Chapter 1: Technical Measurement and Vector

5. Newton’s law of universal gravitation is represented by

where F is the gravitational force, M and m are masses, and r is a length. Force has the SI units kg ∙ m/s2. What are the SI units of the proportionality constant G?

8. The speed of light is now defined to be 2.99 7924 58 × 108 m/s. Express the speed of light to (a) three significant figures, (b) five significant figures, and (c) seven significant figures.

15.A rectangular building lot measures 100 ft by 150 ft. Determine the area of this lot in square meters (m2).

19. The speed of light is about 3.00 × 108 m/s. Convert this figure to miles per hour.

22.(a) Find a conversion factor to convert from miles per hour to kilometers per hour. (b) For a while, federal law mandated that the maximum highway speed would be 55 mi/h. Use the conversion factor from part (a) to find the speed in kilometers per hour. (c) The maximum highway speed has been raised to 65 mi/h in some places. In kilometers per hour, how much of an increase is this over the 55-mi/h limit?

5. A plane flies from base camp to lake A, a distance of 280 km at a direction of 20.0° north of east. After dropping off supplies, the plane flies to lake B, which is 190 km and 30.0° west of north from lake A. Graphically determine the distance and direction from lake B to the base camp.

6. Vector has a magnitude of 8.00 units and makes an angle of 45.0° with the positive x-axis. Vector also has a magnitude of 8.00 units and is directed along the negative x-axis. Using graphical methods, find (a) the vector sum + and (b) the vector

difference – .

15. A man pushing a mop across a floor causes the mop to undergo two displacements. The first has a magnitude of 150 cm and makes an

angle of 120° with the positive x-axis. The resultant displacement has a magnitude of 140 cm and is directed at an angle of 35.0° to the positive x-axis. Find the magnitude and direction of the second displacement.

35.In Figure P1.35, find (a) the side opposite θ, (b) the side adjacent to φ, (c) cos θ, (d) sin φ, and (e) tan φ.

Figure P1.35

9. A girl delivering newspapers covers her route by traveling 3.00 blocks west, 4.00 blocks north, and then 6.00 blocks east. (a) What is her resultant displacement? (b) What is the total distance she travels?

14.The helicopter view in Figure P3.14 shows two people pulling on a stubborn mule. Find (a) the single force that is equivalent to the two forces shown and (b) the force that a third person would have to exert on the mule to make the net force equal to zero. The forces are measured in units of newtons (N).

Figure P3.14

1

Chapter 2: Translational Equilibrium and Friction

1. A 6.0-kg object undergoes an acceleration of 2.0 m/s2. (a) What is the magnitude of the resultant force acting on it? (b) If this same force is applied to a 4.0-kg object, what acceleration is produced?

13. A 150-N bird feeder is supported by three cables as shown in Figure P4.13. Find the tension in each cable.

Figure P4.13

14.The leg and cast in Figure P4.14 weigh 220 N (w1). Determine the weight w2

and the angle α needed so that no force is exerted on the hip joint by the leg plus the cast.

29.A dockworker loading crates on a ship finds that a 20-kg crate, initially at rest on a horizontal surface, requires a 75-N horizontal force to set it in motion. However, after the crate is in motion, a horizontal force of 60 N is required to keep it moving with a constant speed. Find the coefficients of static and kinetic friction between crate and floor.

34.A woman at an airport is towing her 20.0-kg suitcase at constant speed by pulling on a strap at an angle θ above the horizontal (Fig. P4.34). She pulls on the strap with a 35.0-N force, and the friction force on the suitcase is 20.0 N. Draw a free-body diagram of the

suitcase. (a) What angle does the strap make with the horizontal? (b) What normal force does the ground exert on the suitcase?

Figure P4.34

35.The coefficient of static friction between the 3.00-kg crate and the 35.0° incline of Figure P4.35 is 0.300. What minimum force must be applied to the crate perpendicular to the incline to prevent the crate from sliding down the incline?

Figure P4.35

42.A 2.00-kg block is held in equilibrium on an incline of angle θ = 60.0° by a horizontal force applied in the direction shown in Figure P4.42. If the coefficient of static friction between block and incline is μs = 0.300, determine (a) the minimum value of and (b) the normal force exerted by the incline on the block.

