A mball = 0.5 kg cannonball and is shot with an initial velocity of vA at an angle θ1. The cannonball bounces off the ground at point B. The coefficient of restitution between the ball and ground is e = 0.15. Ignore air resistance. Hint: Assume the ground is so large that it will not move. Values for the figure are given in the following table. Note the figure may not be to scale. Variable Value vA60 msd13 mθ124 degrees For all velocities, include negatives for direction if appropriate. a. Determine the y-component of the velocity of the cannonball right before it hits the ground, (VBy)1 b. Determine the y-component of the velocity of the cannonball right after it hits the ground, (VBy)2. c. Determine the max height the cannonball reaches after it hits the ground, h. Round your final answers to 3 significant digits/figures. (VBy)1 = m s (VBy)2 = m s h = m
A 15.0-kg block rests on a horizontal table and is attached to one end of a massless, horizontal spring. By pulling horizontally on the other end of the spring, someone causes the block to accelerate uniformly and reach a speed of 5.00 m/s in 0.500 s. In the process, the spring is stretched by 0.200 m. The block is then pulled at a constant speed of 5.00 m/s, during which time the spring is stretched by only 0.0500 m. Find (a) the spring constant of the spring and (b) the coefficient of kinetic friction between the block and the table.
When a 0.0622−kg golf ball takes off after being hit, its speed is 44.2 m/s. (a) How much work is done on the ball by the club? (b) Assume that the force of the golf club acts parallel to the motion of the ball and that the club is in contact with the ball for a distance of 0.0177 m. Ignore the weight of the ball and determine the average force applied to the ball by the club. (a) Number Units (b) Number Units
Question 1: The 8−kg ball is connected with a spring as shown. Initially the spring is compressed by 0.2 m. Then under the applied force F, the spring is stretched to 0.6 m. Determine the total work done to the ball during this process. The slope is smooth.
What is the work done by the force F in the figure shown where the particle moves from position s1 to S2? Fs -FS 0 16.3
Consider the motion of two pendula of equal lengths b and equal masses m connected by a spring of force constant k under gravitational force. The spring is unstretched in the equilibrium position. A. (5) Use θ1 and θ2 as the generalized coordinates, write down the kinetic energy T and the potential energy U. B. (5) Express the Lagrangian using the small oscillation assumption (sinθ ≈ θ and cosθ ≈ 1−θ2/2 ) C. (7) Find the tensor (matrix) V and T, and write down the secular equation. D. (8) Determine the eigen-frequencies from the secular equation. E. (10) Find the tensor (matrix) A which transforms T into the unit matrix 1 and V into a diagonal matrix. F. (15) Find normal mode of this motion and describe the motion.
Consider a motion of a mass m attached to a spring of force constant k that is fixed at the end of a vertical pole. The spring rotates about the vertical pole with an angular velocity of ω and the gravitational acceleration is g. A. (10) Construct Lagrangian using spherical coordinate (r, θ, φ) and express the Lagrange's equation of motion. B. (15) Find the solution of the Lagrange's equation of motion when the system is at equilibrium. C. (25) When the system oscillates near the equilibrium, find the normal modes and the eigen frequencies.
Scenario 3: Box begins to tip. Now, consider the case where the force P causes the box to begin tip. In general, the box will tip if (select one): I. The normal force, N, required for equilibrium is not located directly under the weight force, W II. b. The applied force, P, is greater than the static friction force, F, resisting it III. c. The normal force, N, required for equilibrium is not located under the box Considering all the previous calculations we can determine whether the box will move. The box will (select one): I. Not move II. Tip over III. Slide along the floor
2-22. Determine the magnitude and direction of the resultant force, measured counterclockwise from the positive x axis. Solve l by first finding the resultant F′ = F2 + F3 and then forming FR = F′ + F1. Probs. 2-21/22
Practice problems for forces and motion Refer to the figure below. Let the mass of the block be 9.3 kg and the angle θ be 60∘. (a) In the figure above, draw a coordinate system that takes advantage of the symmetry of the problem (i. e., choose suitable x and y axes). (b) Draw the following vectors in the figure above: The force of gravity acting on the block (with x and y components)The normal force acting on the block The tension in the cord (c) Find the tension in the cord. (d) Find the normal force acting on the block. (e) If the cord is cut, find the magnitude of the resulting acceleration of the block.
