Pulling the plates of an isolated charged capacitor apart: does not affect the capacitance does not affect the potential difference decreases the potential difference increases the capacitance increases the potential difference
A parallel-plate capacitor has a plate area of 0.2 m2 and a plate separation of 0.1 mm. If the charge on each plate has a magnitude of 4×10−6 C the potential difference across the plates is approximately: 0 V 4×10−2 V 2×102 V 2×105 V 4×108 V
Two conducting spheres have radii of R1 and R2 with R1 greater than R2. If they are far apart the capacitance is proportional to: R1 R2/(R1 − R2) R22 − R12 (R1 − R2)/R1R2 R22 + R12 none of these
A2−μF and a 1−μF capacitor are connected in parallel and a potential difference is applied across the combination. The 2−μF capacitor has: twice the charge of the 1−μF capacitor half the charge of the 1−μF capacitor twice the potential difference of the 1−μF capacitor half the potential difference of the 1−μF capacitor none of the above
A certain capacitor has a capacitance of 5.0 μF. After it is charged to 5 μC and isolated, the plates are brought closer together so its capacitance becomes 10 μF. The work done by the agent is about: 0 J 1.25×10−6 J −1.25×10−6 J 8.3×10−7 J −8.3×10−7 J
An air-filled parallel-plate capacitor has a capacitance of 1 pF. The plate separation is then doubled and a wax dielectric is inserted, completely filling the space between the plates. As a result, the capacitance becomes 2 pF. The dielectric constant of the wax is: 0.25 0.50 2.0 4.0 8.0
Two capacitors are identical except that one is filled with air and the other with oil. Both capacitors carry the same charge. The ratio of the electric fields Eair/Eoil is: between 0 and 1 0 1 between 1 and infinity infinite
The Earth's electric field creates a potential that increases 100 V for every meter of altitude. If an object of charge +4.5 mC and mass 68 g falls a distance of 1.0 m from rest under the influence of the Earth's electric and gravitational fields, what is its final kinetic energy? 0.22 J 0.45 J 0.67 J 1.1 J 7.2 J
In separate experiments, four different particles each start from far away with the same speed and impinge directly on a gold nucleus. The masses and charges of the particles are particle 1: mass m0, charge q0 particle 2: mass 2m0, charge 2q0 particle 3: mass 2m0, charge q0/2 particle 4: mass m0/2, charge 2q0 Rank the particles according to the distance of closest approach to the gold nucleus, from smallest to largest. 1 and 2 tie, then 3 , then 4 4 , then 1 and 2 tie, then 3 1, 2, 3, 4 4, 3, 2, 1 3 , then 1 and 2 tie, then 4
Eight identical spherical raindrops are each at a potential V, relative to the potential far away. They coalesce to make one spherical raindrop whose potential is: V/8 V/2 2 V 4 V 8 V
The electric potential in a certain region of space is given by V = −7.5x2 + 3x, where V is in volts and x is in meters. In this region the equipotential surfaces are: planes parallel to the x axis planes parallel to the yz plane concentric spheres centered at the origin concentric cylinders with the x axis as the cylinder axis unknown unless the charge is given
Three particles lie on the x axis: particle 1 , with a charge of 1×10−8 C is at x = 1 cm, particle 2 , with a charge of 2×10−8 C, is at x = 2 cm, and particle 3 , with a charge of -3 x10−8 C, is at x = 3 cm. The potential energy of this arrangement, relative to the potential energy for infinite separation, is: +4.9×10−4 J −4.9×10−4 J +8.5×10−4 J −8.5×10−4 J 0 J
An electric dipole consists of two equal and opposite charged particles of mass 1.2 g and charge 3.7 μC separated by 1.7 mm. What is the escape speed of the positive charge - that is, how much speed would you have to give it so it would escape the other charge? 200 m/s 350 m/s 6600 m/s 7.1×104 m/s 2.0×105 m/s
The electric field in a region around the origin is given by E→ = C(xi^ + yj^), where C is a constant. The equipotential surfaces are: concentric cylinders with axes along the z axis concentric cylinders with axes along the x axis concentric spheres centered at the origin planes parallel to the xy plane planes parallel to the yz plane
A distribution of charge produces an electric field along the x-axis of the form E(x) = (327 V/m3)x2. The electric potential at x = 1.50 m is −70 V. What is the electric potential (V) at x = 1.10 m? 153 61.1 −153 75.1 303 −75.1 −303 −61.1 −223 223
A nonconducting sphere has radius R = 1.77 cm and uniformly distributed charge q = +3.56 fC. Take the electric potential at the sphere's center to be V0 = 0. What is V at radial distance from the center (a) r = 1.00 cm and (b) r = R? (Hint: See Module 23.6.) (a) Number Units (b) Number Units
What is the escape speed for an electron initially at rest on the surface of a sphere with a radius of 1.30 cm and a uniformly distributed charge of 1.50×10−15 C? That is, what initial speed must the electron have in order to reach an infinite distance from the sphere and have zero kinetic energy when it gets there? The charge of an electron is 1.602×10−19 C and its mass is 9.109×10−31 kg. Number Units
Suppose N electrons can be placed in either of two configurations. In configuration 1 , they are all placed on the circumference of a narrow ring of radius R and are uniformly distributed so that the distance between adjacent electrons is the same everywhere. In configuration 2,N − 1 electrons are uniformly distributed on the ring and one electron is placed in the center of the ring. (a) What is the smallest value of N for which the second configuration is less energetic than the first? (b) For that value of N, consider any one circumference electron-call it e0. How many other circumference electrons are closer to e0 than the central electron is? (a) Number Units (b) Number Units
