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Physics for Scientists and Engineers A Strategic Approach with Modern Physics 4th edition Randall D. Knight - Solutions

A 5000 kg interceptor rocket is launched at an angle of 44.7°. The thrust of the rocket motor is 140,700 N.(a) Find an equation y(x) that describes the rocket’s trajectory.(b) What is the shape of the trajectory?(c) At what elevation does the rocket reach the speed of sound, 330 m/s?
A 5.0 g coin is placed 15 cm from the center of a turntable. The coin has static and kinetic coefficients of friction with the turntable surface of μs = 0.80 and μk = 0.50. The turntable very slowly speeds up to 60 rpm. Does the coin slide off?
Mass m1on the frictionless table of FIGURE EX8.13 is connected by a string through a hole in the table to a hanging mass m2. With what speed must m1rotate in a circle of radius r if m2is to remain hanging at rest?Figure EX8.13 m1 m2
A satellite orbiting the moon very near the surface has a period of 110 min. What is free-fall acceleration on the surface of the moon?
What is free-fall acceleration toward the sun at the distance of the earth’s orbit? Astronomical data are inside the back cover of the book.
A 9.4 × 1021 kg moon orbits a distant planet in a circular orbit of radius 1.5 × 108 m. It experiences a 1.1 × 1019 N gravitational pull from the planet. What is the moon’s orbital period in earth days?
Communications satellites are placed in circular orbits where they stay directly over a fixed point on the equator as the earth rotates. These are called geosynchronous orbits. The altitude of a geosynchronous orbit is 3.58 × 107 m (≈ 22,000 miles).(a) What is the period of a satellite in a
A car drives over the top of a hill that has a radius of 50 m. What maximum speed can the car have at the top without flying off the road?
The weight of passengers on a roller coaster increases by 50% as the car goes through a dip with a 30 m radius of curvature. What is the car’s speed at the bottom of the dip?
A roller coaster car crosses the top of a circular loop-the-loop at twice the critical speed. What is the ratio of the normal force to the gravitational force?
The normal force equals the magnitude of the gravitational force as a roller coaster car crosses the top of a 40-m-diameter loop-the-loop. What is the car’s speed at the top?
A student has 65-cm-long arms. What is the minimum angular velocity (in rpm) for swinging a bucket of water in a vertical circle without spilling any? The distance from the handle to the bottom of the bucket is 35 cm.
While at the county fair, you decide to ride the Ferris wheel. Having eaten too many candy apples and elephant ears, you find the motion somewhat unpleasant. To take your mind off your stomach, you wonder about the motion of the ride. You estimate the radius of the big wheel to be 15 m, and you use
A 500 g ball swings in a vertical circle at the end of a 1.5-m-long string. When the ball is at the bottom of the circle, the tension in the string is 15 N. What is the speed of the ball at that point?
A 500 g ball moves in a vertical circle on a 102-cm-long string. If the speed at the top is 4.0 m/s, then the speed at the bottom will be 7.5 m/s.(a) What is the gravitational force acting on the ball?(b) What is the tension in the string when the ball is at the top?(c) What is the tension in the
A heavy ball with a weight of 100 N (m = 10.2 kg) is hung from the ceiling of a lecture hall on a 4.5-m-long rope. The ball is pulled to one side and released to swing as a pendulum, reaching a speed of 5.5 m/s as it passes through the lowest point. What is the tension in the rope at that point?
A toy train rolls around a horizontal 1.0-m-diameter track. The coefficient of rolling friction is 0.10. How long does it take the train to stop if it’s released with an angular speed of 30 rpm?
A new car is tested on a 200-m-diameter track. If the car speeds up at a steady 1.5 m/s2, how long after starting is the magnitude of its centripetal acceleration equal to the tangential acceleration?
