24.0° below the horizontal. The coefficient of kinetic friction between the package and the ramp is mk = 0.310. Calculate (a) the work done on the package by friction; (b) the work done

> Consider the blocks in Exercise 6.7 as they move 75.0 cm. Find the total work done on each one (a) if there is no friction between the table and the 20.0-N block, and (b) if

> While doing a chin-up, a man lifts his body 0.40 m. (a) How much work must the man do per kilogram of body mass? (b) The muscles involved in doing a chin-up can generate about 70 J of work per kilogram of muscle mass. If the man can just barely do a 0.40

> A luggage handler pulls a 20.0-kg suitcase up a ramp inclined at 32.0° above the horizontal by a force

> A balky cow is leaving the barn as you try harder and harder to push her back in. In coordinates with the origin at the barn door, the cow walks from x = 0 to x = 6.9 m as you apply a force with x-component Fx = -[20.0 N +(3.0 N/m)x]. How much work does

> You are an engineer working for a manufacturing company. You are designing a mechanism that uses a cable to drag heavy metal blocks a distance of 8.00 m along a ramp that is sloped at 40.0° above the horizontal. The coefficient of kinetic friction betwee

> A road heading due east passes over a small hill. You drive a car of mass m at constant speed v over the top of the hill, where the shape of the roadway is well approximated as an arc of a circle with radius R. Sensors have been placed on the road surfac

> In your physics lab, a block of mass m is at rest on a horizontal surface. You attach a light cord to the block and apply a horizontal force to the free end of the cord. You find that the block remains at rest until the tension T in the cord exceeds 20.0

> A helium balloon hovers in midair, neither ascending nor descending. Is it in equilibrium? What forces act on it?

> A physics major is working to pay her college tuition by performing in a traveling carnival. She rides a motorcycle inside a hollow, transparent plastic sphere. After gaining sufficient speed, she travels in a vertical circle with radius 13.0 m. She has

> A small bead can slide without friction on a circular hoop that is in a vertical plane and has a radius of 0.100 m. The hoop rotates at a constant rate of 4.00 rev>s about a vertical diameter (Fig. P5.107). (a) Find the angle b at which the bead is in

> A 70-kg person rides in a 30-kg cart moving at 12 m/s at the top of a hill that is in the shape of an arc of a circle with a radius of 40 m. (a) What is the apparent weight of the person as the cart passes over the top of the hill? (b) Determine the maxi

> On the ride “Spindletop” at the amusement park Six Flags Over Texas, people stood against the inner wall of a hollow vertical cylinder with radius 2.5 m. The cylinder started to rotate, and when it reached a constant rotation rate of 0.60 rev/s, the floo

> A 4.00-kg block is attached to a vertical rod by means of two strings. When the system rotates about the axis of the rod, the strings are extended as shown in Fig. P5.104 and the tension in the upper string is 80.0 N. (a) What is the tension in the lower

> You throw a rock downward into water with a speed of 3mg/k, where k is the coefficient in Eq. (5.5). Assume that the relationship between fluid resistance and speed is as given in Eq. (5.5), and calculate the speed of the rock as a function of time.

> You are riding in a school bus. As the bus rounds a flat curve at constant speed, a lunch box with mass 0.500 kg, suspended from the ceiling of the bus by a string 1.80 m long, is found to hang at rest relative to the bus when the string makes an angle o

> Blocks A, B, and C are placed as in Fig. P5.101 and connected by ropes of negligible mass. Both A and B weigh 25.0 N each, and the coefficient of kinetic friction between each block and the surface is 0.35. Block C descends with constant velocity. (a) Dr

> Consider a wet roadway banked as in Example 5.22 (Section 5.4), where there is a coefficient of static friction of 0.30 and a coefficient of kinetic friction of 0.25 between the tires and the roadway. The radius of the curve is R = 50 m. (a) If the bank

> A curve with a 120-m radius on a level road is banked at the correct angle for a speed of 20 m/s. If an automobile rounds this curve at 30 m/s, what is the minimum coefficient of static friction needed between tires and road to prevent skidding?