Assume that a stationary electron is a point of charge. What is the energy density u of its electric field at radial distances (a) r = 1.60 mm, (b) r = 1.60 μm, (c) r = 1.60 nm, and (d) r = 1.60 pm? (e) What is u in the limit as r → 0? (Select option "1" if u → 0 or option "2" if u → ∞.) (a) Number Units (b) Number Units (c) Number Units (d) Number Units (e)
A certain parallel-plate capacitor is filled with a dielectric for which K = 4.41. The area of each plate is 0.0742 m2, and the plates are separated by 2.20 mm. The capacitor will fail (short out and burn up) if the electric field between the plates exceeds 227 kN/C. What is the maximum energy that can be stored in the capacitor? Number Units
A plane, diving with constant speed at an angle of 42.6∘ with the vertical, releases a projectile at an altitude of 696 m. The projectile hits the ground 5.26 s after release. (a) What is the speed of the plane? (b) How far does the projectile travel horizontally during its flight? What were the magnitudes of the (c) horizontal and (d) vertical components of its velocity just before striking the ground? (State your answers to (c) and (d) as positive numbers.) (a) Number Units (b) Number Units (c) Number Units (d) Number Units
If a→ − b→ = 4.4 c→, a→ + b→ = 3.7 c→, and c→ = 4.8 i^ + 4.3 j^, then what are (a) the x component of a→, (b) the y component of a→, (c) the x component of b→, and (d) the y component of b→ ? (a) Number Units (b) Number Units (c) Number Units (d) Number Units
Component values of R = 2 Ω, C = 0.800 mF, and L = 2 mH are used to construct the circuit given. If vC(0−) = 1 V and no current initially flows through the inductor, calculate i(t) at t = 1 ms, 2 ms, and 3 ms. (Round the final answers to three decimal places. ) The value of (t) at t = 1 ms is A. The value of (t) at t = 2 ms is A. The value of (1) at t = 3 ms is A.
(a) A block of mass m = 2.80 kg is suspended as shown in the diagram below. Assume the pulley to be frictionless and the mass of the strings to be negligible. If the system is in equilibrium, what will be the reading of the spring scale in newtons? (b) Two blocks each of mass m = 2.80 kg are connected as shown in the diagram below. Assume the pulley to be frictionless and the mass of the strings to be negligible. If the system is in equilibrium, what will be the reading of the spring scale in newtons? N (c) A block of mass m = 2.80 kg is in equilibrium on an incline plane of angle θ = 27.0∘ when connected as shown in the diagram below. Assume the mass of the strings to be negligible. If the system is in equilibrium, what will be the reading of the spring scale in newtons? N
You pull with a force of 290 N on a rope that is attached to a block of mass 24 kg, and the block slides across the floor at a constant speed of 1.2 m/s. The rope makes an angle of 20 degrees with the horizontal. What is the direction of dp→dt of the block? What is the net force on the block? F→net = N Which objects exert forces on the block with nonzero x-components? floor Earth rope you What is the x-component of the tension force exerted by the rope on the block? (A component may be positive or negative.) FTx = N What is the x-component of the force exerted by the floor on the block (the friction force)? Ffx = N Which objects exert forces on the block with nonzero y-components? floor rope you Earth What is the y-component of the force exerted by the rope on the block? FTy = N What is the y-component of the force exerted by the Earth on the block? FEEarth = N What is the y-component of the force exerted by the floor on the block (sometimes called the "normal" force, because it is perpendicular to the floor)? FNy = N
What frequencies (in Hz) will a 1.70 m long tube produce in the audible range (20 Hz−20, 000 Hz) at 24.0∘C for the following cases? (a) the tube is closed at one end lowest frequency Hz second lowest frequency Hz highest frequency (rounded to the nearest Hz) Hz (b) the tube is open at both ends lowest frequency Hz second lowest frequency Hz highest frequency (rounded to the nearest Hz) Hz
Two vectors a→ and b→ have the components, in meters, ax = 3.40, ay = 2.21, bx = 1.75, by = 6.36. (a) Find the angle between the directions of a→ and b→. There are two vectors in the xy plane that are perpendicular to a→ and have a magnitude of 9.39 m. One, vector c→, has a positive x component and the other, vector d→, a negative x component. What are (b) the x component and (c) the y component of c→, and (d) the x component and (e) the y component of vector d→ ? (a) Number Units ∘ (degrees) (b) Number Units (c) Number Units (d) Number Units (e) Number Units
In the figure R1 = 10.8 kΩ, R2 = 15.8 kΩ, C = 0.436 μF, and the ideal battery has emf δ = 25.0 V. First, the switch is closed a long time so that the steady state is reached. Then the switch is opened at time t = 0. What is the current in resistor 2 at t = 4.10 ms? Number Units
In the figure the electric field lines on the left have twice the separation as those on the right. (a) If the magnitude of the field at A is 57 N/C, what is the magnitude of the force on a proton at A? (b) What is the magnitude of the field at B? (a) Number Units (b) Number Units
A parallel-plate capacitor with area 0.280 m2 and plate separation of 4.80 mm is connected to a 4.00−V battery. (a) What is the capacitance? F (b) How much charge is stored on the plates? C (c) What is the electric field between the plates? N/C (d) Find the magnitude of the charge density on each plate. C/m2 (e) Without disconnecting the battery, the plates are moved farther apart: Qualitatively, what happens to each of the previous answers?
