Find the charge q(t) on the capacitor and the current i(t) in the given LRC-series circuit. L = 1 h, R = 100 Ω, C = 0.0004 f, E(t) = 20 V, q(0) = 0 C, i(0) = 5 A q(t) = A i(t) = C Find the maximum charge on the capacitor. (Round your answer to four decimal places.) C
A capacitor of capacitance C1 = 7.71 mF is connected in parallel with a capacitor of capacitance C2 = 3.18 mF, and a potential difference of 124 V is applied across the pair. (a) Calculate the equivalent capacitance. What are (b) charge q1 and (c) potential difference V1 on capacitor 1 and (d) q2 and (e) V2 on capacitor 2? (a) Number Units (b) Number Units (c) Number Units (d) Number Units (e) Number Units
While moving in, a new homeowner is pushing a box across the floor at a constant velocity. The coefficient of kinetic friction between the box and the floor is 0.413. The pushing force is directed downward at an angle θ below the horizontal. When θ is greater than a certain value, it is not possible to move the box, no matter how large the pushing force is. Find that value of θ. Number Units
A hockey puck of mass 0.170 kg is approaching a hockey player at a speed of 14.0 m/s, moving in the negative x-direction as shown in the figure. The hockey player hits it back in the positive x-direction at a speed of 21.0 m/s. If the hockey stick is in contact with the hockey puck for 0.00150 s, what average force (in N) did the hockey player exert on the hockey puck? (Indicate the direction with the sign of your answer.) After (i) What average force (in N) did the hockey puck exert on the hockey player? (Indicate the direction with the sign of your answer.) N What impulse (in N⋅s) did the hockey player exert on the hockey puck? (Indicate the direction with the sign of your answer.) N⋅s What impulse (in N⋅s) did the hockey puck exert on the hockey player? (Indicate the direction with the sign of your answer.) N⋅s
A 64.0-kg person, standing on a diving board, dives straight down into the water. Just before striking the water, her speed is 5.85 m/s. At a time of 1.80 s after entering the water, her speed is reduced to 2.24 m/s. What is the magnitude of the average net force that acts on her when she is in the water?
Three identical point charges, each of mass m = 0.200 kg, hang from three strings, as shown in the figure below. If the lengths of the left and right strings are each L = 26.0 cm, and if the angle θ is 45∘, determine the value of q. C
Copper and aluminum are being considered for a high-voltage transmission line that must carry a current of 77.3 A. The resistance per unit length is to be 0.122 Ω/km. The densities of copper and aluminum are 8960 and 2600 kg/m3, respectively. Compute (a) the magnitude J of the current density and (b) the mass per unit length λ for a copper cable and (c) J and (d) λ for an aluminum cable. (a) Number Units (b) Number Units (c) Number Units (d) Number Units
Copper and aluminum are being considered for a high-voltage transmission line that must carry a current of 76.5 A. The resistance per unit length is to be 0.155 Ω/km. The densities of copper and aluminum are 8960 and 2600 kg/m3, respectively. Compute (a) the magnitude J of the current density and (b) the mass per unit length λ for a copper cable and (c) J and (d) λ for an aluminum cable. (a) Number Units (b) Number Units (c) Number Units (d) Number Units
In the figure a 23 V battery is connected across capacitors of capacitances C1 = C6 = 3.5 μF and C3 = C5 = 1.5C2 = 1.5C4 = 5.0 μF. What are (a) the equivalent capacitance Ceq of the capacitors and (b) the charge stored by Ceq? What are (c) V1 and (d) q1 of capacitor 1, (e) V2 and (f) q2 of capacitor 2, and (g)V3 and (h)q3 of capacitor 3? (a) Number (b) Number (c) Number Units (d) Number Units (e) Number Units (f) Number Units (g) Number Units (h) Number Units
In the figure, point P2 is at perpendicular distance R = 23.0 cm from one end of straight wire of length L = 12.4 cm carrying current i = 0.785 A. (Note that the wire is not long.) What is the magnitude of the magnetic field at P2? Number Units
A loaded ore car has a mass of 950 kg and rolls on rails with negligible friction. It starts from rest and is pulled up a mine shaft by a cable connected to a winch. The shaft is inclined at 35.5∘ above the horizontal. The car accelerates uniformly to a speed of 2.25 m/s in 11.5 s and then continues at constant speed. (a) What power must the winch motor provide when the car is moving at constant speed? kW (b) What maximum power must the motor provide? kW (c) What total energy transfers out of the motor by work by the time the car moves off the end of the track, which is of length 1,250 m? J
Two point charges, Q1 = 3.0 μC and Q2 = −1.5 μC, are placed on the x axis. Suppose that Q2 is placed at the origin, and Q1 is placed at the coordinate x1 = −5.0 cm (Figure 1). Figure 1 of 1 Part A At what point(s) along the x axis is the electric field zero? Determine the x-coordinate(s) of the point(s). Express your answer using two significant figures. If there is more than one answer, enter your answers in ascending order separated by commas. xE = cm Submit Previous Answers Request Answer Part B At what point(s) along the x axis is the potential zero? Determine the x-coordinate(s) of the point(s). Express your answer using two significant figures. If there is more than one answer, enter your answers in ascending order separated by commas. xV = cm