The force P is applied to the 53−kg block when it is at rest. Determine the magnitude and direction of the friction force exerted by the surface on the block if (a) P = 0, (b) P = 164 N, and (c) P = 261 N. (d) What value of P is required to initiate motion up the incline? The static and kinetic coefficients of friction between the block and the incline are μ5 = 0.19 and μk = 0.13, respectively. The friction force is positive if up the incline, negative if down the incline. Answers: (a) F = N (b) F = N (c) F = N (d) P = N
The helicopter view in the figure shows two people pulling on a stubborn mule. The person on the right pulls with a force F→1 of magnitude 109 N and direction of θ1 = 55.0∘. The person on the left pulls with a force F→2 of magnitude 99.9 N and direction of θ2 = 63.0∘. (i) (a) Find the single force that is equivalent to the two forces shown. The forces are measured in units of newtons (symbolized N ). N i^ + N j^ (b) Find the force that a third person would have to exert on the mule to make the resultant force equal to zero. N i^ + N j^
In the figure below, a crate of mass m = 170 kg is pushed at constant speed up the frictionless ramp(θ = 25.0∘) by a horizontal force F→. (a) What is the magnitude of F→? (b) What is the force on the crate from the ramp?
For the mass-spring system subjected to the harmonic force shown, if the maximum amplitude of the total response is 0.75 m, find the spring constant k. Set mass = 1 kg. (10 pts) a) 25.0 N/m b) 17.0 N/m c) 32.5 N/m d) 12.0 N/m
(a) In a minor rail yard accident, a runaway goods truck of mass 1.85×104 kg collides at u = 20.0 ms−1 with a stationary truck of mass 2.20×104 kg, as shown in Figure 3. The trucks lock together and travel at the same speed after the collision. Assume friction is negligible. Figure 3 Sketch of the runaway and stationary goods trucks, for use in Question 10. (i) Show that the speed of the trucks after the collision is 9.14 ms−1. (ii) One of the truck wheels can be modelled as a solid disk of radius 4.60×10−1 m and moment of inertia 36.5 kgm2. Calculate the magnitude of the wheel's angular momentum after the collision. (iii) The truck's linear velocity vector is in the positive x-direction using the Cartesian coordinate system shown in Figure 3. What is the direction of the wheel's angular momentum vector? Briefly explain your reasoning. (b) The train driver sounds the train's whistle. The whistle is a pipe that is open at one end and closed at the other, and it has a length of 0.480 m. The speed of sound in air is 343 ms−1. (i) Sketch the standing wave pattern of the air pressure in the whistle for its fundamental resonant frequency. Clearly indicate the open and closed ends of the whistle pipe. (ii) Hence calculate the frequency of the sound made by the whistle's fundamental resonance. (c) An observer standing on a bridge above the train track hears the whistle as the train approaches at a speed of 40.0 ms−1. (i) Show that the whistle frequency perceived by the observer is 13.2% greater than the frequency perceived by the driver. (ii) Describe how the sound of the whistle, as heard by the observer, will change as the train approaches and goes past the bridge.