An 85,000 kg stunt plane performs a loop-the-loop, flying in a 260-m-diameter vertical circle. At the point where the plane is flying straight down, its speed is 55 m/s and it is speeding up at a rate of 12 m/s per second.(a) What is the magnitude of the net force on the plane? You can neglect air
Three cars are driving at 25 m/s along the road shown in FIGURE EX8.30. Car B is at the bottom of a hill and car C is at the top. Both hills have a 200 m radius of curvature. Suppose each car suddenly brakes hard and starts to skid. What is the tangential acceleration (i.e., the acceleration
Derive Equations 8.3 for the acceleration of a projectile subject to drag. vVv? + v; PCA ах 2m (8.3) pCA ‚Vv² + v,² Ay Vy 2m
A 100 g bead slides along a frictionless wire with the parabolic shape y = (2 m-1)x2.(a) Find an expression for ay, the vertical component of acceleration, in terms of x, vx, and ax.(b) Suppose the bead is released at some negative value of x and has a speed of 2.3 m/s as it passes through the
Space scientists have a large test chamber from which all the air can be evacuated and in which they can create a horizontal uniform electric field. The electric field exerts a constant horizontal force on a charged object. A 15 g charged projectile is launched with a speed of 6.0 m/s at an angle
The father of Example 8.2 stands at the summit of a conical hill as he spins his 20 kg child around on a 5.0 kg cart with a 2.0-m-long rope. The sides of the hill are inclined at 20°. He again keeps the rope parallel to the ground, and friction is negligible. What rope tension will allow the cart
A rocket-powered hockey puck has a thrust of 2.0 N and a total mass of 1.0 kg. It is released from rest on a frictionless table, 4.0 m from the edge of a 2.0 m drop. The front of the rocket is pointed directly toward the edge. How far does the puck land from the base of the table?
A 500 g model rocket is resting horizontally at the top edge of a 40-m-high wall when it is accidentally bumped. The bump pushes it off the edge with a horizontal speed of 0.5 m/s and at the same time causes the engine to ignite. When the engine fires, it exerts a constant 20 N horizontal thrust
A 2.0 kg projectile with initial velocity v = 8.0 î m/s experiences the variable force F = -2.0t î + 4.0t2 ĵ N, where t is in s.(a) What is the projectile’s speed at t = 2.0 s?(b) At what instant of time is the projectile moving parallel to the y-axis?
A 75 kg man weighs himself at the north pole and at the equator. Which scale reading is higher? By how much? Assume the earth is spherical.
A concrete highway curve of radius 70 m is banked at a 15° angle. What is the maximum speed with which a 1500 kg rubber tired car can take this curve without sliding?
a. An object of mass m swings in a horizontal circle on a string of length L that tilts downward at angle θ. Find an expression for the angular velocity ω.b. A student ties a 500 g rock to a 1.0-m-long string and swings it around her head in a horizontal circle. At what angular speed, in rpm,
You’ve taken your neighbor’s young child to the carnival to ride the rides. She wants to ride The Rocket. Eight rocket shaped cars hang by chains from the outside edge of a large steel disk. A vertical axle through the center of the ride turns the disk, causing the cars to revolve in a circle.
A 4.4-cm-diameter, 24 g plastic ball is attached to a 1.2-m-long string and swung in a vertical circle. The ball’s speed is 6.1 m/s at the point where it is moving straight up. What is the magnitude of the net force on the ball? Air resistance is not negligible.
A charged particle of mass m moving with speed v in a plane perpendicular to a magnetic field experiences a force F = (qvB, perpendicular to v), where q is the amount of charge and B is the magnetic field strength. Because the force is always perpendicular to the particle’s velocity, the particle
Two wires are tied to the 2.0 kg sphere shown in FIGURE P8.45. The sphere revolves in a horizontal circle at constant speed. a. For what speed is the tension the same in both wires?b. What is the tension? 60° 1.0 m 60° FIGURE P8.45
Two wires are tied to the 300 g sphere shown in FIGURE P8.46. The sphere revolves in a horizontal circle at a constant speed of 7.5 m/s. What is the tension in each of the wires?FIGURE P8.46 1.0 m 0.50 m 0.50 m 1.0 m
A conical pendulum is formed by attaching a ball of mass m to a string of length L, then allowing the ball to move in a horizontal circle of radius r. FIGURE P8.47 shows that the string traces out the surface of a cone, hence the name.a. Find an expression for the tension T in the string.b. Find an
The 10 mg bead in FIGURE P8.48 is free to slide on a frictionless wire loop. The loop rotates about a vertical axis with angular velocity Ï‰. If v is less than some critical value Ï‰c, the bead sits at the bottom of the spinning loop. When Ï‰ > Ï‰c, the
In an old-fashioned amusement park ride, passengers stand inside a 5.0-m-diameter hollow steel cylinder with their backs against the wall. The cylinder begins to rotate about a vertical axis. Then the floor on which the passengers are standing suddenly drops away! If all goes well, the passengers
The ultracentrifuge is an important tool for separating and analyzing proteins. Because of the enormous centripetal accelerations, the centrifuge must be carefully balanced, with each sample matched by a sample of identical mass on the opposite side. Any difference in the masses of opposing samples