Figure P4.42

45.(a) What is the resultant force exerted by the two cables supporting the traffic light in Figure P4.45? (b) What is the weight of the light?

Chapter 3: Torque and Rotational Equilibrium

1. If the torque required to loosen a nut that is holding a flat tire in place on a car has a magnitude of 40.0 N ∙ m, what minimum force must be exerted by the mechanic at the end of a 30.0-cm lug wrench to accomplish the task?

3. Calculate the net torque (magnitude and direction) on the beam in Figure P8.3 about (a) an axis through O perpendicular to the page and (b) an axis through C perpendicular to the page.

4. Write the necessary equations of equilibrium of the object shown in Figure P8.4. Take the origin of the torque equation about an axis perpendicular to the page through the point O.

9. A cook holds a 2.00-kg carton of milk at arm’s length (Fig. P8.9). What force must be exerted by the biceps

muscle? (Ignore the weight of the forearm.)

17. A 500-N uniform rectangular sign 4.00 m wide and 3.00 m high is suspended from a horizontal, 6.00-m-long, uniform, 100-N rod as indicated in Figure P8.17. The left end of the rod is supported by a hinge, and the right end is supported by a thin cable making a 30.0° angle with the vertical. (a) Find the tension T in the cable. (b) Find the horizontal and vertical components of force exerted on the left end of the rod by the hinge.

20.A 20.0-kg floodlight in a park is supported at the end of a horizontal beam of negligible mass that is hinged to a pole, as shown in Figure P8.20. A cable at an angle of 30.0° with the beam helps to support the light. Find (a) the tension in the cable and (b) the horizontal and vertical forces exerted on the beam by the pole.

21.A uniform plank of length 2.00 m and mass 30.0 kg is supported by three ropes, as indicated by the blue vectors in Figure P8.21. Find the tension in each rope when a 700-N person is 0.500 m from the left end.

26.One end of a uniform 4.0-m-long rod of weight w is supported by a cable. The other end rests against a wall, where it is held by friction. (See Fig. P8.26.) The coefficient of static friction between the wall and the rod is μs = 0.50. Determine the minimum distance x from point A at which an additional weight w (the same as the weight of the rod) can be hung without causing the rod to slip at point A.

Chapter 4: Uniform Acceleration and Circular Motion

5. A motorist drives north for 35.0 minutes at 85.0 km/h and then stops for 15.0 minutes. He then continues north, traveling 130 km in 2.00 h. (a) What is his total displacement? (b) What is his average velocity?

6. A graph of position versus time for a certain particle moving along the x-axis is shown in Figure P2.6. Find the average velocity in the time intervals from (a) 0 to 2.00 s, (b) 0 to 4.00 s, (c) 2.00 s to 4.00 s, (d) 4.00 s to 7.00 s, and (e) 0 to 8.00 s.

12.A race car moves such that its position fits the relationship

x = (5.0 m/s)t + (0.75 m/s3)t3

where x is measured in meters and t in seconds. (a) Plot a graph of the car’s position versus time. (b) Determine the instantaneous velocity of the car at t = 4.0 s, using time intervals of 0.40 s, 0.20 s, and 0.10 s. (c) Compare the average velocity during the first 4.0 s with the results of (b).

13. Find the instantaneous velocities of the tennis player of Figure P2.13 at (a) 0.50 s, (b) 2.0 s, (c) 3.0 s, and (d) 4.5 s.

25. A Cessna aircraft has a lift-off speed of 120 km/h. (a) What minimum constant acceleration does the aircraft require if it is to be airborne after a takeoff run of 240 m? (b) How long does it take the aircraft to become airborne?

34.It is possible to shoot an arrow at a speed as high as 100 m/s. (a) If friction is neglected, how high would an arrow launched at this speed rise if shot straight up? (b) How long would the arrow be in the air?

37. A small mailbag is released from a helicopter that is descending steadily at 1.50 m/s. After 2.00 s, (a) what is the speed of the mailbag, and (b) how far is it below the helicopter? (c) What are your answers to parts (a) and (b) if the helicopter is rising steadily at 1.50 m/s?

