A conductor consists of a circular loop of radius R = 20 cm and two straight, long sections as shown in figure. The wire lies in the plane of the paper and carries a current of i = 7.0 A. The magnitude of the magnetic field at the centre of the loop is: 1.93×10^−5 T 5.8×10^−5 T none of these 2.9×10^−5 T 2.5×10^−5 T
A uniform rectangular block is attached to a cart that is accelerating up a 20∘ incline at 3 m/s2. The block is attached to a cart by a hinge at Point A and a roller at Point B. a. What is the force that the roller is applying to the block at Point B? b. What is the force that the hinge is applying to the block at Point A?
A small block of mass m = 0.500 kg is fired with an initial speed of v0 = 4.30 m/s along a horizontal section of frictionless track, as shown in the top portion of the figure below. The block then moves along the frictionless, semicircular, vertical tracks of radius R = 1.45 m. (a) Determine the force exerted by the track on the block at points (A) and (B). track force at (A) N track force at (B) N (b) The bottom of the track consists of a section (L = 0.411 m) with friction. Determine the coefficient of kinetic friction between the block and that portion of the bottom track if the block just makes it to point C on the first trip. Hint: If the block just makes it to point (C), the force of contact exerted by the track on the block at that point is zero.
A magnetic field directed into the page changes with time according to B = 0.0250 t2 + 1.40, where B is in teslas and t is in seconds. The field has a circular cross section of radius R = 2.50 cm (see figure below). (a) When t = 2.20 s and r2 = 0.0200 m, what is the magnitude of the electric field at point P2? N/C (b) When t = 2.20 s and r2 = 0.0200 m, what is the direction of the electric field at point P2? perpendicular to r2 and counterclockwise into the page perpendicular to r2 and clockwise out of the page
The top of a circular wire, with diameter 1.0 m, is firmly connected to a vertical steel rod. The wire passes through the hole in the center of a precious red ring, initially situated almost at the lowest point (point A ). As the rod spins up slowly about its vertical axis, the ring moves slowly upward along the wire, toward point B, as shown. Find the maximum angular speed, in rotations per second, at which the ring remains in the position where the angle ϕ = 45∘. Assume the coefficient of friction between the ring and the wire is 0.40.
A 0.9-kg block B is connected by a cord to a 1.6−kg block A that is suspended as shown from two springs, each with a constant of k = 180 N/m, and a dashpot with a damping coefficient of c = 60 N⋅s/m. Knowing that the system is at rest when the cord connecting A and B is cut, determine the velocity of block A after 0.1 s. The velocity of block A after 0.1 s is mm/s.
The elastic cord (acts like a spring) has an original length of l = 2 m and a spring constant of 105 N m. The ball has a mass of 2.4 kg. If the ball travels in a circular path: a) What is the angle, θ that the cord makes with the vertical axis if the spring is stretched 0.4 m (noted as d in the drawing)? θ = degrees b) What is the velocity if the spring is stretched 0.4 m? V = m s c) What is the angle, θ that the cord makes with the vertical axis if the spring is stretched 0.28 m θ = degrees d) What is velocity if the spring is stretched 0.28 m? V = m s
Over a region of radius R, there is a spatially uniform magnetic field B. (See below.) At t = 0, B = 1.2 T, after which it decreases at a constant rate to zero in 34 s. the change in the magnetic field with respect to time. Do not substitute numerical values; use variables only. ) E(r) = { r ≤ R r ≥ R (b) Assume that R = 12.0 cm. How much work (in J) is done by the electric field on a proton that is carried once clockwise around a circular path of radius 6.0 cm? (c) How much work (in J) is done by the electric field on a proton that is carried once counterclockwise around a circular path of any radius r ≥ R ? Felec = N Fmag = N
A small circular loop with radius b≪a is to be placed at the origin with its plane lying along one of the three principal planes (i. e., xy, xz, yz planes). Which one of the three planes would maximize the mutual inductance between the wire and the small circular loop? Find the value of the mutual inductance.