In an amusement park ride called The Roundup, passengers stand inside a 16-m-diameter rotating ring. After the ring has acquired sufficient speed, it tilts into a vertical plane, as shown in FIGURE P8.51. a. Suppose the ring rotates once every 4.5 s. If a rider??s mass is 55 kg, with how much
Suppose you swing a ball of mass m in a vertical circle on a string of length L. As you probably know from experience, there is a minimum angular velocity ωmin you must maintain if you want the ball to complete the full circle without the string going slack at the top.a. Find an expression for
A 30 g ball rolls around a 40-cm-diameter L-shaped track, shown in FIGURE P8.53, at 60 rpm. What is the magnitude of the net force that the track exerts on the ball? Rolling friction can be neglected. FIGURE P8.53
FIGURE P8.54 shows a small block of mass m sliding around the inside of an L-shaped track of radius r. The bottom of the track is frictionless; the coefficient of kinetic friction between the block and the wall of the track is Î¼k. The block€™s speed is v0at t0= 0.Find an
The physics of circular motion sets an upper limit to the speed of human walking. (If you need to go faster, your gait changes from a walk to a run.) If you take a few steps and watch what’s happening, you’ll see that your body pivots in circular motion over your forward foot as you bring your
A 100 g ball on a 60-cm-long string is swung in a vertical circle about a point 200 cm above the floor. The tension in the string when the ball is at the very bottom of the circle is 5.0 N. A very sharp knife is suddenly inserted, as shown in FIGURE P8.56, to cut the string directly below the point
A 60 g ball is tied to the end of a 50-cm-long string and swung in a vertical circle. The center of the circle, as shown in FIGURE P8.57, is 150 cm above the floor. The ball is swung at the minimum speed necessary to make it over the top without the string going slack. If the string is released at
Elm Street has a pronounced dip at the bottom of a steep hill before going back uphill on the other side. Your science teacher has asked everyone in the class to measure the radius of curvature of the dip. Some of your classmates are using surveying equipment, but you decide to base your
A 100 g ball on a 60-cm-long string is swung in a vertical circle about a point 200 cm above the floor. The string suddenly breaks when it is parallel to the ground and the ball is moving upward. The ball reaches a height 600 cm above the floor. What was the tension in the string an instant before
Scientists design a new particle accelerator in which protons (mass 1.7 × 10-27 kg) follow a circular trajectory given by r = c cos(kt2) î + c sin(kt2) ĵ, where c = 5.0 m and k = 8.0 × 104 rad/s2 are constants and t is the elapsed time.a. What is the radius of the circle?b. What is the
A 1500 kg car starts from rest and drives around a flat 50-m-diameter circular track. The forward force provided by the car’s drive wheels is a constant 1000 N.a. What are the magnitude and direction of the car’s acceleration at t = 10 s? Give the direction as an angle from the r-axis.b. If the
A 500 g steel block rotates on a steel table while attached to a 2.0-m-long massless rod. Compressed air fed through the rod is ejected from a nozzle on the back of the block, exerting a thrust force of 3.5 N. The nozzle is 70° from the radial line, as shown in FIGURE P8.62. The block starts
a. Write a realistic problem for which this is the correct equation. Be sure that the answer your problem requests is consistent with the equation given.b. Finish the solution of the problem.60 N = (0.30 kg)ω2(0.50 m)
A 2.0 kg ball swings in a vertical circle on the end of an 80-cm-long string. The tension in the string is 20 N when its angle from the highest point on the circle is θ = 30°.a. What is the ball’s speed when θ = 30°?b. What are the magnitude and direction of the ball’s acceleration when θ
a. Write a realistic problem for which this is the correct equation. Be sure that the answer your problem requests is consistent with the equation given.b. Finish the solution of the problem.(1500 kg)(9.8 m/s2) - 11,760 N = (1500 kg) v2/(200 m)
Sam (75 kg) takes off up a 50-m-high, 10° frictionless slope on his jet-powered skis. The skis have a thrust of 200 N. He keeps his skis tilted at 10° after becoming airborne, as shown in FIGURE CP8.66. How far does Sam land from the base of the cliff? T10 Start 50 m ] 10° FIGURE CP8.66
In the absence of air resistance, a projectile that lands at the elevation from which it was launched achieves maximum range when launched at a 45° angle. Suppose a projectile of mass m is launched with speed v0 into a headwind that exerts a constant, horizontal retarding force Fwind =
A small bead slides around a horizontal circle at height y inside the cone shown in FIGURE CP8.69. Find an expression for the bead€™s speed in terms of a, h, y, and g. a FIGURE CP8.69
A 500 g steel block rotates on a steel table while attached to a 1.2-m-long hollow tube as shown in FIGURE CP8.70. Compressed air fed through the tube and ejected from a nozzle on the back of the block exerts a thrust force of 4.0 N perpendicular to the tube.The maximum tension the tube can
If a vertical cylinder of water (or any other liquid) rotates about its axis, as shown in FIGURE CP8.71, the surface forms a smooth curve. Assuming that the water rotates as a unit (i.e., all the water rotates with the same angular velocity), show that the shape of the surface is a parabola
Determine [B]-1 by row reduction.