39. A student throws a set of keys vertically upward to his fraternity brother, who is in a window 4.00 m above. The brother’s outstretched hand catches the keys 1.50 s later. (a) With what initial velocity were the keys thrown? (b) What was the velocity of the keys just before they were caught?

21.A brick is thrown upward from the top of a building at an angle of 25° to the horizontal and with an initial speed of 15 m/s. If the brick is in flight for 3.0 s, how tall is the building?

24.A fireman 50.0 m away from a burning building directs a stream of water from a ground-level fire hose at an angle of 30.0° above the horizontal. If the speed of the stream as it leaves the hose is 40.0 m/s, at what height will the stream of water strike the building?

25. A projectile is launched with an initial speed of 60.0 m/s at an angle of 30.0° above the horizontal. The projectile lands on a hillside 4.00 s later. Neglect air friction. (a) What is the projectile’s velocity at the highest point of its trajectory? (b) What is the straight-line distance from where the projectile was launched to where it hits its target?

Chapter 5: Work, Energy and Power

1. A weight lifter lifts a 350-N set of weights from ground level to a position over his head, a vertical distance of 2.00 m. How much work does the weight lifter do, assuming he moves the weights at constant speed?

5. A sledge loaded with bricks has a total mass of 18.0 kg and is pulled at constant speed by a rope inclined at 20.0° above the horizontal. The sledge moves a distance of 20.0 m on a horizontal surface. The coefficient of kinetic friction between the sledge and surface is 0.500. (a) What is the tension in the rope? (b) How much work is done by the rope on the sledge? (c) What is the mechanical energy lost due to friction?

7. A mechanic pushes a 2.50 × 103-kg car from rest to a speed of v, doing 5 000 J of work in the process. During this time, the car moves 25.0 m. Neglecting friction between car and road, find (a) v and (b) the horizontal force exerted on the car.

14.A 0.60-kg particle has a speed of 2.0 m/s at point A and a kinetic energy of 7.5 J at point B. What is (a) its kinetic energy at A? (b) its speed at point B? (c) the total work done on the particle as it moves from A to B?

15. A 2 000-kg car moves down a level highway under the actions of two forces: a 1 000-N forward force exerted on the drive wheels by the road and a 950-N resistive force. Use the work–energy theorem to find the speed of the car after it has moved a distance of 20 m, assuming that it starts from rest.

21.A daredevil on a motorcycle leaves the end of a ramp with a speed of 35.0 m/s as in Figure P5.21. If his speed is 33.0 m/s when he reaches the peak of the path, what is the maximum height that he reaches? Ignore friction and air resistance.

26.A 0.400-kg bead slides on a curved wire, starting from rest at point in Figure P5.26. If the wire is frictionless, find the speed of the bead (a) at and (b) at .

40.A skier of mass 70 kg is pulled up a slope by a motor-driven cable. (a) How much work is required to pull him 60 m up a 30° slope (assumed frictionless) at a constant speed of 2.0 m/s? (b) What power must a motor have to perform this task?

43. The electric motor of a model train accelerates the train from rest to 0.620 m/s in 21.0 ms. The total mass of the train is 875 g. Find the average power delivered to the train during its acceleration.

46.A 650-kg elevator starts from rest and moves upwards for 3.00 s with constant acceleration until it reaches its cruising speed, 1.75 m/s. (a) What is the average power of the elevator motor during this period? (b) How does this amount of power compare with its power during an upward trip with constant speed?

Chapter 6: Impulse and Momentum

1. A ball of mass 0.150 kg is dropped from rest from a height of 1.25 m. It rebounds from the floor to reach a height of 0.960 m. What impulse was given to the ball by the floor?

3. Calculate the magnitude of the linear momentum for the following cases: (a) a proton with mass 1.67 × 10–27 kg, moving with a speed of 5.00 × 106 m/s; (b) a 15.0-g bullet moving with a speed of 300 m/s; (c) a 75.0-kg sprinter running with a speed of 10.0 m/s; (d) the Earth (mass = 5.98 × 1024 kg) moving with an orbital speed equal to 2.98 × 104 m/s.