A 5-lb block resides on a smooth horizontal surface. The block is attached to an elastic band. The opposite end of the band is attached to a pin at location A. The band has an unstretched length of 3 ft. The block is released from position B from rest. Determine the speed of the block when it reaches location C on the figure.
Below figure shows an arrangement known as a Helmholtz coil. It consists of two circular coaxial coils, each of 600 turns and radius R = 50.0 cm, separated by a distance S = R. The two coils carry equal currents i = 2.5 A in the same direction. Find the magnitude of the net magnetic field at P, midway between the coils.
The figure below illustrates a single wire carrying a current I. The wire is either pointing directly at the point P, or it is bent into a circular arc centered on point P. The angle which the circular arc forms is θ. The entire setup is lying in a plane, and the radius of curvature of the circular part is R. (a) Convince me that the straight portions of the circuit do not contribute to the magnetic field at point P. (b) Determine the magnetic field at P
Consider an infinite wire with current I and a circular loop near the wire. If the current in the wire is constant and the loop is moving in the +x direction. What can we say about the direction of the current inside the loop? Clockwise Counter clockwise Zero The given is not sufficient to determine the
Figure shows a rigid structure consisting of a circular hoop of radius R and mass M, and a square made of four thin bars, each of length R and mass M. The rigid structure rotates at a constant speed about a vertical axis, with a period of rotation of 2 s. Assume R = 0.2 m and M = 3 kg. Which is the closest to the the angular momentum about that axis?
In the figure below, two circular arcs have radii a = 13.6 cm and b = 10.0 cm, subtend angle θ = 74.0∘, carry current i = 0.260 A, and share the same center of curvature P. What is the magnitude and direction of the net magnetic field at P? (Take out of the page to be positive. Indicate the direction with the sign of your answer.) T
In the figure below, a long circular pipe with outside radius R = 1.54 cm carries a (uniformly distributed) current i = 13.8 mA into the page. A wire runs parallel to the pipe at a distance of 3.00 R from center to center. Find the (a) magnitude and (b) direction (into or out of the page) of the current in the wire such that the ratio of the magnitude of the net magnetic field at point P to the magnitude of the net magnetic field at the center of the pipe is 2.43, but it has the opposite direction.
The figure below shows three circular, nonconducting arcs of radius R = 7.20 cm. The charges on the arcs are q1 = 4.36 pC, q2 = −2.00 q1, and q3 = +3.00q1. With V = 0 at infinity, what is the net electric potential of the arcs at the common center of curvature? V
A mass swings from a cord in uniform circular motion as shown in figure 5 . Report answers in Cartesian coordinates. (a) At what angle in degrees (θ) is the mass swinging at, given that it's time period of rotation (T) is 2 s ? (b) What is the magnitude of the tension in the cord? (c) What is the velocity of the mass, located at point P = (x, 0, 0) ? (d) What is the acceleration of the mass at point P = (x, 0, 0) ? (e) What increase in velocity would be necessary for the mass to raise the plane of rotation's height by 0.2 meters? y-axis Figure 5: Mass swinging around a fixed axis, with mass m, cord length R and angle θ.
A circular wire splits current so that 65% of the current is directed along the top of the loop, and 35% of the current is directed along the bottom, as shown in the diagram below. Use the Biot-Savart Law to calculate the magnetic field (magnitude and direction) at the center of the loop if R = 2.0 cm and I = 4.0 A. Enter your solution in microTeslas and define negative to be "into the board" and positive to be "out of the board". Hint: Convince yourself that the straight part of the wires do not contribute to the field at the center. Split the circle into two parts, top and bottom, and use the right hand rule to determine the direction of B at the center due to the top and bottom.
In the Bohr model of hydrogen, the electron moves in a circular orbit around the nucleus. Determine the angular speed of the electron, in revolutions per second, when it is in (a) the ground state and (b) the n = 7 state.