> A force

> Jack sits in the chair of a Ferris wheel that is rotating at a constant 0.100 rev/s. As Jack passes through the highest point of his circular path, the upward force that the chair exerts on him is equal to one-fourth of his weight. What is the radius of

> Block A, with weight 3w, slides down an inclined plane S of slope angle 36.9° at a constant speed while plank B, with weight w, rests on top of A. The plank is attached by a cord to the wall (Fig. P5.97). (a) Draw a diagram of all the forces a

> Two blocks, with masses 4.00 kg and 8.00 kg, are connected by a string and slide down a 30.0° inclined plane (Fig. P5.96). The coefficient of kinetic friction between the 4.00-kg block and the plane is 0.25; that between the 8.00-kg block and

> A block is placed against the vertical front of a cart (Fig. P5.95). What acceleration must the cart have so that block A does not fall? The coefficient of static friction between the block and the cart is

> You are riding in an elevator on the way to the 18th floor of your dormitory. The elevator is accelerating upward with a = 1.90 m/s2. Beside you is the box containing your new computer; the box and its contents have a total mass of 36.0 kg. While the ele

> Two objects, with masses 5.00 kg and 2.00 kg, hang 0.600 m above the floor from the ends of a cord that is 6.00 m long and passes over a frictionless pulley. Both objects start from rest. Find the maximum height reached by the 2.00-kg object.

> Block B, with mass 5.00 kg, rests on block A, with mass 8.00 kg, which in turn is on a horizontal tabletop (Fig. P5.92). There is no friction between block A and the tabletop, but the coefficient of static friction between blocks A and B is 0.750. A ligh

> In terms of m1, m2, and g, find the acceleration of each block in Fig. P5.91. There is no friction anywhere in the system. Fig. P5.91: Figure P5.91 m m2

> Two blocks connected by a cord passing over a small, frictionless pulley rest on frictionless planes (Fig. P5.90). (a) Which way will the system move when the blocks are released from rest? (b) What is the acceleration of the blocks? (c) What is the tens

> Block A in Fig. P5.89 has mass 4.00 kg, and block B has mass 12.0 kg. The coefficient of kinetic friction between block B and the horizontal surface is 0.25. (a) What is the mass of block C if block B is moving to the right and speeding up with an accele

> For the cases shown in Fig. Q6.8, the object is released from rest at the top and feels no friction or air resistance. In which (if any) cases will the mass have (i) the greatest speed at the bottom and (ii) the most work done on it by the time it reache

> Block A in Fig. P5.87 weighs 1.90 N, and block B weighs 4.20 N. The coefficient of kinetic friction between all surfaces is 0.30. Find the magnitude of the horizontal force F S necessary to drag block B to the left at constant speed if A and B are connec

> You are called as an expert witness in a trial for a traffic violation. The facts are these: A driver slammed on his brakes and came to a stop with constant acceleration. Measurements of his tires and the skid marks on the pavement indicate that he locke

> Two identical 15.0-kg balls, each 25.0 cm in diameter, are suspended by two 35.0-cm wires (Fig. P5.85). The entire apparatus is supported by a single 18.0-cm wire, and the surfaces of the balls are perfectly smooth. (a) Find the tension in each of the th

> If the coefficient of static friction between a table and a uniform, massive rope is

> A 40.0-kg packing case is initially at rest on the floor of a 1500-kg pickup truck. The coefficient of static friction between the case and the truck floor is 0.30, and the coefficient of kinetic friction is 0.20. Before each acceleration given below, th

> A hammer is hanging by a light rope from the ceiling of a bus. The ceiling is parallel to the roadway. The bus is traveling in a straight line on a horizontal street. You observe that the hammer hangs at rest with respect to the bus when the angle betwee

> You are standing on a bathroom scale in an elevator in a tall building. Your mass is 64 kg. The elevator starts from rest and travels upward with a speed that varies with time according to v(t)=(3.0 m/s2)t +(0.20 m/s3)t2. When t = 4.0 s, what is the read

> You are designing an elevator for a hospital. The force exerted on a passenger by the floor of the elevator is not to exceed 1.60 times the passenger’s weight. The elevator accelerates upward with constant acceleration for a distance of 3.0 m and then st

> Block A in Fig. P5.79 weighs 1.20 N, and block B weighs 3.60 N. The coefficient of kinetic friction between all surfaces is 0.300. Find the magnitude of the horizontal force F S necessary to drag block B to the left at constant speed (a) if A rests on B

> In Example 5.5 (Section 5.1), how does the work done on the bucket by the tension in the cable compare with the work done on the cart by the tension in the cable? Example 5.5: Your firm needs to haul granite blocks up a 15° slope out of a qu

