Two infinite, nonconducting sheets of charge are parallel to each other as shown in the figure below. The sheet on the left has a uniform surface charge density σ, and the one on the right has a uniform charge density −σ. Calculate the electric field at the following points. (Use any variable or symbol stated above along with the following as necessary: ε0.) (a) to the left of the two sheets magnitude E = direction Select ⋯ (b) in between the two sheets magnitude E = direction (c) to the right of the two sheets magnitude E = direction - Select-- (d) Find the electric fields in all three regions if both sheets have positive uniform surface charge densities of value σ. to the left of the two sheets magnitude E = direction - Select − in between the two sheets magnitude E = direction - -Select-- to the right of the two sheets magnitude E = direction - -Select--
Two cars cover the same distance in a straight line. Car A covers the distance at a constant velocity. Car B starts from rest and maintains a constant acceleration. Both cars cover a distance of 550 m in 228 s. Assume that they are moving in the +x direction. Determine (a) the constant velocity of car A, (b) the final velocity of car B, and (c) the acceleration of car B. (a) VA = (b) VB = (c) aB =
A projectile is shot directly away from Earth's surface. Neglect the rotation of the Earth. What multiple of Earth's radius RE gives the radial distance (from the Earth's center) the projectile reaches if (a) its initial speed is 0.610 of the escape speed from Earth and (b) its initial kinetic energy is 0.610 of the kinetic energy required to escape Earth? (Give your answers as unitless numbers.) (c) What is the least initial mechanical energy required at launch if the projectile is to escape Earth? (a) Number Units (b) Number Units (c) Number Units
A tourist being chased by an angry bear is running in a straight line toward his car at a speed of 5.56 m/s. The car is a distance d away. The bear is 24.2 m behind the tourist and running at 6.71 m/s. The tourist reaches the car safely. What is the maximum possible value for d? Number Units
A displacement vector r→ in the xy plane is 33.0 m long and directed at angle θ = 29.0∘ in the figure. Determine (a) the x component and (b) the y component of the vector. (a) Number Units (b) Number Units
In the figure two large, thin metal plates are parallel and close to each other. On their inner faces, the plates have excess surface charge densities of opposite signs and magnitude 6.52 ×10−22 C/m2. What is the magnitude of the electric field at points (a) to the left of the plates, (b) to the right of them, and (c) between them? (a) Number Units (b) Number Units (c) Number Units
A simple harmonic oscillator consists of a block of mass 1.10 kg attached to a spring of spring constant 220 N/m. When t = 2.20 s, the position and velocity of the block are x = 0.163 m and v = 3.930 m/s. (a) What is the amplitude of the oscillations? What were the (b) position and (c) velocity of the block at t = 0 s? (a) Number Units (b) Number Units (c) Number Units
A gymnast with mass 49.0 kg stands on the end of a uniform balance beam as shown in the figure. The beam is 5.50 m long and has a mass of 250 kg (excluding the mass of the two supports). Each support is 0.560 m from its end of the beam. In unit-vector notation, what are the forces on the beam due to (a) support 1 and (b) support 2? (a) Number j Units (b) Number j Units
Multiple Concept Example 9 deals with the concepts that are important in this problem. A grasshopper makes four jumps. The displacement vectors are (1) 30.0 cm, due west; (2) 30.0 cm, 39.0∘ south of west; (3) 16.0 cm, 51.0∘ south of east; and (4) 24.0 cm, 74.0∘ north of east. Find (a) the magnitude and (b) direction of the resultant displacement. Express the direction as a positive angle with respect to due west. (a) Number Units (b) Number Units
A block of mass m rests on a rough horizontal surface and is attached to a spring of stiffness k. The coefficients of both static and kinetic friction are μ. The block is displaced a distance x0 to the right of the unstretched position of the spring and released from rest. If the value of X0 is large enough, the spring force will overcome the maximum available static friction force and the block will slide toward the unstretched position of the spring with an acceleration a = μg − kmx, where x represents the amount of stretch (or compression) in the spring at any given location in the motion. Use the values m = 5 kg, k = 150 N/m, μ = 0.40, and x0 = 200 mm and determine the final spring stretch (or compression) xf when the block comes to a complete stop.