You are excited that the weather is finally warm enough to throw a barbecue. You and your friends buy the biggest pack of hot dogs the world has ever seen and you carry it home in the grocery bag. It's so heavy that you end up dragging it along the ground. Your bag has a mass of 12.3 kg and the coefficient of kinetic friction between your bag and the ground is μk = 0.21. It's time to catch up to your friends, so you take off, still dragging the bag. You pull on the bag with a force of 51 N at an angle of 45 degrees above the horizontal. What is the magnitude of the Normal force acting on the bag? N = N What is the magnitude of the kinetic friction force acting on the bag? fk = N What is the net acceleration of the bag? a = ms2
The weight in the following diagram has a mass of 0.750 kg and the cart has a mass of 0.52 kg. There is a friction force of 2.1 N acting on the cart. What is the tension in the string? 4.2 N 4.1 N 4.4 N 4.3 N
A mom is pulling her son and daughter who are sitting in two sleds that are connected by a rope. The mass of the girl and sled 1 is 54 kg, the mass of the boy and sled 2 is 61 kg. The mom is pulling so that the sleds move at a constant velocity. If the coefficient of kinetic friction between the sleds and the ice is 0.24 , what is the tension in the string between them? 140 N 150 N 160 N 170 N
(a) Two forces, F1 and F2, are acting on an object as shown below. i. Write F1 and F2 in terms of the unit vectors i and j ii. Find the resultant force, R_, on the object in terms of i and j. (R = F1 + F2) iii. Determine the magnitude of R. iv. In what direction will the object initially start moving? v. Assume that the magnitude of F1 can be changed. Determine what the magnitude of F1 should be so that the object moves straight ahead. (Assume that straight ahead is in the direction of i).
A uniform disc with a mass of 2 kg and radius R = 0.5 m, rolls without slipping down an incline AB as shown in the figure below. Calculate the linear acceleration, reaction force and friction force. If the incline is pin jointed at A and constrained without friction at B determine the horizontal reaction at A (Statics Revision).
The three freight cars are rolling along the horizontal track with the velocities shown. After the impacts occur, the three cars become coupled together and move with a common velocity ν. The weights of the loaded cars A, B, and C are 130,000, 100,000, and 150,000 lb, respectively. Determine v and calculate the percentage loss n of energy of the system due to coupling.
A 15 kg uniform disk A with a radius of 0.4 m is rotating without friction about its center at 10 rad/s. Then another disk B is dropped onto the first disk. The second disk has a mass of 15 kg and radius of 0.3 m. The second disk is initially not rotating. There is friction between the disks. What is the angular speed of both disks when they stop slipping relative to each other? STATE 1 STATE 2
The disk and rod in the figure below are spinning around axis OA at a rate of ωs = 200 rad/s and have a steady precession rate of ωp = 3 rad/s. If the spinning rate is doubled (ωs = 400 rad/s), what will be the new steady precession rate?
Water is poured into a container that has a leak. The mass m of the water is given as a function of time t by m = 4.70t 0.800 − 2.90t + 20.0, with t ≥ 0, m in grams, and t in seconds. (a) At what time is the water mass greatest, and (b) what is that greatest mass? What is the rate of mass change at (c) t = 2.00 s and (d) t = 5.50 s? (a) Number: Unit: (b) Number: Unit: (c) Number: Unit: (d) Number: Unit:
12-83. The flight path of the helicopter as it takes off from A is defined by the parametric equations x = (2t2) m and y = (0.04t3) m, where t is the time in seconds. Determine the distance the helicopter is from point A and the magnitudes of its velocity and acceleration when t = 10 s.
The 19.8-cm-diameter disk can rotate on an axle through its center. What is the net torque about the axle? (a = 3.8 cm, θ = 47∘, F1 = 16 N, F2 = 92 N, F3 = 32 N, F4 = 25 N.)
The uniform rectangular block shown is moving along a friction-less surface with a velocity v1 when it strikes a small obstruction at B. Assuming that the impact between corner A and obstruction B is perfectly plastic, determine: (a) The angular velocity of the block immediately after it impacts the B, in terms of v1. (b) If the maximum angle (θ) the block rotates to is 30∘, find v1.
A rectangular loop of side lengths a = 10 cm and b = 30 cm lying in the xy-plane carries a current I = 5 A as shown in the figure. The uniform magnetic field in the medium is given as B = 2x^ + 3z^ a) The force on the loop tries to the loop. b) The torque on the loop is T = along the direction.