> High-speed motion pictures (3500 frames/second) of a jumping 210-

> A block with mass m1 is placed on an inclined plane with slope angle a and is connected to a hanging block with mass m2 by a cord passing over a small, frictionless pulley (Fig. P5.74). The coefficient of static friction is ms, and the coefficient of kin

> Block A in Fig. P5.76 weighs 60.0 N. The coefficient of static friction between the block and the surface on which it rests is 0.25. The weight w is 12.0 N, and the system is in equilibrium. (a) Find the friction force exerted on block A. (b) Find the ma

> You place a book of mass 5.00 kg against a vertical wall. You apply a constant force

> In Fig. P5.74,

> An 8.00-kg box sits on a ramp that is inclined at 33.0° above the horizontal. The coefficient of kinetic friction between the box and the surface of the ramp is

> A 6.00-kg box sits on a ramp that is inclined at 37.0° above the horizontal. The coefficient of kinetic friction between the box and the ramp is

> Two boxes connected by a light horizontal rope are on a horizontal surface (Fig. E5.37). The coefficient of kinetic friction between each box and the surface is

> A 5.00-kg box sits at rest at the bottom of a ramp that is 8.00 m long and is inclined at 30.0o above the horizontal. The coefficient of kinetic friction is

> A 3.00-kg box that is several hundred meters above the earth’s surface is suspended from the end of a short vertical rope of negligible mass. A time-dependent upward force is applied to the upper end of the rope and results in a tension in the rope of T(

> If work W is required to stretch a spring a distance x from its un stretched length, what work (in terms of W) is required to stretch the spring an additional distance x?

> A 2.00-kg box is suspended from the end of a light vertical rope. A time-dependent force is applied to the upper end of the rope, and the box moves upward with a velocity magnitude that varies in time according to v(t)=(2.00 m/s2)t + (0.600 m/s3)t2. What

> When you do a chin-up, you raise your chin just over a bar (the chinning bar), supporting yourself with only your arms. Typically, the body below the arms is raised by about 30 cm in a time of 1.0 s, starting from rest. Assume that the entire body of a 6

> A box is sliding with a constant speed of 4.00 m/s in the +x-direction on a horizontal, frictionless surface. At x = 0 the box encounters a rough patch of the surface, and then the surface becomes even rougher. Between x = 0 and x = 2.00 m, the coefficie

> A solid uniform 45.0-kg ball of diameter 32.0 cm is supported against a vertical, frictionless wall by a thin 30.0-cm wire of negligible mass (Fig. P5.65). (a) Draw a free-body diagram for the ball, and use the diagram to find the tension in the wire. (b

> A horizontal wire holds a solid uniform ball of mass m in place on a tilted ramp that rises 35.0° above the horizontal. The surface of this ramp is perfectly smooth, and the wire is directed away from the center of the ball (Fig. P5.64). (a) D

> In a repair shop a truck engine that has mass 409 kg is held in place by four light cables (Fig. P5.63). Cable A is horizontal, cables B and D are vertical, and cable C makes an angle of 37.1o with a vertical wall. If the tension in cable A is 722 N, wha

> In Fig. P5.62 a worker lifts a weight w by pulling down on a rope with a force F S. The upper pulley is attached to the ceiling by a chain, and the lower pulley is attached to the weight by another chain. Draw one or more free-body diagrams to find the t

> Two ropes are connected to a steel cable that supports a hanging weight (Fig. P5.61). (a) Draw a free-body diagram showing all of the forces acting at the knot that connects the two ropes to the steel cable. Based on your diagram, which of the two ropes

> An adventurous archaeologist crosses between two rock cliffs by slowly going hand over hand along a rope stretched between the cliffs. He stops to rest at the middle of the rope (Fig. P5.60). The rope will break if the tension in it exceeds 2.50 Ã

> You are a Starfleet captain going boldly where no man has gone before. You land on a distant planet and visit an engineering testing lab. In one experiment a short, light rope is attached to the top of a block and a constant upward force F is applied to

> When a certain force is applied to an ideal spring, the spring stretches a distance x from its un stretched length and does work W. If instead twice the force is applied, what distance (in terms of x) does the spring stretch from its un stretched length,