A crate of mass m = 57.1 kg is on a horizontal surface. Assume there is no friction between the crate and the surface. Two forces with magnitude F = 38 N are applied to the crate, as shown. One force is horizontal, and the other makes and angle of ϕ = 37∘ with horizontal, as shown. 50% Part (a) Write an expression for the magnitude of the acceleration of the crate in terms of F, m, and ϕ. 50% Part (b) What is the magnitude of the acceleration of the crate in m/s2?
The spring mass system which is initially at rest starts free vibration with an initial displacement of x0 = 0.12 m and an initial speed of v0 = 0.6 m/sec. The mass is 2 kg, and the spring constant is k = 288 N/m. Calculate the position x, and speed v of the block at t = 1 sec. (30 Points) ω = k/m, x = v0 ωsin(ωt) + x0 cos(ωt)
A horizontal wire is hung from the ceiling of a room by two massless strings. The wire has a length of 0.19 m and a mass of 0.005 kg. A uniform magnetic field of magnitude 0.080 T is directed from the ceiling to the floor. When a current of I = 39 A exists in the wire, the wire swings upward and, at equilibrium, makes an angle ϕ with respect to the vertical, as the drawing shows. Find (a) the angle and (b) the tension in each of the two strings. (a) ϕ = (b) T =
Three capacitors (4.6, 7.8, and 18.0 μF) are connected in series across a 60.0−V battery. Find the voltage across the 4.6−μF capacitor. Number Units
When an electron moves from A to B along an electric field line in the figure, the electric field does 4.70×10−19 J of work on it. What are the electric potential differences (a) VB − VA, (b) VC − VA, and (c) VC − VB ? (a) Number Units (b) Number Units (c) Number Units
A particle of charge +17.6 μC and mass 5.87×10−5 kg is released from rest in a region where there is a constant electric field of +683 N/C. What is the displacement of the particle after a time of 3.01×10−2 s ? Number Units
One cubic centimeter of a typical cumulus cloud contains 320 water drops, which have a typical radius of 10 μm. (a) How many cubic meters of water are in a cylindrical cumulus cloud of height 2.8 km and radius 0.9 km ? (b) How many 1-liter pop bottles would that water fill? (c) Water has a density of 1000 kg/m3. How much mass does the water in the cloud have? (a) Number Units (b) Number Units (c) Number Units
The square surface shown in the figure measures 4.3 mm on each side. It is immersed in a uniform electric field with magnitude E = 2200 N/C and with field lines at an angle of 35∘ with a normal to the surface, as shown. Take that normal to be "outward," as though the surface were one face of a box. Calculate the electric flux through the surface.
Consider a ball of radius r and mass m struck horizontally by the cue stick at height h = 7 cm with a force P, as depicted in the figure below. The ball starts at rest, and the force from the cue stick is much larger than the friction force. The moment of inertia of the ball is IG = 25 mr2, the ball rolls without slipping after the impact, and the linear velocity of the point B on top of the ball is v = 15 cm/s after the impact. a. Calculate the ball's radius r. b. Determine the angular velocity of the ball ω immediately after the impact. c. What is the kinetic energy of the ball immediately after the impact?