10.A 0.500-kg football is thrown toward the east with a speed of 15.0 m/s. A stationary receiver catches the ball and brings it to rest in 0.020 0 s. (a) What is the impulse delivered to the ball as it’s caught? (b) What is the average force exerted on the receiver?

11.The force shown in the force vs. time diagram in Figure P6.11 acts on a 1.5-kg object. Find (a) the impulse of the force, (b) the final velocity of the object if it is initially at rest, and (c) the final velocity of the object if it is initially moving along the x-axis with a velocity of –2.0 m/s.

13. The forces shown in the force vs. time diagram in Figure P6.13 act on a 1.5-kg particle. Find (a) the impulse for the interval from t = 0 to t = 3.0 s and (b) the impulse for the interval from t = 0 to t = 5.0 s. (c) If the forces act on a 1.5-kg particle that is initially at rest, find the particle’s speed at t = 3.0 s and at t = 5.0 s.

20.A rifle with a weight of 30 N fires a 5.0-g bullet with a speed of 300 m/s. (a) Find the recoil speed of the rifle. (b) If a 700-N man holds the rifle firmly against his shoulder, find the recoil speed of the man and rifle.

32.(a) Three carts of masses 4.0 kg, 10 kg, and 3.0 kg move on a frictionless horizontal track with speeds of 5.0 m/s, 3.0 m/s, and 4.0 m/s, as shown in Figure P6.32. The carts stick together after colliding. Find the final velocity of the three carts. (b) Does your answer require that all carts collide and stick together at the same time?

35.A 25.0-g object moving to the right at 20.0 cm/s overtakes and collides elastically with a 10.0-g object moving in the same direction at 15.0 cm/s. Find the velocity of each object after the collision

Chapter 7: Rotation of Rigid Bodies

1. The tires on a new compact car have a diameter of 2.0 ft and are warranted for 60 000 miles. (a) Determine the angle (in radians) through which one of these tires will rotate during the warranty period. (b) How many revolutions of the tire are equivalent to your answer in (a)?

2. A wheel has a radius of 4.1 m. How far (path length) does a point on the circumference travel if the wheel is rotated through angles of 30°, 30 rad, and 30 rev, respectively?

3. Find the angular speed of Earth about the Sun in radians per second and degrees per day.

4. A potter’s wheel moves from rest to an angular speed of 0.20 rev/s in 30 s. Find its angular acceleration in radians per second per second.

5. A dentist’s drill starts from rest. After 3.20 s of constant angular acceleration, it turns at a rate of 2.51 × 104 rev/min. (a) Find the drill’s angular acceleration. (b) Determine the angle (in radians) through which the drill rotates during this period.

6. A centrifuge in a medical laboratory rotates at an angular speed of 3 600 rev/min. When switched off, it rotates through 50.0 revolutions before coming to rest. Find the constant angular acceleration of the centrifuge.

7. A machine part rotates at an angular speed of 0.60 rad/s; its speed is then increased to 2.2 rad/s at an angular acceleration of 0.70 rad/s2. Find the angle through which the part rotates before reaching this final speed.

12.A coin with a diameter of 2.40 cm is dropped on edge onto a horizontal surface. The coin starts out with an initial angular speed of 18.0 rad/s and rolls in a straight line without slipping. If the rotation slows with an angular acceleration of magnitude 1.90 rad/s2, how far does the coin roll before coming to rest?

13. A rotating wheel requires 3.00 s to rotate 37.0 revolutions. Its angular velocity at the end of the 3.00-s interval

is 98.0 rad/s. What is the constant angular acceleration of the wheel?

Chapter 8: The Electric Force

1. A charge of 4.5 × 10−9 C is located 3.2 m from a charge of −2.8 × 10−9 C. Find the electrostatic force exerted by one charge on the other.

3. An alpha particle (charge = +2.0e) is sent at high speed toward a gold nucleus (charge = +79e). What is the electrical force acting on the alpha particle when it is 2.0 × 10−14 m from the gold nucleus?