Derive the stiffness matrix for a beam element with a nodal linkage€”that is, the shear is 0 at node i, but the usual shear and moment resistance are present at node j (see following figure). m; m, L. f, = 0
Determine [D]-1 by row reduction.
Show that ([A] [B])T= [A]T[B]Tby using [b1 b12 b13 [B] = b21 b22 b23 α12 [4] = a22 a21
Determine the solution of the following simultaneous equations by the inverse method.1x1 + 3x2 = 54x1 - 1x2 = 12
Determine the solution of the following simultaneous equations by the inverse method.1x1 + 3x2 = 54x1 - 1x2 = 12
Solve the following system of simultaneous equations by Gaussian elimination.x1 + 4x2 - 5x3 = 43x2 + 4x3 = -1-2x1 -1x2 + 2x3 = -3
Given thatx1 = 2y1 - y2 z1 = -x1 - x2x2 = y1 - y2 z2 = 2x1 + x2a. Write these relationships in matrix form.b. Express [z] in terms of {y}.c. Express [y] in terms of [z].
Solve Problem B.1 by Gauss–Seidel iteration.Data from problem B.1Determine the solution of the following simultaneous equations by the inverse method.1x1 + 3x2 = 54x1 - 1x2 = 12
Solve Problems A.1 through A.6 using matrices [A], [B], [C], [D], and [E] given by(a) |A| + |B|(b) |A| + |B|(c) |A| |C|T(d) |D| {B}(e) |D| |C|(f) |C| |D| 3 1 01 -1 0 3 2 0 [4] [B] [C] -2 8 3 1 [D] = {E} = 3 4 0 2.
Evaluate the matrix [B] for the quadratic quadrilateral element shown in Figure 10€“15 on page 521 (Section 10.5).(a)(b) 3. (20, 15) (12, 15) (10, 10)- (20, 10) (20, 20) (12, 16) (10, 10) (20, 10)
Determine the Jacobian matrix |J| and its determinant for the elements shown in Figure P10 11. Show that the determinant of |J|for rectangular and parallelogram shaped elements is equal to A/4, where A is the physical area of the element and 4 actually represents the area of the rectangle of sides
FIGURE EX1.11 shows two dots of a motion diagram and vector1Copy this figure, then add dot 4 and the next velocity vector2 if the acceleration vectorat dot 3(a) Points right and(b) Points left?Figure Ex 1.11 2.
A rubber ball is dropped onto a ramp that is tilted at 20°, as shown in FIGURE P4.59. A bouncing ball obeys the €œlaw of reflection,€ which says that the ball leaves the surface at the same angle it approached the surface. The ball€™s next bounce is 3.0 m to the
A javelin thrower standing at rest holds the center of the javelin behind her head, then accelerates it through a distance of 70 cm as she throws. She releases the javelin 2.0 m above the ground traveling at an angle of 30° above the horizontal. Top-rated javelin throwers do throw at about a 30°
A stunt man drives a car at a speed of 20 m/s off a 30-m-high cliff. The road leading to the cliff is inclined upward at an angle of 20°.a. How far from the base of the cliff does the car land?b. What is the car’s impact speed?
A 35 g steel ball is held by a ceiling-mounted electromagnet 3.5 m above the floor. A compressed-air cannon sits on the floor, 4.0 m to one side of the point directly under the ball. When a button is pressed, the ball drops and, simultaneously, the cannon fires a 25 g plastic ball. The two balls
You are target shooting using a toy gun that fires a small ball at a speed of 15 m/s. When the gun is fired at an angle of 30° above horizontal, the ball hits the bull’s-eye of a target at the same height as the gun. Then the target distance is halved. At what angle must you aim the gun to hit
A tennis player hits a ball 2.0 m above the ground. The ball leaves his racquet with a speed of 20.0 m/s at an angle 5.0° above the horizontal. The horizontal distance to the net is 7.0 m, and the net is 1.0 m high. Does the ball clear the net? If so, by how much? If not, by how much does it miss?
A ball is thrown toward a cliff of height h with a speed of 30 m/s and an angle of 60° above horizontal. It lands on the edge of the cliff 4.0 s later.a. How high is the cliff?b. What was the maximum height of the ball?c. What is the ball’s impact speed?
A gray kangaroo can bound across level ground with each jump carrying it 10 m from the takeoff point. Typically the kangaroo leaves the ground at a 20° angle. If this is so:a. What is its takeoff speed?b. What is its maximum height above the ground?