In the diagram shown, Block A is 34.5 kg and Block B is 11 kg. The incline on Block A's side makes an angle of 61.5∘ with the horizontal and the incline on Block B's side makes an angle of 29∘ with the horizontal. The coefficient of kinetic friction of Block A's incline is 0.16 and that of Block B's incline is 0.104 . Assume that Block A is initially (at t = 0) sliding up its incline at 5.2 m/s. Also assume the pulley is massless and frictionless. In your submitted work, be sure to show your neatly drawn free body diagrams for each mass (using a straight-edge). Identify each vector force (draw arrows) in the diagram and draw your axes for each diagram and show the component breakdown for each force. . . points will be lost for sloppy or incomplete drawings. You should have FOUR FBDs. . . one for each mass as Block A slides UP the incline (while Block B slides DOWN its incline), and one for each mass when Block A slides DOWN its incline (while Block B slides UP its incline). (A)Calculate the magnitude of the acceleration (in m/s2) of the blocks as Block A is on the way UP its incline. 20.1 5.36 2.40 9.25 6.16 13.0 (B)Calculate the tension (in N) in the rope as Block A is on the way UP its incline. 233 95.9 43.0 110. 359 165 (C)Calculate the magnitude of the acceleration (in m/s2)of the blocks as Block A is on the way DOWN its incline. 15.0 9.70 1.79 4.60 4.00 6.90 (D)Calculate the tension (in N) in the rope as Block A is on the way DOWN its incline. 367 238 98.0 43.9 113 169 (E)Assuming the ramps and ropes are long enough, over what total distance (in meters) will the blocks have moved along their inclines after 3.5 seconds from start of the motion? (HINT: This is asking for distance, not displacement. ALSO, recognize that at some point over this 3.5 second time interval the blocks will stop and reverse direction.) 27.6 18.4 38.9 7.18 16.0 60.0
While sliding a couch across a floor, Andrea and Jennifer exert forces F→A and F→J on the couch. Andrea's force is due north with a magnitude of 150.0 N and Jennifer's force is 25∘ east of north with a magnitude of 170.0 N. (a) Find the net force (in N) in component form. F→net =N (b) Find the magnitude (in N) and direction (in degrees counterclockwise from the east axis) of the net force. magnitude N direction counterclockwise from the east axis (c) If Andrea and Jennifer's housemates, David and Stephanie, disagree with the move and want to prevent its relocation, with what combined force F→DS (in N) should they push so that the couch does not move? (Express your answer in vector form.) F→DS = N
A particle has a charge of q = +5.4 μC and is located at the origin. As the drawing shows, an electric field of Ex = +205 N/C exists along the +x axis. A magnetic field also exists, and its x and y components are Bx = +1.5 T and By = +1.1 T. Calculate the force (magnitude and direction) exerted on the particle by each of the three fields when it is (a) stationary, (b) moving along the +x axis at a speed of 345 m/s and (c) moving along the +z axis at a speed of 345 m/s. (a) FE = FBx = FBy = (b) FE = FBx = FBy = (c) FE = FBX = FBy =
You want to get from a point A on the straight shore of the beach to a buoy which is 56 meters out in the water from a point B on the shore. B is 70 meters from you down the shore. If you can swim at a speed of 5 meters per second and run at a speed of 7 meters per second, at what point along the shore, x meters from B, should you stop running and start swimming if you want to reach the buoy in the least time possible? Find a formula for the time spent in terms of x T(x) = Find the value for x that will minimize the total time spent running and swimming. x =
Below is a velocity (meters second) versus time (seconds) graph for two bikers. Compare the velocity of Bike 1 (solid line) at t = 3 seconds and t = 8 seconds. At which moment is Bike 1 moving more slowly? When is Bike 1 moving the slowest? How can you tell? Compute the average rate of change for the velocity of Bike 1 from t = 3 to t = 8. Include units. Show how you get your answer. Estimate the instantaneous rate of change for the velocity for Bike 1 at t = 8. Explain.
Sphere A is traveling with velocity vA = 10 ft/sec as shown, when it collides with sphere B which is initially at rest. If mA = 3 mB, θ = 30∘, and the coefficient of restitution is 0.3, determine the speeds of the spheres immediately after impact. (20 points)
Only two forces act on an object (mass = 2.42 kg), as in the drawing. Find (a) the magnitude and (b) the direction (relative to the x axis) of the acceleration of the object.
You have two capacitors, one with capacitance 10.7×10−6 F and the other of unknown capacitance. You connect the two capacitors in series with a voltage of 361 V applied across the capacitor pair. You discover that, as a result, the unknown capacitor has a charge of 0.00173 C. Find its capacitance C. C =
The man shown below is pushing on a refrigerator that sits on a level floor. Assume the entire floor, including the portion under the man, is frictionless. The force exerted by the man has a magnitude of 112 N and the refrigerator has a mass of 192 kg. Use Newton's third law along with his second law to find the acceleration of the man. Assume he has a mass of 69 kg. (The force F→ is pointing in the positive direction. Indicate the direction with the sign of your answer.) m/s2
A spaceship moves past Earth with a speed of 0.908 c. As it is passing, a person on Earth measures the spaceship's length to be 76.7 m. (a) Determine the spaceship's proper length (in m). m (b) Determine the time (in s) required for the spaceship to pass a point on Earth as measured by a person on Earth. s (c) Determine the time (in s) required for the spaceship to pass a point on Earth as measured by an astronaut onboard the spaceship. s
An object is made of glass and has the shape of a cube 0.12 m on a side, according to an observer at rest relative to it. However, an observer moving at high speed parallel to one of the object's edges and knowing that the object's mass is 2.4 kg determines its density to be 9100 kg/m3, which is much greater than the density of glass. What is the moving observer's speed (in units of c) relative to the cube? Number Units
A force of 130 N is used to drag a crate 4 m across a floor. The force is directed at an angle upward from the crate so that the vertical component of the force is 120 N and the horizontal component is 50 N, as shown in the diagram. a. What is the work done by the horizontal component of the force? b. What is the work done by the vertical component of the force? c. What is the total work done by the 130 -N force? E5 Diagram
The figure shows cross-sections through two large, parallel, nonconducting sheets with identical distributions of positive charge with surface charge density σ = 1.13×10−22 C/m2. What is the y component of the electric field at points (a) above the sheets, (b) between them, and (c) below them? (a) Number Units (b) Number Units (c) Number Units
a) Applying the Biot-Savart law and integration calculus determine the magnitude of the magnetic field that is generated by the infinite long current carrying straight wire (number 1) in the figure as a function or distance r measured from it. b) Calculate the force that wire 1 exerts on the AB segment of current carrying wire 2 . Wire 2 is perpendicular to wire 1 . For the solution the result of question a) is have to be used. Draw the force into the figure. Data: I1 = 100[A], I2 = 50[A], a = 0,01[m], b = 0,04[m], μ = μ0 = 4π⋅10−7[Vs Am].