The figure shows a rectangular, 30 -turn coil of wire, of dimensions 10 cm by 4.1 cm. It carries a current of 0.10 A and is hinged along one long side. It is mounted in the xy plane, at an angle of 30∘ to the direction of a uniform magnetic field of magnitude 0.43 T. Find the (a) x, (b) y, and (c) z components of the torque acting on the coil about the hinge line. (a) Number Units (b) Number Units (c) Number Units
A disk is placed at the top of a ramp. When released, the disk rolls down the ramp. Point P is allowed to freely slide along a rail that ranges from the center of the disk to the edge. Find the acceleration of Point P with respect to a fixed frame using two methods: Taking the derivative of the position vector with respect to a fixed frame, A Using the magic formula. Assume the distance from the center of the disk to point P is R and the distance from the center of the disk to the origin is L.
The figure gives the torque I that acts on an initially stationary disk that can rotate about its center like a merry-go-round. What is the angular momentum of the disk about the rotation axis at times (a) t = 7.0 s and (b) t = 20 s?
A rectangular coil consists of N = 120 closely wrapped turns and has dimensions a = 0.400 m and b = 0.300 m. The coil is hinged along the y axis, and its plane makes an angle θ = 30.0∘ with the x axis (figure). (a) What is the magnitude of the torque exerted on the coil by a uniform magnetic field B = 0.500 T directed in the positive x direction when the current is I = 1.20 A in the direction shown? N⋅m (b) If you are looking downward from the positive y direction, what is the expected direction of rotation of the coil? clockwise counterclockwise
Two couples act on a rectangle with a base of 7 m and a height of 4 m. Determine the magnitude and direction of the resultant moment, knowing that F = 80 N and G = 25 N.
A solid sphere with a mass of M = 1.00 kilogram and a radius of R = 6 centimeters starts at rest and rolls down a ramp that is 1.00 meter long and makes a 30∘ angle with the horizontal. The ramp connects with a horizontal track where a second, identical ball is located 1.00 meter away from the junction of the two sections. The two spheres collide. The rotational inertia for a solid sphere is I = 25 MR2. Show complete work for all answers. Assume that friction is negligible. a. Determine the time that elapses between the release of the sphere at the top of the ramp and the collision between the two spheres. b. Determine the angular momentum (both magnitude and direction) of the sphere when it has reached the bottom of the ramp. c. Calculate the linear velocity of the center of mass of the system consisting of both spheres after the collision.
A steel rod whose cross-sectional moment of inertia is I is bent into the shape shown, and fixed at point A. If a vertical force P is applied at point C, what is the horizontal deflection at D? A. 2Pr3 3El B. Pr3 3EI C. Pr3 4El D. Pr3 2EI E. None of the above
A solid disk rolls at an initial linear velocity of 2.40 m/s until it eventually stops, as shown in the diagram below: a. (4 Points) Draw the angular velocity vector (ω→) and the angular acceleration vector (α→) for that motion. b. (4 Points) Based on that information, draw the rigid free-body diagram. c. (9 Points) If the disk has a mass of 1.20 kg and a radius of 0.15 meters, and the coefficient of friction is μ = 0.65, how far does the disk travel from its starting position, in meters? (Note: Idisk = 12 MR2)
On mountainous downhill roads, escape routes are sometimes placed to the side of the road for trucks whose brakes might fail. Figure 1 of 1 Part A Assuming a constant upward slope of 27∘, calculate the horizontal component of the acceleration of a truck that slowed from 85 km/h to rest in 8.0 s as shown in the figure. (Figure 1) Express your answer to two significant figures and include the appropriate units. Submit Request Answer Part B Calculate the vertical component of the acceleration of a truck. Express your answer to two significant figures and include the appropriate units. Submit Request Answer