In the figure, two long straight wires are perpendicular to the page and separated by distance d1 = 0.75 cm. Wire 1 carries 5.4 A into the page. What are the (a) magnitude and (b) direction (into or out of the page) of the current in wire 2 if the net magnetic field due to the two currents is zero at point P located a distance d2 = 1.50 cm from wire 2? (a) Number Units (b)
A person has far points of 6.4 m from the right eye and 9.1 m from the left eye. Write a prescription for the refractive power of (a) right and (b) left corrective contact lenses. (a) Number Units (b) Number Units
In 0.904 s, a 9.96-kg block is pulled through a distance of 4.48 m on a frictionless horizontal surface, starting from rest. The block has a constant acceleration and is pulled by means of a horizontal spring that is attached to the block. The spring constant of the spring is 430 N/m. By how much does the spring stretch? Number Units
Flying Circus of Physics The maximum depth dmax that a diver can snorkel is set by the density of the water and the fact that human lungs can function against a maximum pressure difference (between inside and outside the chest cavity) of 0.050 atm. What is the difference in dmax for fresh water and the water of the DeadSea (the saltiest natural water in the world, with a density of 1.37×103 kg/m3)? Number Units
A 0.200−kg object is attached to a spring that has a force constant of 55.0 N/m. The object is pulled 6.00 cm to the right of equilibrium and released from rest to slide on a horizontal, frictionless table. Calculate the maximum speed vmax of the object. vmax = m/s Find the location x of the object relative to equilibrium when it has one-third of the maximum speed, is moving to the right, and is speeding up. x =
A block with mass M slides down a ramp and goes around a frictionless loop as shown. It's initial height above the bottom of the loop is Δh = 4R and the block starts at rest. (Please note the diagram below is not drawn to scale.) What will the magnitude of the normal force the track exerts on the block at position 2 be? 2Mg 4Mg Mg 3Mg Zero
Two dimensions. In the figure, three point particles are fixed in place in an xy plane. Particle A has mass mA = 4 g, particle B has mass 2.00mA, and particle C has mass 3.00mA. A fourth particle D, with mass 4.00mA, is to be placed near the other three particles. At what (a) x coordinate and (b) y coordinate should particle D be placed so that the net gravitational force on particle A from particles B, C, and D is zero (d = 21 cm)? (a) Number Units (b) Number Units
The 2.00 kg block in the figure is tied to the wall with a massless rope. It sits on top of the 4.00 kg block. The lower block is pulled to the right with a force of 45.0 N. The tension in the lower rope is 45.0 N) The upper block (2 kg) remains stationary throughout. The coefficient of kinetic friction at both the upper and lower surfaces of the 4.00 kg block is 0.400(μK = . 400). What is the tension in the rope holding the 2.0 kg block? What is the acceleration of the 4.0 kg block? (you will be graded on the correctness of your fbds) Put your FBDs here
Consider 1.1 kg of austenite containing 1.0 wt%C, cooled to below 727∘C (1341∘F). Using the iron-iron carbide phase diagram, Animated Figure 9.24, determine the following: (a) How many kilograms of total ferrite form kg (b) How many kilograms of total cementite form kg (c) How many kilograms of pearlite form kg (d) How many kilograms of the proeutectoid phase form kg
At a snow tubing hill, a tow rope is used to pull riders parallel to the slope up the hill at a constant speed. The slope of the hill is 7.4 degrees above horizontal. The distance along the slope is 65.0 m and the coefficient of kinetic friction between the tube and snow is 0.25. Click to reload image What is the net work done by all forces on the 52.0 kg tube and rider between the 10.0 m mark and the 50.0 m mark in the trip? -4300 J +2700 J -1100 J +7600 J 0 J
A thin stick of mass 0.2 kg and length L = 0.5 m is attached to the rim of a metal disk of mass M = 2.0 kg and radius R = 0.3 m. The stick is free to rotate around a horizontal axis through its other end (see the following figure). (a) If the combination is released with the stick horizontal, what is the speed of the center of the disk when the stick is vertical? (b) What is the acceleration of the center of the disk at the instant the stick is released? (c) At the instant the stick passes through the vertical? (a) (b)
In the figure a 56 kg rock climber is in a lie-back climb along a fissure, with hands pulling on one side of the fissure and feet pressed against the opposite side. The fissure has width w = 0.10 m, and the center of mass of the climber is a horizontal distance d = 0.40 m from the fissure. The coefficient of static friction between hands and rock is μ1 = 0.40, and between boots and rock it is μ2 = 1.30. The climber adjusts the vertical distance h between hands and feet until the (identical) pull by the hands and push by the feet is the least that keeps him from slipping down the fissure. (He is on the verge of sliding.) (a) What is the least horizontal pull by the hands and push by the feet that will keep the climber stable? (b) What is the value of h? (a) Number Units (b) Number Units
Two snowy peaks are at heights H = 860 m and h = 610 m above the valley between them. A ski run extends between the peaks, with a total length of 3.93 km and an average slope of θ = 22∘ (see the figure). (a) A skier starts from rest at the top of the higher peak. At what speed will he arrive at the top of the lower peak if he coasts without using ski poles? Ignore friction. (b) Approximately what coefficient of kinetic friction between snow and skis would make him stop just at the top of the lower peak?