Two metal spheres, each of radius 3.1 cm, have a center-to-center separation of 2.4 m. Sphere 1 has a charge of +1.4×10−8 C; sphere 2 has a charge of −3.7×10−8 C. Assume that the separation is large enough for us to assume that the charge on each sphere is uniformly distributed (the spheres do not affect each other). With V = 0 at infinity, calculate in volts (a) the potential at the point halfway between their centers and the potential on the surface of (b) sphere 1 and (c) sphere 2. (a) Number Units (b) Number Units (c) Number Units
In the figure the electric field lines on the left have twice the separation as those on the right. (a) If the magnitude of the field at A is 32 N/C, what is the magnitude of the force on a proton at A? (b) What is the magnitude of the field at B ? (a) Number Units (b) Number Units
Two vectors are given by a→ = 2.3 i^ + 1.4→j^ and b→ = 5.5 i^ + 4.3 j^. Find (a) |a→×b→|, (b) a→⋅b→, (c) (a→ + b→)⋅b→, and (d) the component of a→ along the direction of b→. (a) Number Units (b) Number Units (c) Number Units (d) Number Units
A tube is open only at one end. A certain harmonic produced by the tube has a frequency of 630 Hz. The next higher harmonic has a frequency of 881 Hz. The speed of sound in air is 343 m/s. (a) What is the integer n that describes the harmonic whose frequency is 630 Hz? (b) What is the length of the tube? (a) Number Units (b) Number Units
What beat frequencies (in Hz ) will be present in the following situations? (a) if the musical notes B and C are played together (frequencies of 249 and 264 Hz) Hz (b) if the musical notes D and F are played together (frequencies of 297 and 352 Hz) Hz (c) if all four are played together (Enter your answers as a comma-separated list.) Hz
A lab technician builds a parallel-plate capacitor with adjustable spacing between the plates. When the plates are at their initial separation, the capacitance is 4.00 μF. (a) At this capacitance, the capacitor is connected to a 12.00 V battery. After fully charging, how much energy (in μJ) is stored in the capacitor? μJ (b) The battery is then disconnected. Without discharging the capacitor, the lab technician then doubles the separation between the plates. At this point, how much energy (in μJ) is stored in the capacitor? μJ (c) Without changing this new separation between the plates, the capacitor is discharged, and then reconnected to the 12.00 V battery. Now, after fully charging, how much energy (in μJ) is stored in the capacitor? μJ
Three blocks are in contact with one another on a frictionless, horizontal surface as in the figure below. A horizontal force F→ is applied to m1, where m1 = 1.90 kg, m2 = 3.73 kg, m3 = 4.92 kg, and F = 20.0 N. (Take the +x-direction to be to the right. Due to the nature of this problem, do not use rounded intermediate values in your calculations-including answers submitted in WebAssign.) (a) Find the acceleration of the blocks. (Enter your answer in m/s2. Indicate the direction with the sign of your answer.) m/s2 (b) Find the net force on each block. (Enter your answers in N. Indicate the direction with the signs of your answers.) F1,net = N F2,net = NnF3,net = N (c) Find the magnitudes of the contact forces between the blocks (in N). P12 = N P23 = N
The figure shows cross-sections through two large, parallel, nonconducting sheets with identical distributions of positive charge with surface charge density σ = 1.78×10−22 C/m2. What is the y component of the electric field at points (a) above the sheets, (b) between them, and (c) below them? (a) Number Units (b) Number Units (c) Number Units
In the figure, block 1 with mass m1 starts from rest at height h = 2.00 m on a frictionless ramp and then slides down and has an elastic collision with block 2 with mass m2. The masses are related by m1 = 2.00 m2. What is the speed (m/s) of block 2 just after the collision? 0.45 14.7 5.63 1.23 5.44 9.39 4.01 2.34 8.35 11.2
In the figure below, block 1 of mass m1 slides from rest along a frictionless ramp from height h = 2.20 m and then collides with stationary block 2, which has mass m2 = 2.00m1. After the collision, block 2 slides into a region where the coefficient of kinetic friction μk is 0.600 and comes to a stop in distance d within that region. (a) What is the value of distance d if the collision is elastic? m (b) What is the value of distance d if the collision is completely inelastic? m
A 30.0−g metal ball having net charge Q = 5.10 μC is thrown out of a window horizontally north at a speed v = 21.4 m/s. The window is at a height h = 19.8 m above the ground. A uniform, horizontal magnetic field of magnitude B = 0.0100 T is perpendicular to the plane of the ball's trajectory and directed toward the west. (a) Assuming the ball follows the same trajectory as it would in the absence of the magnetic fleld, find the magnetic force acting on the ball just before it hits the ground. (Let the +x-direction be toward the north, the +y-direction be up and the +z-direction be east.) F→B = N (b) Based on the result of part (a), is it justified for three-significant-digit precision to assume the trajectory is unaffected by the magnetic field? Yes No Explain. This answer has not been graded yet.