A fireworks rocket is moving at a speed of 56.820441163779 m/s. The rocket suddenly breaks into two pieces of equal mass, which fly off with velocities v1 and v2, as shown in the drawing. What is the magnitude of (a) v1 and (b) v2? (a) Number Units (b) Number Units
A rocket is tracked by radar from its launching point A. When it is 10 seconds into its flight, the following radar measurements are recorded: r = 2450 m, r˙ = 412 m/s, r¨ = 3.60 m/s2, θ = 25∘, θ˙ = 0.0540 rad/s, θ¨ = −0.0281 rad/s2. For this instant determine the angle β between the horizontal and the direction of the trajectory of the rocket and find the magnitudes of its velocity v and acceleration a. Answers: β = v = m/s a = m/s2
An object with mass 2 kg is suspended from two points on the ceiling 15 cm apart by two strings of length 8 cm and 10 cm. Find the tension in the string labeled t1. (4 marks)
A 83.0−kg person is being pulled away from a burning building as shown in the figure below. (a) Calculate the tension in the first rope, T1, if the person is momentarily motionless. (Enter the magnitude only.) N (b) Calculate the tension in the second rope, T2, if the person is momentarily motionless. (Enter the magnitude only.) N
A rocket runs out of fuel in the position shown and continues in unpowered flight above the atmosphere. If its velocity in this position was 630 mi/hr, calculate the maximum additional altitude h acquired and the corresponding time t to reach it. The gravitational acceleration during this phase of its flight is 30.8 ft/sec2. v = 630 mi/hr Answers: h = mi t = sec
Give the following problem a try. If you get stuck, here is one way to work it: Essential Solution Video. The polymer bar shown in the figure below has a width of b = 46 mm, a depth of d = 99 mm, and a height of h = 256 mm. At a compressive load of P = 115 kN, the bar height contracts by Δh = −2.30 mm, and the bar depth elongates by Δd = 0.39 mm. At this load, the stress in the polymer bar is less than its proportional limit. Determine: (a) the modulus of elasticity. (b) Poisson's ratio. (c) the change in the bar width b. (a) E = GPa (b) v = (c) Δb = mm
When a rocket reaches an altitude of 40 m it begins to travel along the parabolic path (y−40)2 = 160 x, where the coordinates are measured in meters. If the component of velocity in the vertical direction is constant at Vy = 180 m/sec, determine the magnitudes of the rocket's velocity and acceleration when it reaches an altitude of 80 m.
A rocket is launched at an angle of θ = 50∘ above the horizontal with an initial speed vi = 75 m/s, as shown below. It moves for 25 s along its initial line of motion with an acceleration of 20.2 m/s2. At this time, its engines fail and the rocket proceeds to move as a free body. (a) What is the rocket's maximum altitude? m (b) What is the rocket's total time of flight? s (c) What is the rocket's horizontal range? m
A firefighter, a distance d from a burning building, directs a stream of water from a fire hose at angle θi above the horizontal as in the figure. If the initial speed of the stream is vi, at what height h does the water strike the building? (Use any variable or symbol stated above along with the following as necessary: g.) h =
0.5 kg of N2 undergoes a two-step process along the processes shown in the figure (1-2) and (2-3), in a closed system. Please answer the following questions. a. Compute the work for this two-step process. b. Determine the change in internal energy for process 1-2. c. Determine the heat transported during process 2-3. d. Next, the owner of the system decides to return from state (3) to state (1) following a straight-line path. On a P-v diagram represent the new three-step process (1-2-3) and determine the total heat transfer and the net direction of transport, in or out.
A 3 kg crate slides down a ramp. The ramp is 1 m in length and inclined at an angle 30∘, as shown in the Figure. The crate starts from rest at the top, experiences a constant frictional force of magnitude 5 N, and continues to move a short distance on the floor after it leaves the ramp. Use energy methods to determine the speed of the crate at the bottom of the ramp.