A block of mass m = 30 kg is being pulled with forces F1 = 122 N and F2 = 103 N that are in opposite directions as shown in the figure below. If the block does not move in the presence of these forces, what is the magnitude of the static force of friction acting on the block? Express your answer in units of N using zero decimal places. You can take g = 9.80 m/s2 if necessary.
A 21 kg bear slides, from rest, 7.7 m down a lodgepole pine tree, moving with a speed of 5.1 m/s just before hitting the ground. (a) What change occurs in the gravitational potential energy of the bear-Earth system during the slide? (b) What is the kinetic energy of the bear just before hitting the ground? (c) What is the average frictional force that acts on the sliding bear?
A 3.7-kg object moving to the right with a speed of 4.5 m/s makes a head-on, elastic collision with a 0.8-kg object that is initially at rest. What is the velocity of the 0.8-kg object after the collision? greater than 4.5 m/s less than 4.5 m/s equal to 4.5 m/s zero impossible to say based on the information provided
According to Equation 20.7, an ac voltage V is given as a function of time t by V = Vosin2πft, where Vo is the peak voltage and f is the frequency (in hertz). For a frequency of 48.4 Hz, what is the smallest value of the time at which the voltage equals one-half of the peak-value?
A diver of weight 420 N stands at the end of a diving board of length L = 3.7 m and negligible mass (see the figure below). The board is fixed to two pedestals separated by distance d = 1.4 m. Take the upward direction to be positive. Of the forces acting on the board, what are (a) the force from the left pedestal and (b) the force from the right pedestal? (a) Number Units (b) Number Units
In the figure, light initially in material 1 refracts into material 2, crosses that material, and is then incident at the critical angle on the interface between materials 2 and 3. The indices of refraction are n1 = 1.58, n2 = 1.38, n3 = 1.20. (a) What is angle θ? (b) If θ is increased, is there refraction of light into material 3? (a) Number Units (b)
The circuit in the figure consists of switch S, a 4.70 V ideal battery, a 50.0 MΩ resistor, and an airfilled capacitor. The capacitor has parallel circular plates of radius 4.80 cm, separated by 3.50 mm. At time t = 0, switch S is closed to begin charging the capacitor. The electric field between the plates is uniform. At t = 240 μs, what is the magnitude of the magnetic field within the capacitor, at radial distance 2.90 cm?
In the figure, a 4.5 kg block is accelerated from rest by a compressed spring of spring constant 640 N/m. The block leaves the spring at the spring's relaxed length and then travels over a horizontal floor with a coefficient of kinetic friction μk = 0.263. The frictional force stops the block in distance D = 8.0 m. What are (a) the increase in the thermal energy of the blockfloor system, (b) the maximum kinetic energy of the block, and (c) the original compression distance of the spring?
At the instant of the figure, a 9.80 kg particle P has a position vector r→ of magnitude 6.10 m and angle θ1 = 47.0∘ and a velocity vector v→ of magnitude 4.80 m/s and angle θ2 = 33.0∘. Force F→, of magnitude 1.20 N and angle θ3 = 33.0∘ acts on P. All three vectors lie in the xy plane. About the origin, what are the magnitude of (a) the angular momentum of the particle and (b) the torque acting on the particle? (a) Number Units (b) Number Units
When a resistor is connected across the terminals of an ac generator (114 V) that has a fixed frequency, there is a current of 0.343 A in the resistor. When an inductor is connected across the terminals of the same generator, there is a current of 0.420 A in the inductor. When both the resistor and the inductor are connected in series between the terminals of this generator, what is (a) the impedance of the series combination and (b) the phase angle between the current and the voltage of the generator? Note: The ac current and voltage are rms values and power is an average value unless indicated otherwise. Circuit 1 Circuit 2 Circuit 3 (a) Number Units (b) Number Units
In the figure, a real inverted image I of an object O is formed by a certain lens (not shown); the object-image separation d = 40.0 cm, measured along the central axis of the lens. The image is exactly half the size of the object. (a) What kind of lens must be used to produce this image? (b) How far from the object must the lens be placed? (c) What is the focal length of the lens?