Because Earth's rotation is gradually slowing, the length of each day increases: The day at the end of 1.0 century is 1.0 ms longer than the day at the start of the century. In 85 centuries, what is the total of the daily increases in time (that is, the sum of the gain on the first day, the gain on the second day, etc.)? Number Units
Find the mass m of the counterweight needed to balance a truck with mass M = 1680 kg truck on an incline of θ = 45∘. Assume both pulleys are frictionless and massless. kg
A box is pulled a distance d across the floor by a force F that makes an angle θ with the horizontal, as shown in the figure. If the magnitude of the force and the distance are kept constant, but the angle θ is increased toward 90∘, then the work done by the force in dragging the box increases decreases stays the same not possible to say
The corner of a rectangular piece of wood is attached to a rod that is free to rotate as shown. The length of the longer side of the rectangle is 6.0 m, which is three times the length of the shorter side. Three equal forces are applied to two of the corners and the midpoint of the shorter side with magnitudes of 20 N as shown below. What is the magnitude of the net torque and direction of rotation on the block, if any? 80 Nm, clockwise 60 Nm, counterclockwise 60 Nm, clockwise 0 Nm, no rotation
A 2.72-μF and a 4.08- μF capacitor are connected in series across a 35.0-V battery. A 9.47-μF capacitor is then connected in parallel across the 2.72−μF capacitor. Determine the voltage across the 9.47−μF capacitor. Number Units
The block weighs 20 lb. It collides with the wall at a speed of 30 ft/s. If the coefficient of restitution is 0.6, what is the speed of the block immediately after impact? Note that conservation of linear momentum is not useful because the wall is immovable, which means it is part of the earth and has infinite mass.
A car moves clockwise around a circular path with radius 61.1 m. The car started from rest at the point farthest to the west on the path, and has a constant tangential acceleration of 2.50 m/s2. At this point, what is the radial acceleration component of the car? m/s2 Required information
A string is attached between two rigids walls that are positioned L = 2.00 meters apart. The string is set into motion so that it exhibits the standing wave pattern shown in the figure. The frequency of oscillation of the string in this standing wave mode is 5.0 Hz. Calculate the wave speed for waves on this string. 8.00 m/s 16.0 m/s 2.00 m/s 4.00 m/s 1.00 m/s
A mass m0 is attached to a spring and hung vertically. The mass is raised a short distance in the vertical direction and released. The mass oscillates with a frequency f0. If the mass is replaced with a mass 16 times as large, and the experiment was repeated, what would be the frequency of the oscillations in terms of f0 ? f0/4 16f0 4f0 f0/32 f0/16
In the figure particles 2 and 4 , of charge −e, are fixed in place on a y axis, at y2 = −11.5 cm and y4 = 5.75 cm. Particles 1 and 3 , of charge −e, can be moved along the x axis. Particle 5 , of charge +e, is fixed at the origin. Initially particle 1 is at x1 = −11.5 cm and particle 3 is at x3 = 11.5 cm. (a) To what x value must particle 1 be moved to rotate the direction of the net electric force F→ net on particle 5 by 30∘ counterclockwise? (b) With particle 1 fixed at its new position, to what x value must you move particle 3 to rotate back to its original direction?