At t = 0, a 0.30 kg rubber ball (B) moving at 6.0 m/s, θ = 36.87∘ below the horizontal strikes a smooth 1.6 kg cube (C) at rest on a smooth horizontal floor as shown. For the 0.020 seconds it is in contact with block, the normal force the ball exerts on the cube is given by: N(t) = (30720t − 1536000t2)i^ N, with t in seconds. Ignore gravity during the collision, and take cosθ = 4/5, sinθ = 3/5. a) [2] What is the speed the cube (C) after the collision? b) [5] What is the rebound velocity of the ball (B) after the collision? (i.e. speed and angle ϕ in the diagram) c) [3] What is the coefficient of restitution for this collision?
A jogger travels a route that has two parts. The first is a displacement A→ of 2.80 km due south, and the second involves a displacement B→ that points due east. The resultant displacement A→ + B→ has a magnitude of 3.90 km. (a) What is the magnitude of B→, and (b) what is the direction of A→+B→ as a positive angle relative to due south? Suppose that A→ − B→ had a magnitude of 3.90 km. (c) What then would be the magnitude of B→, and (d) what is the direction of A→⋅B→ relative to due south? (a) Number Units (b) Number Units (c) Number Units (d) Number Units
The drawing shows two transverse waves traveling on two strings. The linear density of each string is 0.0879 kg/m, and the tension is provided by a 26.0 -N block that is hanging from the string. Determine the speed of the wave in part (a) and part (b) of the drawing. (a) Number Units (b) Number Units
A crow is flying horizontally with a constant speed of 3.25 m/s when it releases a clam from its beak. The clam lands on the rocky beach 2.25 s later. Consider the moment just before the clam lands. (Neglect air resistance.) (a) What is its horizontal component of velocity? m/s (b) What is its vertical component of velocity? m/s (c) Select all of the following which would apply to your answers for (a) and (b), if the speed of the crow were decreased. The horizontal component would increase. The vertical component would decrease. The horizontal component would decrease. The vertical component would increase. Explain.
A boat is traveling in the water with a speed of 50 miles an hour. There is a current going directly west at a speed of 10 miles an hour. What direction should the boat steer toward so that its course ends up directly north? You can give your answer either as the angle shown or as a velocity vector (x, y).
The 83-kg man dives from the 43−kg canoe. The velocity indicated in the figure is that of the man relative to the canoe just after loss of contact. If the man, woman, and canoe are initially at rest, determine the horizontal component of the absolute velocity of the canoe (positive if to the right, negative if to the left) just after separation. Neglect drag on the canoe, and assume that the 51−kg woman remains motionless relative to the canoe. Answer: vcanoe = m/s
*15-40. The boy B jumps off the canoe at A with a velocity 5 m/s relative to the canoe as shown. If he lands in the second canoe C, determine the final speed of both canoes after the motion. Each canoe has a mass of 40 kg. The boy's mass is 30 kg, and the girl D has a mass of 25 kg. Both canoes are originally at rest.
A network of capacitors with various capacitance values is shown in Fig. 2 below. a. Calculate the equivalent capacitance of this network. b. A potential difference, Vab = 10 V, is applied between the points a and b in the network. Calculate the potential difference ("voltage drop") across each capacitor in the network. C2 = 3 μF C1 = 2 μF C3 = 3 μF Fig. 2
Question 3: The capacitors in the figure are initially uncharged and are connected, as in the diagram, with switch S open. The applied potential difference is Vab = +80 V. a) What is the charge on each capacitor? b) What is the total energy stored in this configuration of four capacitors? c) What is the charge on each capacitor after switch S is closed? d) What is the total energy now stored in this configuration of four capacitors?
