A charged particle is held at the center of two concentric conducting spherical shells. Figure (a) shows a cross section. Figure (b) gives the net flux Φ through a Gaussian sphere centered on the particle, as a function of the radius r of the sphere. The scale of the vertical axis is set by Φs = 4.5×105 N⋅m2/C. What are (a) the charge of the central particle and the net charges of (b) shell A and (c) shell B? (a) (b) (a) Number Units C (b) Number Units (c) Number Units
The space between two concentric conducting spherical shells of radii b = 1.80 cm and a = 1.20 cm is filled with a substance of dielectric constant K = 16.4. A potential difference V = 56.0 V is applied across the inner and outer shells. Determine (a) the capacitance of the device, (b) the free charge q on the inner shell, and (c) the charge q induced along the surface of the inner shell. (a) Number Units (b) Number Units (c) Number Units
A wire loop of radius 12 cm and resistance 11 Ω is located in a uniform magnetic field that changes in magnitude as given in the figure. The loop's plane is perpendicular to the magnetic field. What is the magnitude of the emf in volts induced in the loop during the time intervals (a) t−0 to 2.0 s; (b) 2.0 s to 4.0 s; and (c) 4.0 s tot -6.0 s? (a) Number Units (b) Number Units (c) Number Units
Exercise 6. Sphere A collides with sphere B as shown in the figure. If the coefficient of restitution is e = 0.5, determine the x- and y-components of the velocity of each sphere immediately after impact. Motion is confined to the x-y plane.
A rectangular coil of N turns and of length a and width b is rotated at frequency f in a uniform magnetic field of magnitude B, as indicated in the figure. The coil is connected to co-rotating cylinders, against which metal brushes slide to make contact. The emf induced in the coil is given (as a function of time t) by E = 2πfNabBsin(2πft) = E0sin(2πft) This is the principle of the commercial alternating-current generator. What value of Nab gives an emf with ε0 = 200 V when the loop is rotated at 45.2 rev/s in a uniform magnetic field of 0.380 T? Number Units
A positively charged insulating sphere with volume charge density ρ is surrounded with a concentric insulating shell of inner radius R and outer radius 2 R, as shown in the picture below. The insulating shell is negatively charged and has volume charge density −ρ. For the best results, solve each part of this problem on paper, and check the multiple choice answers provided only after you have your own answer 1. Electric field inside the inner sphere. a) Consider a Gaussian surface of radius 0 < r < R. What is the charge enclosed by this Gaussian surface? Q1(r) = 4πr2ρ Q1(r) = 4πr23ρ Q1(r) = 4πR2ρ Q1(r) = 4πR23ρ
The space between two concentric conducting spherical shells of radii b = 1.80 cm and a = 1.10 cm is filled with a substance of dielectric constant k = 18.8. A potential difference V = 97.0 V is applied across the inner and outer shells. Determine (a) the capacitance of the device, (b) the free charge q on the inner shell, and (c) the charge q induced along the surface of the inner shell. (a) Number Units (b) Number Units (c) Number Units
In the figure, a wire loop of dimensions L = 43.1 cm and W = 26.6 cm lies in a magnetic field. What are the (a) magnitude 8 and (b) direction (clockwise or counterclockwise-or "none" if ε = 0) of the emf induced in the loop if B→ = (6.60×10−2 T/m)yk^? What are (c) 8 and (d) the direction if B→ = (6.13×10−2 T/s)tk^? What are (e)s and (f) the direction if B→ = (8.17×10−2 T/m⋅s)ytk^? What are (g)s and (h) the direction if B→ = (3.00×10−2 T/m⋅s)xtj^? What are (i)g and (j) the direction if B→−(5.00×10−2 T/m⋅s)yti^? (a) Number (b) (c) Number Units (d) (e) Number Units (f)
A cylinder has a magnetic flux of 12 Wb directed inward through its bottom end and a magnetic flux of 24 Wb directed into the curved side. What is the magnitude ΦB of the magnetic flux through the top of the cylinder? ΦB = Wb What is the direction of the magnetic flux through the top of the cylinder? inward outward
A long and narrow rectangular loop of wire of width 0.080 m is moving toward the bottom of the screen with a speed of 0.025 m/s (see the drawing). The loop is leaving a region in which a 3.3-T magnetic field exists; the magnetic field outside this region is zero. During a time of 2.5 s, what is the magnitude of the change in the magnetic flux? Number Units
In the figure, set R = 188 Ω, C = 74.2 μF, L = 188 mH, fd = 60.0 Hz, and εm = 7.03 V. What are (a) Z, (b) φ, and (c) I? (a) Number Units (b) Number Units (c) Number Units
In the figure, a stone is projected at a cliff of height h with an initial speed of 46.0 m/s directed at an angle θ0 = 62.0∘ above the horizontal. The stone strikes at A, 5.09 s after launching. Find (a) the height h of the cliff, (b) the speed of the stone just before impact at A, and (c) the maximum height H reached above the ground. Use g = 9.80 m/s2. (a) Number Units (b) Number Units (c) Number Units
In the figure, a stone is projected at a cliff of height h with an initial speed of 44.0 m/s directed at an angle θ0 = 66.0∘ above the horizontal. The stone strikes at A, 5.88 s after launching. Find (a) the height h of the cliff, (b) the speed of the stone just before impact at A, and (c) the maximum height H reached above the ground. Use g = 9.80 m/s2. (a) Number Units (b) Number Units (c) Number Units
In the figure, an electron accelerated from rest through potential difference V1 = 1.18 kV enters the gap between two parallel plates having separation d = 17.5 mm and potential difference V2 = 119 V. The lower plate is at the lower potential. Neglect fringing and assume that the electron's velocity vector is perpendicular to the electric field vector between the plates. In unit-vector notation, what uniform magnetic field allows the electron to travel in a straight line in the gap?