A projectile is launched from ground level at angle θ and speed v0 into a headwind that causes a constant horizontal acceleration of magnitude a opposite the direction of motion.a. Find an expression in terms of α and g for the launch angle that gives maximum range.b. What is the angle for
a. A projectile is launched with speed v0 and angle θ. Derive an expression for the projectile’s maximum height h.b. A baseball is hit with a speed of 33.6 m/s. Calculate its height and the distance traveled if it is hit at angles of 30.0°, 45.0°, and 60.0°?
A projectile’s horizontal range over level ground is v02 sin 2θ/g. At what launch angle or angles will the projectile land at half of its maximum possible range?
Starting from rest, a DVD steadily accelerates to 500 rpm in 1.0 s, rotates at this angular speed for 3.0 s, then steadily decelerates to a halt in 2.0 s. How many revolutions does it make?
A bicycle wheel is rotating at 50 rpm when the cyclist begins to pedal harder, giving the wheel a constant angular acceleration of 0.50 rad / s2.a. What is the wheel’s angular velocity, in rpm, 10 s later?b. How many revolutions does the wheel make during this time?
An electric fan goes from rest to 1800 rpm in 4.0 s. What is its angular acceleration?
A 5.0-m-diameter merry-go-round is initially turning with a 4.0 s period. It slows down and stops in 20 s.a. Before slowing, what is the speed of a child on the rim?b. How many revolutions does the merry-go-round make as it stops?
A wheel initially rotating at 60 rpm experiences the angular acceleration shown in FIGURE EX4.39. What is the wheel€™s angular velocity, in rpm, at t = 3.0 s?Figure Ex 4.39 (rad/s?) 04 -t (s) 3
FIGURE EX4.38 shows the angular- velocity-versus-time graph for a particle moving in a circle. How many revolutions does the object make during the first 4 s?Figure Ex 4.38 w (rad/s) 20- 10- 0+ -t (s) 4 1 2
FIGURE EX4.37 shows the angular acceleration graph of a turntable that starts from rest. What is the turntable€™s angular velocity at(a) t = 1 s,(b) t = 2 s, and(c) t = 3 s?Figure Ex 4.37 a (rad/s) 5- 4- 3- 2- 1- 0+ -t (s) 4
FIGURE EX4.36 shows the angular velocity graph of the crankshaft in a car. What is the crankshaft€™s angular acceleration at(a) t = 1 s,(b) t = 3 s, and(c) t = 5 s?Figure Ex 4.37 w (rad/s) 250 - 200- 150 100- 50- t(s)
Your roommate is working on his bicycle and has the bike upside down. He spins the 60-cm-diameter wheel, and you notice that a pebble stuck in the tread goes by three times every second. What are the pebble’s speed and acceleration?
A speck of dust on a spinning DVD has a centripetal acceleration of 20 m/s2.a. What is the acceleration of a different speck of dust that is twice as far from the center of the disk?b. What would be the acceleration of the first speck of dust if the disk’s angular velocity was doubled?
The radius of the earth’s very nearly circular orbit around the sun is 1.5 × 1011 m. Find the magnitude of the earth’s(a) Velocity,(b) Angular velocity, and(c) Centripetal acceleration as it travels around the sun. Assume a year of 365 days?
To withstand “g-forces” of up to 10 g’s, caused by suddenly pulling out of a steep dive, fighter jet pilots train on a “human centrifuge.” 10 g’s is an acceleration of 98 m/s2. If the length of the centrifuge arm is 12 m, at what speed is the rider moving when she experiences 10 g’s?
Peregrine falcons are known for their maneuvering ability. In a tight circular turn, a falcon can attain a centripetal acceleration 1.5 times the free-fall acceleration. What is the radius of the turn if the falcon is flying at 25 m/s?
A 3000-m-high mountain is located on the equator. How much faster does a climber on top of the mountain move than a surfer at a nearby beach? The earth’s radius is 6400 km.
How fast must a plane fly along the earth’s equator so that the sun stands still relative to the passengers? In which direction must the plane fly, east to west or west to east? Give your answer in both km/h and mph. The earth’s radius is 6400 km.
As the earth rotates, what is the speed of(a) A physics student in Miami, Florida, at latitude 26°, and(b) A physics student in Fairbanks, Alaska, at latitude 65°? Ignore the revolution of the earth around the sun. The radius of the earth is 6400 km?
An old-fashioned single-play vinyl record rotates on a turntable at 45 rpm. What are(a) The angular velocity in rad/s and(b) The period of the motion?

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