> An 8.00-kg box sits on a level floor. You give the box a sharp push and find that it travels 8.22 m in 2.8 s before coming to rest again. (a) You measure that with a different push the box traveled 4.20 m in 2.0 s. Do you think the box has a constant acc

> The table* gives automobile performance data for a few types of cars: (a) During an acceleration of 0 to 60 mph, which car has the largest average net force acting on it? The smallest? (b) During this acceleration, for which car would the average net f

> The position of a training helicopter (weight 2.75 × 105 N) in a test is given by

> A mysterious rocket-propelled object of mass 45.0 kg is initially at rest in the middle of the horizontal, frictionless surface of an ice-covered lake. Then a force directed east and with magnitude F(t) = (16.8 N/s)t is applied. How far does the object t

> You have landed on an unknown planet, Newtonia, and want to know what objects weigh there. When you push a certain tool, starting from rest, on a frictionless horizontal surface with a 12.0-N force, the tool moves 16.0 m in the first 2.00 s. You next obs

> Boxes A and B are connected to each end of a light vertical rope (Fig. P4.49). A constant upward force F = 80.0 N is applied to box A. Starting from rest, box B descends 12.0 m in 4.00 s. The tension in the rope connecting the two boxes is 36.0 N. What a

> The two blocks in Fig. P4.48 are connected by a heavy uniform rope with a mass of 4.00 kg. An upward force of 200 N is applied as shown. (a) Draw three free-body diagrams: one for the 6.00-kg block, one for the 4.00-kg rope, and another one for the 5.00-

> A 75.0-kg man steps off a platform 3.10 m above the ground. He keeps his legs straight as he falls, but his knees begin to bend at the moment his feet touch the ground; treated as a particle, he moves an additional 0.60 m before coming to rest. (a) What

> A nail in a pine board stops a 4.9-N hammer head from an initial downward velocity of 3.2 m/s in a distance of 0.45 cm. In addition, the person using the hammer exerts a 15-N downward force on it. Assume that the acceleration of the hammer head is consta

> After an annual checkup, you leave your physician’s office, where you weighed 683 N. You then get into an elevator that, conveniently, has a scale. Find the magnitude and direction of the elevator’s acceleration if the scale reads (a) 725 N and (b) 595 N

> “A ball is thrown from the edge of a high cliff. Regardless of the angle at which it is thrown, due to air resistance, the ball will eventually end up moving vertically downward.” Justify this statement.

> A loaded elevator with very worn cables has a total mass of 2200 kg, and the cables can withstand a maximum tension of 28,000 N. (a) Draw the free-body force diagram for the elevator. In terms of the forces on your diagram, what is the net force on the e

> The froghopper (Philaenus spumarius), the champion leaper of the insect world, has a mass of 12.3 mg and leaves the ground (in the most energetic jumps) at 4.0 m>s from a vertical start. The jump itself lasts a mere 1.0 ms before the insect is clear of t

> A 6.50-kg instrument is hanging by a vertical wire inside a spaceship that is blasting off from rest at the earth’s surface. This spaceship reaches an altitude of 276 m in 15.0 s with constant acceleration. (a) Draw a free-body diagram for the instrument

> To study damage to aircraft that collide with large birds, you design a test gun that will accelerate chicken-sized objects so that their displacement along the gun barrel is given by x =(9.0 × 103 m>s2)t2 –(8.0 × 104 m>s3)t3. The object leaves the end o

> Two blocks connected by a light horizontal rope sit at rest on a horizontal, frictionless surface. Block A has mass 15.0 kg, and block B has mass m. A constant horizontal force F = 60.0 N is applied to block A (Fig. P4.40). In the first 5.00 s after the

> Two crates, one with mass 4.00 kg and the other with mass 6.00 kg, sit on the frictionless surface of a frozen pond, connected by a light rope (Fig. P4.39). A woman wearing golf shoes (for traction) pulls horizontally on the 6.00-kg crate with a force F

> The fastest served tennis ball, served by “Big Bill” Tilden in 1931, was measured at 73.14 m/s. The mass of a tennis ball is 57 g, and the ball, which starts from rest, is typically in contact with the tennis racquet for 30.0 ms. Assuming constant accele

> The fastest pitched baseball was measured at 46 m/s. A typical baseball has a mass of 145 g. If the pitcher exerted his force (assumed to be horizontal and constant) over a distance of 1.0 m, (a) what force did he produce on the ball during this record-s