5. The nucleus of 8Be, which consists of 4 protons and 4 neutrons, is very unstable and spontaneously breaks into two alpha particles (helium nuclei, each consisting of 2 protons and 2 neutrons). (a) What is the force between the two alpha particles when they are 5.00 × 10−15 m apart, and (b) what will be the magnitude of the acceleration of the alpha particles due to this force? Note that the mass of an alpha particle is 4.0026 u.

8. An electron is released a short distance above the surface of the Earth. A second electron directly below it exerts an electrostatic force on the first electron just great enough to cancel the gravitational force on it. How far below the first electron is the second?

9. Two identical conducting spheres are placed with their centers 0.30 m apart. One is given a charge of 12 × 10−9 C, the other a charge of −18 × 10−9 C. (a) Find the electrostatic force exerted on one sphere by the other. (b) The spheres are connected by a conducting wire. Find the electrostatic force between the two after equilibrium is reached.

10.Calculate the magnitude and direction of the Coulomb force on each of the three charges shown in Figure P15.10.

Figure P15.10 (Problems 10 and 18)

12.Three charges are arranged as shown in Figure P15.12. Find the magnitude

and direction of the electrostatic force on the 6.00-nC charge.

Figure P15.12

13. Two small metallic spheres, each of mass 0.20 g, are suspended as pendulums by light strings from a common point as shown in Figure P15.13. The spheres are given the same electric charge, and it is found that they come to equilibrium when each string is at an angle of 5.0° with the vertical. If each string is 30.0 cm long, what is the magnitude of the charge on each sphere?

Figure P15.13

Chapter 9: The Electric Field

15.An object with a net charge of 24 μC is placed in a uniform electric field of 610 N/C, directed vertically. What is the mass of the object if it “floats” in the electric field?

17. An airplane is flying through a thundercloud at a height of 2 000 m. (This is a very dangerous thing to do because of updrafts, turbulence, and the possibility of electric discharge.) If there are charge concentrations of +40.0 C at a height of 3 000 m within the cloud and −40.0 C at a height of 1000 m, what is the electric field at the aircraft?

21. A proton accelerates from rest in a uniform electric field of 640 N/C. At some later time, its speed is 1.20 × 106

m/s. (a) Find the magnitude of the acceleration of the proton. (b) How long does it take the proton to reach this speed? (c) How far has it moved in that interval? (d) What is its kinetic energy at the later time?

22.Three charges are at the corners of an equilateral triangle, as shown in Figure P15.22. Calculate the electric field at a point midway between the two charges on the x-axis.

Figure P15.22

23. In Figure P15.23, determine the point (other than infinity) at which the total electric field is zero.

Figure P15.23

28.A flat surface having an area of 3.2 m2

is rotated in a uniform electric field of magnitude E = 6.2 × 105 N/C. Determine the electric flux through this area (a) when the electric field is perpendicular to the surface and (b) when the electric field is parallel to the surface.

29. An electric field of intensity 3.50 kN/C is applied along the x-axis. Calculate the electric flux through a rectangular plane 0.350 m wide and 0.700 m long if (a) the plane is parallel to the yz-plane; (b) the plane is parallel to the xy-plane; and (c) the plane contains the y-axis, and its normal makes an angle of 40.0° with the x-axis.

31.A 40-cm-diameter loop is rotated in a uniform electric field until the position of maximum electric flux is found. The flux in that position is measured to be 5.2 × 105 N·m2/C. Calculate the electric field strength in this region.

32.A point charge of +5.00 μC is located at the center of a sphere with a radius of 12.0 cm. Determine the electric flux through the surface of the sphere.

33. A point charge q is located at the center of a spherical shell of radius a that has a charge −q uniformly distributed on its surface. Find the electric field (a) for all points outside the spherical shell and (b) for a point inside the shell a distance r from the center.

Chapter 10: Electric Potential

1. A proton moves 2.00 cm parallel to a uniform electric field of E = 200 N/C. (a) How much work is done by the field on the proton? (b) What change occurs in the potential energy of the proton? (c) What potential difference did the proton move through?

2. A uniform electric field of magnitude 250 V/m is directed in the positive x-direction. A 12-μC charge moves from the origin to the point (x, y) = (20 cm, 50 cm). (a) What was the change in the potential energy of this charge? (b) Through what potential difference did the charge move?