The circuit in the figure consists of switch S, a 5.60 V ideal battery, a 25.0 MΩ resistor, and an airfilled capacitor. The capacitor has parallel circular plates of radius 4.80 cm, separated by 5.00 mm. At time t = 0, switch S is closed to begin charging the capacitor. The electric field between the plates is uniform. At t = 210 μs, what is the magnitude of the magnetic field within the capacitor, at radial distance 2.60 cm? Number Units
The disk of mass 100 [kg] and radius 1.0 [m] is held in equilibrium on the circular surface by a couple M. The coefficient of static friction between the disk and the surface is 0.3 Calculate the largest value M [N−m] without causing the disk to slip.
A 10,000 kg spacecraft is in a circular orbit 400 km above the surface of the Earth. It fires its rockets and quickly doubles its kinetic energy, putting it into an elliptical orbit. What is the semimajor axis (km) of the orbit? The radius of the Earth is 6.37×106 m and its mass is 5.98×1024 kg. 3200 infinity 1.60×103 9.57×103 1600 6.94×103 800 566 7.97×103 7.17×103
Blocks A and B are connected by rope 1 and are pulled at constant speed across a rough surface by rope 2, which is attached to block B, as shown. Compare the magnitude of the tensions in ropes 1 and 2.
A 3.02 kg block is pushed along a horizontal floor by a force F→ of magnitude 34.0 N at a downward angle θ = 40.0∘. The coefficient of kinetic friction between the block and the floor is 0.240 . Calculate the magnitudes of (a) the frictional force on the block from the floor and (b) the block's acceleration. (a) Number Units N (b) Number Units m/s^2
A block released from rest at position A slides with negligible friction down an inclined track, around a vertical loop, and then along a horizontal portion of the track, as shown above. The block never leaves the track. After the block is released, in which of the following sequences of positions is the speed of the block ordered from fastest to slowest?
Block A in figure 3 below has a mass of 4 kg and is on the verge of tipping as it begins to slide due to force P. Determine the coefficient of static friction between the block and the horizontal surface
The uniform solid block in figure below has mass 0.27 kg and edge length a = 3.6 cm, b = 7.4 cm, and c = 2.4 cm. Calculate its rotational inertia about an axis through one corner and perpendicular to the large faces. 4.7e−4 kgm^2
A block of mass m sits at rest on a rough inclined ramp that makes an angle θ with the horizontal. What must be true about force of static friction f on the block? f = mgsinθ f > mg f > mgcosθ f > mgsinθ
Assume the system accelerates with block "A" moving downward. The coefficient of kinetic friction between the blocks and the ramp is 0.15 The tension force between B and C is 120 N. Find the acceleration of the whole system. [4]
A block of mass of 3 kg is being pushed by of force F = 100 N at an angle of θ = 10∘ to the horizontal for a total of t = 5 s. What is the power generated by force F immediately after this time? The crate starts at rest and μk = 0.6. P = W
George and Paula are running around a circular track. George starts at the westernmost point of the track, and Paula starts at the easternmost point. The illustration below shows their starting positions and running directions. They start running toward each other at constant speeds. George runs at 7 feet per second. Paula takes 50 seconds to run a lap of the track. George and Paula pass each other after 12 seconds. After running for 3 minutes, how far east of his starting point is George? (Round your answer to three decimal places.) ft
The figure shows an arrangement known as a Helmholtz coil. It consists of two circular coaxial coils, each of N = 284 turns and radius R = 24.9 cm, separated by a distance s = R. The two coils carry equal currents i = 9.46 mA in the same direction. Find the magnitude of the net magnetic field at P, midway between the coils. Number Units
A glass block is constructed by three parallel layers of different glasses as shown in Figure A3. The refractive indices of the three layers are 1.70, 1.60 and 1.50, respectively. A light ray which travels into the glass block with an incident angle of 32∘ then emits from the bottom surface of the block. Find the refracted angle r of the transmitted ray Figure A3
In the figure below, a wire forms a closed circular loop, with radius R = 5.3 m and resistance 5.7 Ω. The circle is centered on a long straight wire; at time t = 0, the current in the long straight wire is 7.0 A rightward. Thereafter, the current changes according to i = 7.0 A − (2.0 A/s2)t2. (The straight wire is insulated; so there is no electrical contact between it and the wire of the loop. ) What is the magnitude of the current induced in the loop at times t > 0? Number Units
Consider the situations below where a uniform magnetic field B0 is directed into the paper. A semi-circular conductor of diameter L, with current 'I' flowing as shown. Calculate the net magnetic force on this conductor (magnitude and direction) by considering force 'dF' on a small section 'dl' and then integrating.