In part (a) of the figure an electron is shot directly away from a uniformly charged plastic sheet, at speed vs = 2.80×105 m/s. The sheet is nonconducting, flat, and very large. Part (b) of the figure gives the electron's vertical velocity component v versus time t until the return to the launch point. What is the sheet's surface charge density? Assume ts = 14.0 ps. (a) (b) Number Units
The figure shows a closed Gaussian surface in the shape of a cube of edge length 2.50 m. It lies in a region where the electric field is given by E→ = (4.70x + 3.05)i^ + 6.45 j^ + 6.50 k^ N/C, with x in meters. What is the net charge contained by the cube? Number Units
An infinite, nonconducting sheet has a surface charge density σ = +8.58 pC/m2. (a) How much work is done by the electric field due to the sheet if a particle of charge q0 = 9.61×10−19 C is moved from the sheet to a point P at distance d = 4.49 cm from the sheet? (b) If the electric potential V is defined to be zero on the sheet, what is V at P ? (a) Number Units (b) Number Units
In the rectangle of the figure the sides have lengths 6.02 cm and 17.0 cm, q1 = −4.54 μC, and q2 = +1.68 μC. With V = 0 at infinity, what is the electric potential at (a) corner A and (b) corner B? (c) How much work is required to move a charge q3 = +3.42 μC from B to A along a diagonal of the rectangle? (d) Does this work increase or decrease the electric potential energy of the three-charge system? Is more, less, or the same work required if q3 is moved along a path that is (e) inside the rectangle but not on a diagonal and (f) outside the rectangle? (a) (b) Units (c) Units (d) (e) (f)
Zero, a hypothetical planet, has a mass of 4.0×1023 kg, a radius of 3.2×106 m, and no atmosphere. A 10 kg space probe is to be launched vertically from its surface. (a) If the probe is launched with an initial kinetic energy of 5.0×107 J, what will be its kinetic energy when it is 4.0×106 m from the center of Zero? (b) If the probe is to achieve a maximum distance of 8.0×106 m from the center of Zero, with what initial kinetic energy must it be launched from the surface of Zero? (a) Number: Units: (b) Number: Units:
Two Earth satellites, A and B, each of mass m, are to be launched into circular orbits about Earth's center. Satellite A is to orbit at an altitude of 6070 km. Satellite B is to orbit at an altitude of 19600 km. The radius of Earth RE is 6370 km. (a) What is the ratio of the potential energy of satellite B to that of satellite A, in orbit? (b) What is the ratio of the kinetic energy of satellite B to that of satellite A, in orbit? (c) Which satellite (answer A or B) has the greater total energy if each has a mass of 27.4 kg? (d) By how much? (a) Number Units (b) Number Units (c) (d) Number Units
A bowler holds a bowling ball with mass M = 7.2 kg in the palm of his hand. Lower arm has mass m = 1.6 kg. As the figure shows, his upper arm is vertical and his lower arm is horizontal. What is the magnitude of (a) the force of the biceps muscle on the lower arm and (b) the force between the bony structures at the elbow contact point?
A 116-kg crate is being pushed across a horizontal floor by a force P that makes an angle of 19.1∘ below the horizontal. The coefficient of kinetic friction is 0.240. What should be the magnitude of P, so that the net work done by it and the kinetic frictional force is zero? Number Units
The large block shown is x = 18.0 cm wide, y = 19.0 cm long, and z = 27.00 cm high with a mass of 2.55 kg. This block is passing through air (density of air ρair = 1.43 kg/m3). See the hint panel for the drag force equation. Calculate the terminal velocity vT of the block if it is traveling downward with a drag coefficient of Γ = 0.882. vT =m/s
A small mass is placed on the conical surface at the radius of 55 mm. If the angular velocity of the cone about its axis is gradually increased, determine the maximum angular velocity for which the small mass will not slip. The coefficient of static friction is 0.8996 and θ = 16∘. Answer:
During a transcranial magnetic stimulation (TMS) treatment, a magnetic field, typically of magnitude 5.00 T, is produced in the brain using external coils. During the treatment, the current in the coils (and hence the magnetic field in the brain) rises from zero to its peak in about 75.0 μs. Assume that the magnetic field is uniform over a circular area of diameter 2.00×10−2 m inside the brain. What is the magnitude |E| of the average induced emf around this region of the brain during the treatment? |E| = V
A coil of 15 turns and radius 10.0 cm surrounds a long solenoid of radius 2.10 cm and 1.00×103 turns/meter (see figure below). The current in the solenoid changes as I = 6.00 sin(120t), where I is in amperes and t is in seconds. Find the induced emf (in volts) in the 15-turn coil as a function of time. (Do not include units in your answer.) ε =
For the circuit shown below, what are the following? (a) the total impedance (in Ω) Ω (b) the phase angle between the current and the emf (in rad) rad (c) Write an expression for i(t). (Use the following as necessary: t. Assume i(t) is in amps and t is in seconds. Do not include units in your answer.) i(t) =
An ac generator has emf ε = εmsin(ωdt − π/4), where εm = 28.7 V and ωd = 432 rad/s. The current produced in a connected circuit is i(t) = I sin(ωdt − 3π/4), where I = 483 mA. At what time after t = 0 does (a) the generator emf first reach a 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 (c) (d) Number Units
i) Figure shows a system consisting of a pulley, 2 blocks and a spring where block A with a 5 kg mass slides on a horizontal smooth surface. If it is known that the spring constant, k = 150 N/m and the force developed by the spring is 70 N when the 25 kg block B is released, determine the velocity of block B after it falls 1.5 m by using the Principle of Work and Energy. Include relevant free body diagram in your solution. ii) Suggest the new velocity of block B if the coefficient of kinetic friction between block A and the horizontal surface is μk = 0.5.
In the setup above, the 8.1 kg cart is released from rest, allowing the 3.4 kg hanging mass to accelerate both objects. If there is a frictional force of 23 N acting on the cart, at what rate will the two objects accelerate, in m/s2?
The athlete released the shotput ball at a speed of v = 8 m/s; the release angle θ = 40 deg; the release height h = 1.7 m. What is the horizontal range of the shotput ball (d)? The unit of the answer is meter. We need to input the single value. Do not include units.