A boy ran towards the edge of the cliff to dive into the sea as shown in the figure below. (a) How fast must he run to make sure that he hits the water and not the rocky ledge below? (b) Assuming that he is able to run at a speed of 5 ms−1, what is his body's speed when he hits the water assuming negligible air friction? (Take g to be 10 ms−2 and give your answers to 3 significant figures)
As preparation for this problem, review Conceptual Example 9. From the top of a cliff overlooking a lake, a person throws two stones, as shown in the drawing. The cliff is 25.4 m high. The two stones described have identical initial speeds of v0 = 13.4 m/s and are thrown at an angle θ = 37.8∘, one below the horizontal and one above the horizontal. What is the distance between the points where the stones strike the water? Neglect air resistance. Number Units
A mountain climber, in the process of crossing between two cliffs by a rope, pauses to rest. She weighs 560 N. As the drawing shows, she is closer to the left cliff than to the right cliff, with the result that the tensions in the left and right sides of the rope are not the same. Find the tensions in the rope to the left and to the right of the mountain climber. TL = TR =
A diver jumps off a cliff of h at an angle of θ = 34∘ (see figure below). He reaches a maximum height of hmax = 3 m above the top of the cliff before falling to the water below. He hits the water x = 41 m from the base of the cliff. Determine the speed of the diver just before he hits the water, vA = ?. Express your answer in units of m/s. Take g = 9.80 m/s2. Round your answer to zero decimal places.
A stunt driver is filming a scene for an action movie in which they drive a car off a cliff and land in the water below. As shown in the diagram, the cliff has a height h = 8.95 m and is sloped upwards at an angle θ = 15.3 degrees. The stunt driver carefully manages their speed so they are travelling at vi = 6.02 ms−1 as they leave the cliff. Part 1) What is the car's initial velocity in unit vector notation (where i^ is a unit vector to the right and j^ is a unit vector upwards)? vi = i^ + j^ ms−1 Part 2) How long will the car 'fly'? That is, how much time will pass between the car leaving the cliff and landing in the water? t = s Part 3) What is the maximum height the car will reach, as measured from the water? hmax = m
The 3.70 kg cube in the figure has edge lengths d = 5.90 cm and is mounted on an axle through its center. A spring (k = 1500 N/m) connects the cube's upper corner to a rigid wall. Initially the spring is at its rest length. If the cube is rotated 4.00∘ and released, what is the period of the resulting SHM? Number Units
A mass m = 0.3 kg is attached to a spring of spring constant k = 2×103 N/m. When the spring is fully extended to the right, it contains 500 J of stored energy. a) Calculate the acceleration when the spring is fully extended. Give your answer in m/s2. Which way is it pointing? b) When the mass is released, calculate the period of oscillation, in seconds.
The switch in the figure below is connected to position a for a long time interval. At t = 0, the switch is thrown to position b. After this time, what are the following? (Let C = 1.40 μF.) (a) the frequency of oscillation of the LC circuit Hz (b) the maximum charge that appears on the capacitor μC (c) the maximum current in the inductor mA (d) the total energy the circuit possesses at t = 3.00 s μJ
An ac generator has emf ε = εmsin(ωdt − π/4), where εm = 42.0 V and ωd = 346 rad/s. The current produced in a connected circuit is i(t) = Isin(ωdt − 3π/4), where I = 532 mA. At what time after t = 0 does (a) the generator emf first reach maximum and (b) the current first reach a maximum? (c) The circuit contains a single element other than the generator. Is it a capacitor, an inductor, or a resistor? (d) What is the value of the capacitance, inductance, or resistance, as the case may be? (a) Number Units (b) Number Units (c) (d) Number Units
If the force F moves the plate attached to the spring from position 1 to position 2 (or the force displaces the plate by s), then which of the following statement (s) is/are correct? Select all that applies. (b) position 2 The elastic potential energy, Ve developed due to the force is given by (1/2)ks2, and is negative. The elastic potential energy, Ve developed due to the force is given by (1/2)ks2, and is positive. The spring force developed by the plate acts opposite to the applied force and has a tendency of doing a positive work. The elastic potential energy of the spring is given by the product of the force F and the displacement s (or F×s)