Consider the circular sign shown in (Figure 1). Figure 1 of 1 Part A Determine the magnitude of the moment developed at the base A of the circular sign due to the wind with the speed U = 10.5 m/s. The air is at 20∘C. Neglect the drag on the pole. Express your answer to three significant figures and include the appropriate units MA = Submit Request Answer
A 532-kg satellite is in a circular orbit about Earth at a height above Earth equal to Earth's mean radius. (a) Find the satellite's orbital speed. m/s (b) Find the time required for one complete revolution. hr
Determine the magnitudes of the angular acceleration and the force on the bearing at O for (a) the narrow ring of mass m = 46 kg and (b) the flat circular disk of mass m = 46 kg immediately after each is released from rest in the vertical plane with OC horizontal. The distance r is 210 mm. Answers: (a) The ring: a = rad/s2, FO = N (b) The disk a = rad/s2, FO = N
The circular disk of radius r = 0.24 m is released very near the horizontal surface with a velocity of its center vO = 0.62 m/s to the right and a clockwise angular velocity ω = 3.2 rad/s. Determine the velocities of points A and P of the disk. Describe the motion upon contact with the ground. Answers: vA = (i + j) m/s vP = (i + j) m/s
The homogeneous circular cylinder of mass m and radius R carries a slender rod of mass 0.58 m attached to it as shown. If the cylinder rolls on the surface without slipping with a velocity vO of its center O, determine the magnitude of the angular momenta HG and HO of the system about its center of mass G and about O for the instant shown. Answers: HG = mvOR HO = mvOR
Two parallel, circular loops carrying a current of 20 A each are arranged as shown in the figure below. The first loop is situated in the x−y plane with its centre at the origin, and the second loop's centre is at z = 4 m. If the two loops have the same radius a = 3 m, determine the magnetic field at: a) z = 0 b) z = 2 m c) z = 4 m (4 Marks) Figure P2. Two rings of current carrying conductors
In the figure below, a horizontal spring is used to launch an object towards an incline. Assume that there is no friction. The spring constant is 40.0 N/m. The object has mass 0.50 kg. The incline is 30.0∘ to the horizontal. The spring is compressed 0.20 m, then the block is released. After leaving the spring, the object travels horizontally a short distance before reaching the incline. (a) Determine the initial speed of the block just before reaching the incline. (b) After travelling 0.10 metres along (parallel to) the incline, what is the speed of the object? (c) Determine the maximum distance along the incline the block travels before it stops and reverses direction.
A block A(mA = 1 kg) slides off a slope from rest. Its speed is 4 m/s when it reaches the bottom. What is the work done by the friction force?
A circular and a rectangular conducting loop are placed on the xy plane as shown. An emf device on the rectangular loop produces a DC current I which is positive in the indicated direction. There is no such emf device on the circular loop. When the rectangular loop is pulled in the direction shown by the red arrows, what will be the direction of the induced current on the circular loop? Select one: Clockwise Counterclockwise There will be no induced current.
The figure below shows two circular regions R1 and R2 with radii r1 = 22.1 cm and r2 = 32.6 cm. In R1 there is a uniform magnetic field of magnitude B1 = 53.1 mT directed into the page, and in R2 there is a uniform magnetic field of magnitude B2 = 77.1 mT directed out of the page (ignore fringing). Both fields are decreasing at the rate of 10.0 mT/s. Calculate ∮E→⋅ds→ for (a) path 1 , (b) path 2 , and (c) path 3. (a) Number Units (b) Number Units (c) Number Units
Consider a conducting circular loop in a uniform magnetic field B0 directed into-the-page, as shown above. The loop's radius increases with time as r(t) = αt while the loop maintains a constant resistance R. a) Use Lenz's law to find the direction of current flow. b) At time t, over a short time interval Δt, find |ΔΦ|. c) Use Faraday's flux rule to find the resulting magnitude and direction of current flow.