In the figure below, a 70 kg rock climber is in a lie-back climb along a fissure, with hands pulling on one side of the fissure and feet pressed against the opposite side. The fissure has width w = 0.20 m, and the center of mass of the climber is a horizontal distance d = 0.40 m from the fissure. The coefficient of static friction between hands and rock is μ1 = 0.60, and between boots and rock it is μ2 = 1.7. (a) What is the least horizontal pull by the hands and push by the feet that will keep the climber stable? N (b) For the horizontal pull of (a), what must be the vertical distance h between hands and feet? m (c) If the climber encounters wet rock, so that μ1 and μ2 are reduced, what happens to the answers to (a) and (b)? (Select all that apply.) The force in part (a) increases. The force in part (a) decreases. The force in part (a) doesn't change. h increases. h decreases. h does not change.
In the figure, a real inverted image I of an object O is formed by a certain lens (not shown); the object-image separation is d = 58.2 cm, measured along the central axis of the lens. The image is just 1/4 the size of the object. (a) What kind of lens must be used to produce this image? (b) How far from the object must the lens be placed? (c) What is the focal length of the lens? (a) (b) Number Units (c) Number Units
In the figure a 51 kg rock climber is in a lie-back climb along a fissure, with hands pulling on one side of the fissure and feet pressed against the opposite side. The fissure has width w = 0.20 m, and the center of mass of the climber is a horizontal distance d = 0.25 m from the fissure. The coefficient of static friction between hands and rock is μ1 = 0.40, and between boots and rock it is μ2 = 1.20. The climber adjusts the vertical distance h between hands and feet until the (identical) pull by the hands and push by the feet is the least that keeps him from slipping down the fissure. (He is on the verge of sliding.) (a) What is the least horizontal pull by the hands and push by the feet that will keep the climber stable? (b) What is the value of h? (a) Number Units N (b) Number Units
The spring shown in (Figure 1) is compressed 52 cm and used to launch a 100 kg physics student. The track is frictionless until it starts up the incline. The student's coefficient of kinetic friction on the 30∘ incline is 0.12. For help with math skills, you may want to review: Mathematical Expressions Involving Squares For general problem-solving tips and strategies for this topic, you may want to view a Video Tutor Solution of Car rolling down a hill. Figure 1 of 1 k = 80,000 N/m 10 m 30∘ Part A What is the student's speed just after losing contact with the spring? Express your answer with the appropriate units. v = Part B How far up the incline does the student go? Express your answer with the appropriate units. Δs = Value
Consider the 12 kg object located at position (1) in the figure, which is at height h measured relative to position (3) at ground level. If the gravitational potential energy of the object at position (1) is EP1 = 588 J, determine: a) The vertical distance h between positions (1) and (3). b) The potential energy EP2 of the object at position (2), located halfway between positions (1) and (3).
A person slaps her leg with her hand, which results in her hand coming to rest in a time interval of 2.25 ms from an initial speed of 2.75 m/s. The total mass of the hand and the forearm is 1.55 kg. What is the magnitude Favg of the average contact force exerted on the leg? Favg = N Would the contact force on the same hand be any different if the woman clapped her hands together, each with an initial speed of 2.75 m/s, if they come to rest in the same time interval of 2.25 ms? no, because the change in momentum for the first hand will be the same It depends on the coeffcient of friction between the two hands. yes, because the initial momentum of the system will be different due to the second hand yes, because the change in momentum is different no, because the second hand has zero momentum
A person is pulling a large stationary mass of M = 30 kg on a flat surface as shown. Between the floor and M, the static coefficient of friction is μMs = 0.7 and the kinetic coefficient of friction is μMk = 0.3. A smaller stationary mass m = 10 kg is sitting on the top of the large mass; it is secured to the wall by a steel cable as shown. The coefficient of static friction between the surfaces of m and M is μms = 0.6 and coefficient of kinetic friction is μmk = 0.2. If the mass system just about to slip, compute the magnitude of the force F1 that the person must apply. Draw a free body diagram to support your argument, and make sure that your calculation is clear and transparent.
The 2225-N block shown in Fig. P-1 is in contact with 45∘ incline. The coefficient of static friction is 0.25. Compute the value of the horizontal force P necessary to (a) just start the block up the incline or (b) just prevent motion down the incline. (c) If P = 1780 N, what is the amount and direction of the friction force?