The plates of a spherical capacitor have radii 54.6 mm and 59.5 mm. (a) Calculate the capacitance. (b) What must be the plate area of a parallel-plate capacitor with the same plate separation and capacitance? (a) Number Units (b) Number Units
The plates of a spherical capacitor have radii 55.0 mm and 59.3 mm. (a) Calculate the capacitance. (b) What must be the plate area of a parallel-plate capacitor with the same plate separation and capacitance? (a) Number Units (b) Number Units
In the figure a 25 V battery is connected across capacitors of capacitances C1 = C6 = 4.0 μF and C3 = C5 = 1.5 C2 = 1.5 C4 = 4.0 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 Units (b) Number Units (c) Number Units (d) Number Units (e) Number Units (f) Number Units (g) Number Units (h) Number Units
The figure shows capacitor 1 (C1 = 6.42 μF), capacitor 2 (C2 = 4.36 μF), and capacitor 3 (C3 = 7.58 μF) connected to a 13.5 V battery. When switch S is closed so as to connect uncharged capacitor 4 (C4 = 7.79 μF), (a) how much charge passes through point P from the battery and (b) how much charge shows up on capacitor 4? (a) Number Units (b) Number Units
In the figure the battery potential difference V is 15.0 V and each of the seven capacitors has capacitance 11.0 μF. What is the charge on (a) capacitor 1 and (b) capacitor 2? (a) Number Units (b) Number Units
Consider the capacitor network shown and the following statements: C1 = C3 = 6.00 μF and C2 = C4 = 4.00 μF. What is the charge on each capacitor? What is the total energy stored in the circuit? What is the energy stored in C3?
An initially uncharged parallel plate capacitor is connected to a circuit containing a battery with emf ε = 24 V and a resistor, R = 4.7 MΩ as shown in the figure to below. The capacitor whose plates have an area of A = 2.8 mm2 are separated by a distance of d = 4 mm and one third of the capacitor is filled with a dielectric material, κ1 = 2.3 and the rest (two thirds) is filled with another dielectric material, κ2 = 7.9. At t = 0 the switch is closed. 7.4 seconds after the switch is closed the electric field within the first dielectric material (κ1) is observed to be 15×106 N/C. Find the charge on the capacitor at this instant (t = 7.4 s) in terms of permittivity of free space ϵ0 ? Express your answer using zero decimal place.
For the capacitor circuit shown in the figure below: a. What is the equivalent capacitance of this collection of capacitors? b. How much charge does the batter supply when the switch is closed? c. What is the charge on the 10 μF capacitors? d. What is the voltage across the bottom 20 μF capacitor? (2 pts) After the switch is closed for the above capacitor circuit: a. How much energy did the battery supply. b. How much energy is stored in each of the capacitors? c. What is the total energy stored in the capacitors?
For the system of capacitors shown in Fig. a potential difference of 25 V is maintained across ab. (a) What is the equivalent capacitance of this system between a and b? (b) How much charge is stored by this system? (c) How much charge does the 6.5 nF capacitor store? (d) What is the potential difference across the 7.5−nF capacitor?
Determine the equivalent capacitance between A and B for the group of capacitors in the figure shown. (b) If points A and B are connected to the terminals of a 10 V battery, what is the voltage across the 5.0 μF capacitor? Hint: start at the right and the equivalent capacitor of the 24 μF, 12 μF, and 8.0 μF capacitors which are in series. Then redraw the diagram. Continue from there. Finally, when the circuit is completely reduced, use q = CeqV to find the charge q on the equivalent capacitor. All capacitors in series have the same charge and they also have the charge as the equivalent capacitor.
Potential difference in a capacitor A capacitor consists of two large metal disks placed a distance s apart (see the figure). The radius R of each disk is 5.6 m, the gap s between the disks is 1.2 mm, and the thickness t of each disk is 0.5 mm. The disk on the left has a net charge of 3.6×10−4 C and the disk on the right has a net charge of −3.6×10−4 C. Calculate the potential difference V2 − V1, where location 1 is inside the left disk at its center, and location 2 is in the center of the air gap between the disks. Use ε0 = 8.85×10−12 C2/(N⋅m2). V2 − V1 = V