A flexible circular loop 10 cm in diameter lies in a magnetic field with magnitude 2.00 T, directed into the plane of the page as shown on the figure below. The loop is pulled at the points indicated by the arrows, forming a loop of zero area in 0.250 s. a) Find the average induced emf in the circuit. b) What is the direction of the current in R : from a to b or from b to a ? Explain your reasoning. c) Does the operator who pulls on the circuit experience some resisting force? If yes, what is its origin (only a qualitative answer is needed)? Hint: To determine the average emf, remember the difference between the instantaneous speed v = dx dt and the average speed vav = Δx Δt. The same works for the emf.
A block (m = 15 kg) is pushed across the floor a distance of 1.5 m. A force of 53 N is applied at a 30∘ angle above the horizontal as shown in the diagram above. How much work (in joules) was done by the person pushing the block? Report your answer as a positive number.
A circular loop of radius 3 cm carrying current 10 A is located in the x−y plane as shown in Figure Q1(a). In addition, an infinitely long wire carrying current 20 A in a direction parallel with the z axis passing through point (4 cm, 5 cm, 0). Determine the magnetic field intensity, H→, at point (0, 0, 7 cm). [6 marks] Figure Q1(a)
Two blocks are supported at rest as shown. Each block weighs 10 N. Block A rests on a frictionless plane inclined 30 degrees above horizontal. Calculate the angle phi the top string makes from the vertical direction.
The coefficient of static friction for both wedge surfaces is 0.41 and that between the 38−kg concrete block and the 24∘ incline is 0.66. Determine the minimum value of the force P required to begin moving the block up the incline. Neglect the weight of the wedge.
Determine the range of applied force P over which the block of mass m2 will not slip on the wedge-shaped block of mass m1 when the inclination of the block is θ, and the coefficient of kinetic and static friction is μk and μs, respectively. Neglect friction associated with the wheels of the tapered block. [25 points]
a) If the pitching wedge used by the golfer gives the ball an initial angle θo = 40∘, determine the range of initial velocities, Vo that will cause the ball to land within 2 m in horizontal distance of the golf hole (Figure 4(a)). [17 Marks] Figure 4(a)
An object of mass 3.06 kg, moving with an initial velocity of 4.90 i^ m/s, collides with and sticks to an object of mass 2.30 kg with an initial velocity of −3.29 j^ m/s. Find the final velocity of the composite object. v→ = ( ı^ + j^) m/s
Four objects are situated along the y axis as follows: a 1.97−kg object is at +3.07 m, a 2.95−kg object is at +2.57 m, a 2.43−kg object is at the origin, and a 3.99−kg object is at −0.504 m. Where is the center of mass of these objects? x = m y = m
A uniform piece of sheet metal is shaped as shown in the figure below. Compute the x and y coordinates of the center of mass of the piece. x = cm y = cm
Determine whether the 15−kg block shown is in static equilibrium under the loadings shown, and report the magnitude of the friction force (in Newton) when P = 770 N and θ = 42 degrees at the state of static equilibrium. The coefficients of static and kinetic friction between the block and the rough inclined surface are shown in the picture. Report the friction force as positive when it is directed downward, and negative when it is directed upwards.
6.12 Two blocks, each having a mass of 100 kg and resting on a horizontal surface, are to be pushed apart using a 30∘ wedge, as shown. The coefficient of static friction for all contact surfaces is 0.25 . Calculate the vertical force P required to start the wedge and the blocks in motion. Problem 6.12
If the pitching wedge the golfer is using gives the ball an angle θ0 = 50∘ of its initial velocity from the horizontal, what range of its initial speed v0 will cause the ball to land within 3 ft of the hole?
