Shown in the figure below is a capacitor. Each plate has an area of A = 2.71e−02 m2 and has a gap d = 1e−03 meters. At the first moment, the capacitor is empty. At the second moment it is partly filled with a dielectric of constant K = 4.84. The dielectric layer leaves a free area of A1 = 1.084e−02 m2 and covers the filled area A2 = 1.626e−02 m2. Partly Filled Capacitor Write the FORMULA for the capacitance of the empty capacitor. Determine the capacitance of the empty capacitor Cempty = Farads When you partly fill the capacitor, which of these best describes the new configuration: Both series and parallel Parallel Series Neither series nor parallel Determine the formula for the partly filled capacitor Cfilled = Determine the value of the partly filled capacitor Cfilled = Farads
Shown in the figure below is a capacitor. Each plate has an area of A = 1.75 e−02 m2 and has a gap d = 1 e−03 meters. At the first moment, the capacitor is empty. At the second moment is it partly filled with a dielectric of constant K = 2.88. The thickness of the dielectric layer is a = 3e−04 meters leaving a free space of b = 7e−04 meters. Write the FORMULA for the capacitance of the empty capacitor. Determine the capacitance of the empty capacitor Cempty = Farads When you partly fill the capacitor, which of these best describes the new configuration: Both series and parallel Neither series nor parallel Series Parallel Determine the formula for the partly filled capacitor Cfilled = Determine the value of the partly filled capacitor Cfilled = Farads
In an RLC circuit such as that of the figure assume that R = 3.76 Ω, L = 78.7 mH, fd = 86.3 Hz, and εm = 24.8 V. For what values of the capacitance would the average rate at which energy is dissipated in the resistance be (a) a maximum and (b) a minimum? What are (c) the maximum dissipation rate and the corresponding (d) phase angle and (e) power factor? What are (f) the minimum dissipation rate and the corresponding (g) phase angle and (h) power factor? (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 below shows a cross section of a long cylindrical conductor of radius a = 4.22 cm containing a long cylindrical hole of radius b = 1.55 cm. The central axes of the cylinder and hole are parallel and are distance d = 2.01 cm apart; current i = 5.56 A is uniformly distributed over the tinted area. (a) What is the magnitude of the magnetic field at the center of the hole? (b) What is the magnitude if b = 0? (c) What is the magnitude if d = 0? (a) Number Units (b) Number Units (c) Number Units
A concave mirror has a focal length of 22.7 cm. The distance between an object and its image is 39.1 cm. Find (a) the object and (b) image distances, assuming that the object lies beyond the center of curvature and ( c ) the object and (d) image distances, assuming that the object lies between the focal point and the mirror. (a) Number Units (b) Number Units (c) Number Units (d) Number Units
The far point of a nearsighted person is 5.9 m from her eyes, and she wears contacts that enable her to see distant objects clearly. A tree is 18.7 m away and 2.2 m high. (a) When she looks through the contacts at the tree, what is its image distance? (b) How high is the image formed by the contacts? (a) Number Units
Two charges Q1 = 3,4 μC and Q2 = 2,9 μC are placed on the two corners of a rectangle with the sides a = 6,6 mm and b = 11,2 mm as shown in the figure below. How much work is required to bring a thir charge Q3 = 8,3 μC from infinity to point P that is a distance c = 6,7 mm away from Q1? Please take k = 9.0×109 N.m2 /C2 and express your answer using one decimal place in units of J or N.m.
An empty capacitor has a capacitance of 5.57 μF and is connected to a 12−V battery. A dielectric material (K = 4.5) is inserted between the plates of this capacitor. What is the magnitude of the surface charge on the dielectric that is adjacent to either plate of the capacitor? (Hint: The surface charge is equal to the difference in charge on the plates with and without the dielectric.) Number Units
In the figure a current i = 24 A is set up in a long hairpin conductor formed by bending a wire into a semicircle of radius R = 8.3 mm. Point b is midway between the straight sections and so distant from the semicircle that each straight section can be approximated as being an infinite wire. What are the (a) magnitude and (b) direction (into or out of the page) of B→ at a and the (c) magnitude and (d) direction of B→ at b? (a) Number Units (b) (c) Number Units (d)
Four identical capacitors are connected with a resistor in two different ways. When they are connected as in part a of the drawing, the time constant to charge up this circuit is 0.42 s. What is the time constant when they are connected with the same resistor as in part b? (a) (b) Number Units
The figure shows a cross section across a long cylindrical conductor of radius a = 1.78 cm carrying uniform current 62.4 A. What is the magnitude of the current's magnetic field at radial distance (a) 0, (b) 1.33 cm, (c) 1.78 cm (wire's surface), (d) 2.71 cm? (a) Number Units (b) Number Units (c) Number Units (d) Number Units
What is the capacitance of a parallel plate capacitor that contains three materials with different dielectric constants, K1, K2, and K3, distributed as shown in the figure? a. εoA4 d[K2+2 K1 K3 K1+K3] b. 4 εoAd[K2+K1 K3 K1+K3] c. O εoAd[K32+K1 K2 K1+K2] d. εoAd[K3+K1 K24 K1+2 K2] e. εoAd[K1+K2 K3 K2+K3]
A proton moving in the plane of the page has a kinetic energy of 5.92 MeV. It enters a magnetic field of magnitude B = 1.15 T directed into the page, moving at an angle of θ = 45.0 deg with the straight linear boundary of the field, as shown in the figure below. Calculate the distance x from the point of entry to where the proton leaves the field. Determine the angle between the boundary and the proton's velocity vector as it leaves the field.