5. The potential difference between the accelerating plates of a TV set is about 25 kV. If the distance between the plates is 1.5 cm, find the magnitude of the uniform electric field in the region between the plates.

6. To recharge a 12-V battery, a battery charger must move 3.6 × 105 C of charge from the negative terminal to the positive terminal. How much work is done by the charger? Express your answer in joules.

7. Oppositely charged parallel plates are separated by 5.33 mm. A potential difference of 600 V exists between the plates. (a) What is the magnitude of the electric field between the plates? (b) What is the magnitude of the force on an electron between the plates? (c) How much work must be done on the electron to move it to the negative plate if it is initially positioned 2.90 mm from the positive plate?

9. (a) Find the electric potential 1.00 cm from a proton. (b) What is the electric potential difference between two points that are 1.00 cm and 2.00 cm from a proton?

11. (a) Find the electric potential, taking zero at infinity, at the upper right corner (the corner without a charge) of the rectangle in Figure P16.11. (b) Repeat if the 2.00-μC charge is replaced with a charge of −2.00 μC.

Figure P16.11 (Problems 11 and 12)

12.Three charges are situated at corners of a rectangle as in Figure P16.11. How much energy would be expended in moving the 8.00-μC charge to infinity?

14.A point charge of 9.00 × 10−9 C is located at the origin. How much work is required to bring a positive charge of 3.00 × 10−9 C from infinity to the location x = 30.0 cm?

17. In Rutherford’s famous scattering experiments that led to the planetary model of the atom, alpha particles (having charges of +2e and masses of 6.64 × 10−27 kg) were fired toward a gold nucleus with charge +79e. An alpha particle, initially very far from the gold nucleus, is fired at 2.00 × 107

m/s directly toward the nucleus, as in Figure P16.17. How close does the alpha particle get to the gold nucleus before turning around? Assume the gold nucleus remains stationary.

Figure P16.17

Chapter 11: Capacitance

20.(a) How much charge is on each plate of a 4.00-μF capacitor when it is connected to a 12.0-V battery? (b) If this same capacitor is connected to a 1.50-V battery, what charge is stored?

22.The potential difference between a pair of oppositely charged parallel plates is 400 V. (a) If the spacing between the plates is doubled without altering the charge on the plates, what is the new potential difference between the plates? (b) If the plate spacing is doubled while the potential difference between the plates is kept constant, what is the ratio of the final charge on one of the plates to the original charge?

23. An air-filled capacitor consists of two parallel plates, each with an area of 7.60 cm2 and separated by a distance of 1.80 mm. If a 20.0-V potential difference is applied to these plates, calculate (a) the electric field between the plates, (b) the capacitance, and (c) the charge on each plate.

24.A 1-megabit computer memory chip contains many 60.0 × 10−15-F capacitors. Each capacitor has a plate area of 21.0 × 10−12 m2. Determine the plate separation of such a capacitor. (Assume a parallel-plate configuration). The diameter of an atom is on the order of 10−10 m = 1 Å. Express the plate separation in angstroms.

25.A parallel-plate capacitor has an area of 5.00 cm2, and the plates are separated by 1.00 mm with air between them. The capacitor stores a charge of 400 pC. (a) What is the potential difference across the plates of the capacitor? (b) What is the magnitude of the uniform electric field in the region between the plates?

27.A series circuit consists of a 0.050-μF capacitor, a 0.100-μF capacitor, and a 400-V battery. Find the charge (a) on each of the capacitors and (b) on each of the capacitors if they are reconnected in parallel across the battery.

28.Three capacitors, C1 = 5.00 μF, C2 = 4.00 μF, and C3 = 9.00 μF, are connected together. Find the effective capacitance of the group (a) if they are

all in parallel, and (b) if they are all in series.

29.(a) Find the equivalent capacitance of the group of capacitors in Figure P16.29. (b) Find the charge on each capacitor and the potential difference across it.

Figure P16.29

31.Four capacitors are connected as shown in Figure P16.31. (a) Find the equivalent capacitance between points a and b. (b) Calculate the charge on each capacitor if a 15.0-V battery is connected across points a and b.