A block of mass m is sitting at the top of a curved wedge of mass M and height H. This wedge, in turn, is at rest on a table. All surfaces are frictionless. The block is then given a tiny nudge to the right. With what speed does the block move on the table after it leaves the wedge?
A ball falls straight down onto a wedge that is sitting on frictionless ice. The ball has a mass of 3.30 kg, and the wedge has a mass of 4.70 kg. The ball is moving a speed v = 4.6 m/s when it strikes the wedge, which is initially at rest (see the figure). Assuming that the collision is instantaneous and perfectly elastic, what are the velocities of the ball and the wedge after the collision?
A block of mass m slides on a frictionless wedge that makes an angle of π/4 to the horizontal. The wedge, with mass M, sits on a frictionless horizontal surface and is connected to a fixed point by a horizontal spring with force constant k and unstretched length a. Analyse this system in a similar manner to lectures, to answer the following: (a) Write the Lagranian for this system. (b) Use the Lagrangian to derive equations of motion for the block and the wedge. (c) Show that the wedge undergoes simple harmonic motion, with an angular frequency that can be written ω = k M + m(1 − 1 2)
A 15.2-Ibf block B starts from rest and slides on the 25.5 -lbf wedge A, which is supported by a horizontal surface. Neglecting friction. Determine the velocity of B relative to A after it has slid 3.1 ft down the inclined surface of the wedge. vB/A = i + j (ft/s) Determine the corresponding velocity of A. vA/O = i + j (ft/s)
A block of mass m1 = 1.50 kg and a block of mass m2 = 6.40 kg are connected by a massless string over a pulley in the shape of a solid disk having radius R = 0.250 m and mass M = 10.0 kg. The fixed, wedge-shaped ramp makes an angle of θ = 30.0∘ as shown in the figure. The coefficient of kinetic friction is 0.360 for both blocks. Use g = 9.8 m/s2. (b) Determine the acceleration of the two blocks. (Enter the magnitude of the acceleration.) m/s2 (c) Determine the tensions in the string on both sides of the pulley. left of the pulley N right of the pulley N
The coefficient of static friction for both wedge surfaces is 0.50 and that between the 35−kg concrete block and the 29∘ incline is 0.75. Determine the minimum value of the force P required to begin moving the block up the incline. Neglect the weight of the wedge. Answer: P = N
A wedge of mass m = 40.0 kg is located on a plane that is inclined by an angle θ = 20∘ with respect to the horizontal. A force F = 307.9 N in the horizontal direction pushes on the wedge, as shown in the figure. The coefficient of kinetic friction between the wedge and the plane is 0.159. What is the acceleration of the wedge along the plane? m/s2
A wedge with mass M rests on a frictionless, horizontal table top. A block with mass m is placed on the wedge, as shown in Figure 2. There is no friction between the block and the wedge. The system is released from rest. Figure 2 (a) Calculate the acceleration of the wedge and the horizontal and vertical components of the acceleration of the block. (b) Do your answers to part (a) reduce to the correct results when M is very large? (c) As seen by a stationary observer, what is the shape of the trajectory of the block?
The position of the 68 kg pipe is adjusted by the 18∘ wedge under the action of the force P. If the coefficient of static friction between the pipe and the wedge is 0.23 and that between the wedge and the horizontal surface is 0.19, (a) determine whether slipping will occur between the pipe and the vertical wall (b) determine the force P required to move the wedge Figure Q3
A block of mass m1 = 1.95 kg and a block of mass m2 = 6.10 kg are connected by a massless string over a pulley in the shape of a solid disk having radius R = 0.250 m and mass M = 10.0 kg. The fixed, wedge-shaped ramp makes an angle of θ = 30.0∘ as shown in the figure. The coefficient of kinetic friction is 0.360 for both blocks. (i) (a) Draw force diagrams of both blocks and of the pulley. No file chosen (b) Determine the acceleration of the two blocks. (Enter the magnitude of the acceleration.) m/s2 (c) Determine the tensions in the string on both sides of the pulley. left of the pulley N right of the pulley N