The figure shows the circuit of a flashing lamp, like those attached to barrels at highway construction sites. The fluorescent lamp L (of negligible capacitance) is connected in parallel across the capacitor C of an RC circuit. There is a current through the lamp only when the potential difference across it reaches the breakdown voltage VL; then the capacitor discharges completely through the lamp and the lamp flashes briefly. For a lamp with breakdown voltage VL = 62.7 V, wired to a 98.7 V ideal battery and a 0.185 mF capacitor, what resistance R is needed for 2 flashes per second? Number Units
In a discussion person A is talking 1.9 dB louder than person B, and person C is talking 4.0 dB louder than person A. What is the ratio of the sound intensity of person C to the sound intensity of person B? Number Units
A mass-spring system consists of a m = 1.76 kg block connected to a spring of spring constant, k = 283 N/m and resting on a frictionless surface. The spring not stretched with the block resting at its equilibrium position. At t = 0 s, the block is instantaneously smacked from the left so that it moves to the right at a distance A = 0.240 m from its equilibrium position before rebounding. Determine an expression for the kinetic energy of the spring as a function of v.
(a) A mass M1 = 20 kg is suspended by a light string from the ceiling of a lift of mass M2 = 400 kg. i) If the lift accelerates upwards at 1.5 m/s2, what is the tension in the lift cable and in the string? [3 marks] ii) If the string breaks when subjected to a tension of more than 600 N , what is the greatest possible tension in the lift cable so that the string remains intact? [3 marks] (b) [6 marks] A force F = 45 N acts upon a block of mass M1 = 30 kg , that pushes a second block of mass M2 = 10 kg, that pushes a third block of mass M3 = 5 kg (see figure). The whole system moves along a straight line in absence of gravity or friction. Evaluate the acceleration of the whole system and the contact forces F1/2, F2/1 between the blocks 1 and 2 and F2/3, F3/2 between the blocks 2 and 3.
Consider a truck that has a weight of 18000 N , performing a full stop from a speed of 100 km/h on a grade with an angle of 5∘ as shown in the figure. It has a brake application that develops a steady brake force of 8000 N . The truck has a frontal area of 8 m2 and a drag coefficient of 0.5 . Determine the following: 1- The deceleration. 2- The stopping distance. 3- The time required to reach a full stop. 4- The energy dissipated. 5- The brake power at initial application. 6- The average brake power over the stop.
A ladder is leaning against a vertical wall, and both ends of the ladder are at the point of slipping. The coefficient of static friction between the ladder and the horizontal surface is μ1 = 0.135 and the coefficient of friction between the ladder and the wall is μ2 = 0.103. Determine the maximum angle α with the vertical that the ladder can make without falling on the ground. α =
Two blocks are being pulled over a rough table as in the figure below. . There is a coefficient of kinetic friction of 0.4 between the blocks and the table. What is the magnitude of the tension T in the string connecting the blocks if the force F = 50 N? 43.8 N 25 N 13.6 N 22.7 N 35.7 N
The 18−kg block A slides on the surface for which μk = 0.3. The block has a velocity v = 11 m/s when it is s = 3 m from the 11−kg block B. The unstretched spring has a stiffness k = 1000 N/m. Take e = 0.6. The coefficient of friction is the same for both blocks. (Figure 1). Figure 1 of 1 Part A Determine the maximum compression of the spring due to the collision. Express your answer to three significant figures and include the appropriate units. xmax = Value Units
Suppose the arrow in the image below represents some force vector F→. If the magnitude is 7.6 Newtons and the angle the vector makes with the horizontal or "x" axis is 30 degrees, what is the vertical or "y" component of this vector? Do not include units in your answer (enter a numerical result only). Note: The angle is not drawn to scale in this image. Round your answer to the tenths place.