Figure P16.31

Chapter 12: Current and Resistance

13.Calculate the diameter of a 2.0-cm length of tungsten filament in a small lightbulb if its resistance is 0.050 Ω.

15.A potential difference of 12 V is found to produce a current of 0.40 A in a 3.2-m length of wire with a uniform radius of 0.40 cm. What is (a) the resistance of the wire? (b) the resistivity of the wire?

17. A wire 50.0 m long and 2.00 mm in diameter is connected to a source with a potential difference of 9.11 V, and the current is found to be 36.0 A. Assume a temperature of 20°C, and, using Table 17.1, identify the metal out of which the wire is made.

28.If electrical energy costs 12 cents, or $0.12, per kilowatt-hour, how much does it cost to (a) burn a 100-W lightbulb for 24 h? (b) operate an electric oven for 5.0 h if it carries a current of 20.0 A at 220 V?

35. A copper cable is designed to carry a current of 300 A with a power loss of 2.00 W/m. What is the required radius of this cable?

1. A battery having an emf of 9.00 V delivers 117 mA when connected to a 72.0-Ω load. Determine the internal resistance of the battery.

2. A 4.0-Ω resistor, an 8.0-Ω resistor, and a 12-Ω resistor are connected in series with a 24-V battery. What are (a) the equivalent resistance and (b) the current in each resistor? (c) Repeat for the case in which all three resistors are connected in parallel across the battery.

5. (a) Find the equivalent resistance between points a and b in Figure P18.5. (b) Calculate the current in each resistor if a potential difference of 34.0 V is applied between points a and b.

Figure P18.5

8. (a) Find the equivalent resistance of the circuit in Figure P18.8. (b) If the total power supplied to the circuit is 4.00 W, find the emf of the battery.

Figure P18.8

9. Consider the circuit shown in Figure P18.9. Find (a) the current in the 20.0-Ω resistor and (b) the potential difference between points a and b.

Figure P18.9

Chapter 13: Magnetism and the Magnetic Field

1. An electron gun fires electrons into a magnetic field directed straight downward. Find the direction of the force exerted by the field on an electron for each of the following directions of the electron’s velocity: (a) horizontal and due north; (b) horizontal and 30° west of north; (c) due north, but at 30° below the horizontal; (d) straight upward. (Remember that an electron has a negative charge.)

2. (a) Find the direction of the force on a proton (a positively charged particle) moving through the magnetic fields in Figure P19.2, as shown. (b) Repeat part (a), assuming the moving particle is an electron.

Figure P19.2 (Problems 2 and 12) For Problem 12, replace the velocity vector with a current in that direction.

3. Find the direction of the magnetic field acting on the positively charged particle moving in the various situations shown in Figure P19.3 if the direction of the magnetic force acting on it is as indicated.

Figure P19.3 (Problems 3 and 13) For Problem 13, replace the velocity vector with a current in that direction.

5. At the equator, near the surface of Earth, the magnetic field is approximately 50.0 μT northward, and the electric field is about 100 N/C downward in fair weather. Find the gravitational, electric, and magnetic forces on an electron with an instantaneous velocity of 6.00 × 106

m/s directed to the east in this environment.

6. The magnetic field of the Earth at a certain location is directed vertically downward and has a magnitude of 50.0 μT. A proton is moving horizontally toward the west in this field with a speed of 6.20 × 106 m/s. What are the direction and magnitude of the magnetic force the field exerts on the proton?

7. What velocity would a proton need to circle Earth 1 000 km above the magnetic equator, where Earth’s magnetic field is directed horizontally north and has a magnitude of 4.00 × 10−8 T?

8. An electron is accelerated through 2 400 V from rest and then enters a region where there is a uniform 1.70-T magnetic field. What are (a) the maximum and (b) the minimum magnitudes of the magnetic force acting on this electron?

9. A proton moves perpendicularly to a

uniform magnetic field at 1.0 × 107 m/s and exhibits an acceleration of 2.0 × 1013 m/s2 in the +x-direction when its velocity is in the +z-direction. Determine the magnitude and direction of the field.