The figure gives the acceleration a versus time t for a particle moving along an x axis. The a-axis scale is set by as = 15.0 m/s2. At t = −2.0 s, the particle's velocity is 10.0 m/s. What is its velocity at t = 6.0 s? Number Units
Three point charges q1, q2, and q3 are situated at three corners of a rectangle as shown in the diagram below. Here q1 = +6.00 μC, q2 = −6.00 μC, q3 = +4.00 μC. (a) What is the electric potential at the free corner where there is no charge? V (b) What charge should be placed at the free corner for the electric potential at the center of the rectangle to be zero? Include both magnitude and sign if applicable. μC
A person going for a walk follows the path shown in the figure, where y1 = 276 m and θ = 54.0∘. The total trip consists of four straight-line paths. At the end of the walk, what is the person's resultant displacement measured from the starting point? magnitude m direction counterclockwise from the +x axis
Cheetahs can accelerate to a speed of 20.0 m/s in 2.50 s and can continue to accelerate to reach a top speed of 30.0 m/s. Assume the acceleration is constant until the top speed is reached and is zero thereafter. Let the +x-direction point in the direction the cheetah runs. Express the cheetah's top speed vtop in miles per hour (mi/h). vtop = mi/h Starting from a crouched position, how much time taccel does it take a cheetah to reach its top speed, and what distance d does it travel in that time? taccel = s d = m If a cheetah sees a rabbit 134.0 m away, how much time ttotal will it take to reach the rabbit, assuming the rabbit does not move and the cheetah starts from rest? ttotal = s
The displacement vectors A→ and B→ shown in the figure below both have magnitudes of 4.20 m. The direction of vector A→ is θ = 21.0∘. (a) Find A→ + B→ graphically. magnitude m direction - counterclockwise from the +x axis (b) Find A→ − B→ graphically. magnitude m direction - counterclockwise from the +x axis (c) Find B→ − A→ graphically. magnitude m direction - counterclockwise from the +x axis (d) Find A→ − 2 B→ graphically. magnitude m direction - counterclockwise from the +x axis
Two teams engage in a tug of war. Each team has 9 members. The first team's members have an average mass of 67 kg per person and exert an average force of 1355 N per person horizontally. The second team's members have an average mass of 71 kg per person and exert an average force of 1375 N per person horizontally. Hint: Be sure to read the textbook's section on problem solving strategies for Newton's Laws. What is magnitude of the acceleration of the two teams? m/s2 What is the tension in the section of rope between the teams? N
The 82−kg man dives from the 36−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 61-kg woman remains motionless relative to the canoe. Answer: vcanoe = m/s
A cyclotron with dee radius 40.2 cm is operated at an oscillator frequency of 14.1 MHz to accelerate protons. (a) What magnitude B of magnetic field is required to achieve resonance? (b) At that field magnitude, what is the kinetic energy of a proton emerging from the cyclotron? Suppose, instead, that B = 1.50 T. (c) What oscillator frequency is required to achieve resonance now? (d) At that frequency, what is the kinetic energy of an emerging proton? (a) Number Units (b) Number Units (c) Number Units (d) Number Units
Calculate the energy of attraction between a cation with a valence of +4 and an anion with a valence of -2, the centers of which are separated by a distance of 3.3 nm. J
Three nonconducting strips are bent to form arcs and, when assembled, they form part of a circle of radius r = 5.93 cm. The three strips have linear charge densities of λ1 = 97.0 nC/m, λ2 = −179 nc/m, and λ3 = 268 nC/m, respectively, and subtend angles of 60∘, 120∘, and 45∘, respectively, at the center. (a) Determine the electric potential at the center of the circle of which the strips form a part. V (b) You use a fourth nonconducting strip to close the circle. What should be the linear charge density on this strip if the potential at the center of the circle is to be zero? nC/m