In the figure the ideal battery has emf ε = 37 V, the resistances are R1 = 46 kΩ and R2 = 35 kΩ, and the capacitor is uncharged. When the switch is closed at time t = 0, what is the current in (a) resistance 1 and (b) resistance 2? (c) A long time later, what is the current in resistance 2? (a) Number 1 Units (b) Number 2 Units (c) Number 3 Units
In the figure the ideal batteries have emfs ε1 = 19.9 V, ε2 = 9.45 V, and ε3 = 5.40 V, and the resistances are each 2.30 Ω. What are the (a) size and (b) direction (left or right) of current i1? (c) Does battery 1 supply or absorb energy, and (d) what is its power? (e) Does battery 2 supply or absorb energy, and (f) what is its power? (g) Does battery 3 supply or absorb energy, and (h) what is its power? (a) Number Units (b) (c) (d) Number Units (e) (f) Number Units (g) (h) Number Units
In the figure the ideal batteries have emfs E1 = 9.0 V and E2 = 0.500E1, and the resistances are each 3.38 Ω. What is the value of current in (a) resistor 2 and (b) resistor 3? (a) Number Units (b) Number Units
In the figure the current in resistance 6 is i6 = 1.45 A and the resistances are R1 = R2 = R3 = 2.22 Ω, R4 = 17.5 Ω, R5 = 7.71 Ω, and R6 = 3.90 Ω What is the emf of the ideal battery? Number Units
In the figure R1 = 94.0 Ω, R2 = R3 = 55.0 Ω, R4 = 104 Ω, and the ideal battery has emf ε = 6.00 V. (a) What is the equivalent resistance? What is i in (b) resistance 1, (c) resistance 2 , (d) resistance 3 , and (e) resistance 4? (a) Number Units (b) Number Units (c) Number Units (d) Number Units (e) Number Units
How much work is done by the boy pulling his sister 30.0 m in a wagon as shown below? Assume no friction acts on the wagon. Assume units of Joules and 3 significant digits. Do NOT use scientific notation. The boy does work on the system of the wagon and the child when he pulls them as shown.
Three charged particles of q1 = 10.0 nC, q2 = −10.0 nC, and q3 = 5.0 nC are placed on the y-axis, as shown in the figure. Charge q1 has the coordinates (0, 12.0 cm), q2 has the coordinates (0, −12.0 cm), and q3 is located at the origin. (a) Find the electric potential energy (in J) of the configuration of the three fixed charges. J (b) A fourth particle, with a mass of 2.10×10−13 kg and a charge of q4 = 20.0 nC, is released from rest at the point (9.00 cm, 0). Find its speed (in m/s) after it has moved freely to a very large distance away. m/s
A boat is pulled onto shore using two ropes, as shown in the diagram. If a force of 255 N is needed, find the magnitude of force in each rope.
How much work is done by the boy pulling his sister 33 m in a wagon as shown in the figure below? Assume no friction acts on the wagon. (Assume d = 33 m and F = 43 N.) J
In the figure the ideal battery has emf ε = 30.6 V, and the resistances are R1 = R2 = 47 Ω, R3 = R4 = R5 = 6.0 Ω, R6 = 2.5 Ω, and R7 = 1.9 Ω. What are currents (a) i2, (b) i4, (c) i1, (d) i3, and (e) i5? (a) Number Units (b) Number Units (c) Number Units (d) Number Units (e) Number Units
In the figure the ideal battery has emf ε = 36 V, the resistances are R1 = 25 kΩ and R2 = 18 kΩ, and the capacitor is uncharged. When the switch is closed at time t = 0, what is the current in (a) resistance 1 and (b) resistance 2? (c) A long time later, what is the current in resistance 2? (a) Number Units (b) Number Units (c) Number Units
In the circuit shown, assume the battery emf is 17.3 V, R = 1.00 MΩ, and C = 2.20 μF. The switch is closed at t = 0. If the capacitor is initially discharged, then at what time t will the voltage across the capacitor be 15.0 V? s
XYZ Moving Company has a new tool that consists of a heavy-duty ramp that connects the truck to the apartment buildings, so customers can slide their items directly into the truck without using the elevator or stairs. If friction is ignored, the time t (in seconds) required for an item to slide down the ramp is given by the function: t(θ) = 2a gsinθcosθ Where a is the distance from the building to the truck and g ≈ 32 feet per second per second is the acceleration due to gravity. How long would it take an object to slide from the balcony of an apartment to the truck if the distance between the building and the truck is a = 10 feet when:
What are (a) the speed and (b) the period of a 420 kg satellite in an approximately circular orbit 590 km above the surface of Earth? Suppose the satellite loses mechanical energy at the average rate of 1.5×105 J per orbital revolution. Adopting the reasonable approximation that the satellite's orbit becomes a "circle of slowly diminishing radius, ' determine the satellite's (c) altitude, (d) speed, and (e) period at the end of its 1331 th revolution. (f) What is the magnitude of the average retarding force on the satellite? Is angular momentum around Earth's center conserved for (g) the satellite and (h) the satellite-Earth system (assuming that system is isolated)?