Several planets (Jupiter, Saturn, Uranus) are encircled by rings, perhaps composed of material that failed to form a satellite. In addition, many galaxies contain ring-like structures. Consider a homogeneous thin ring of mass of M and outer radius R (see the figure). NOTE: Give your answer in terms of the variables given and G when applicable. (a) What gravitational attraction does it exert on a particle of mass m located on the ring's central axis a distance x from the ring center? F = (b) What is the potential energy of the mass m as a function of its distance x from the ring? U(x) = (c) Calculate −dU/dx, where U is the potential energy of the small mass m. (Is this answer what you expected?) −dU/dx = (d) Suppose that, starting from the distance x shown, the particle falls from rest as a result of the attraction of the ring of matter. What is the speed with which it passes through the center of the ring? v =
Suppose the conducting spherical shell in the figure below carries a charge of 3.80 nC and that a charge of -2.20 nC is at the center of the sphere. If a = 1.80 m and b = 2.30 m, find the electric field at the following. (a) r = 1.50 m magnitude N/C direction (b) r = 2.20 m (c) r = 2.50 m magnitude N/C direction (d) What is the charge distribution on the sphere? inner surface nC outer surface nC
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. Neglect friction associated with the wheels of the tapered block. Ans. 0.0577(m1 + m2)g ≤ P ≤ 0.745(m1 + m2)g
The acceleration of a particle moving only on a horizontal xy plane is given by a→ = 6ti^ + 7tj^, where a→ is in meters per second-squared and t is in seconds. At t = 0, the position vector r→ = (27.0 m)i^ + (39.0 m)j^ locates the particle, which then has the velocity vector v→ = (8.00 m/s)i^ + (1.90 m/s)j^. At t = 2.60 s, what are (a) its position vector in unit-vector notation and (b) the angle between its direction of travel and the positive direction of the x axis? (a) Number i^ + j^ Units (b) Number Units
The three ropes shown in the bird's-eye view of the figure are used to drag a 13.5 kg crate 3.00 m across the floor. a. What is the net force (in component form) on the crate? Start with a free-body diagram. b. What is the magnitude of the acceleration? (Find the components of acceleration first!)
You attach a meter stick to an oak tree, such that the top of the meter stick is 2.67 meters above the ground. Later, an acorn falls from somewhere higher up in the tree. The acorn takes 0.296 seconds to pass the length of the meter stick. Use g = 9.81 m/s2 for the gravitational acceleration. How high h0 above the ground was the acorn before it fell? Assume that the acorn did not run into any branches or h0 = leaves on the way down.
Find the magnitude and direction of the net electric field at point A. The two particles in the diagram each have a charge of +3.3 μC. The distance separating the charges is 7.0 cm. The distance between point A and B is 4.0 cm. magnitude N/C direction counterclockwise from the +x axis
One cubic centimeter of a typical cumulus cloud contains 280 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 2.9 km and radius 1.0 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?
The figure shows an uneven arrangement of electrons (e) and protons (p) on a circular arc of radius r = 2.05 cm, with angles θ1 = 32.0∘, θ2 = 53.0∘, θ3 = 30.0∘, and θ4 = 31.0∘. What are the (a) magnitude and (b) direction (relative to the positive direction of the x axis) of the net electric field produced at the center of the arc? (a) Number Unit (b) Number Unit
A charge of +1 nC(1×10−9 C) and a dipole with charges +q and −q separated by 0.3 mm contribute a net field at location A that is zero, as shown in the figure below. (Assume r1 = 36 cm and r2 = 23 cm.) (a) Which end of the dipole is positively charged? (b) How large is the charge q? (Enter the absolute value.) q = nC