A charge of −2.69 μC is fixed at the center of a compass. Two additional charges are fixed on the circle of the compass (radius = 0.136 m). The charges on the circle are −5.36 μC at the position due north and +4.85 μC at the position due east. What is (a) the magnitude and (b) direction of the net electrostatic force acting on the charge at the center? Specify the direction as an angle relative to due east. (a) Number Units (b) Number Units
Three charges qa, qb = +10 μC and qc = −5 μC, are placed at edges of an equilateral triangle, as shown in the figure below. The sides of the triangle are 0.5 m each. (a) Find the resultant electric field at the location of qa, due to both charges qb and qc. (b) What is the force on qa, given that qa = +1.5 nC?
A scaffold of mass 73 kg and length 4.4 m is supported in a horizontal position by a vertical cable at each end. A window washer of mass 78 kg stands at a point 0.51 m from one end. What is the tension in (a) the nearer (relative to the person) cable and (b) the farther (relative to the person) cable? (a) Number Units (b) Number Units
A concave mirror has a focal length of 24.2 cm. The distance between an object and its image is 33.4 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
In a vacuum, two particles have charges of q1 and q2, where q1 = +2.7 μC. They are separated by a distance of 0.24 m, and particle 1 experiences an attractive force of 3.0 N. What is the value of q2, with its sign? Number Units
In the figure the four particles are fixed in place and have charges q1 = q2 = 4e, q3 = 3e, and q4 = −12e. Distance d = 3.26 μm. What is the magnitude of the net electric field at point P due to the particles?
A block is held at rest on an incline by a rope that is parallel to the incline as shown on the figure below. Hint: you are almost guaranteed to get these questions wrong if you do not draw separate force diagrams for the block, one for parallel to the incline and the other for perpendicular to the incline. What is the newton's second law equation for the forces parallel to the incline? Fs is the static friction force, W is the weight of the block, T is the tension in the string, N is the normal force, and θ is the angle of the incline. Wsinθ = Fs + T Wcosθ = Fs + T Wcosθ = N Wsinθ = N What is the newton's second law equation for the forces perpendicular to the incline? Wsinθ = N Wsinθ = Fs + T Wcosθ = N Wcosθ = Fs + T
Switch S in in the figure is closed at time t = 0, to begin charging an initially uncharged capacitor of capacitance C = 16.4 μF through a resistor of resistance R = 21.3 Ω. At what time is the potential across the capacitor equal to that across the resistor? Number Units
Two charges of equal magnitude but opposite sign are arranged as shown in the figure. Select the statement that correctly describes the electric field and electric potential at the midpoint between the charges. The electric field is zero and the electric potential is non-zero. The electric field is non-zero and the electric potential is zero. The electric field and electric potential are both non-zero. The electric field and electric potential are both zero.
In the figure we move a particle of charge +2e in from infinity to the x axis. How much work do we do? Distance D is 2.70 m. Number Units
The figure below shows a capacitor, with capacitance C = 30.0 μF, and a resistor, with resistance R = 77.5 kΩ, connected in series to a battery, with E = 21.0 V. The circuit has a switch, which is initially open. (a) What is the circuit's time constant (in s)? s (b) After the switch is closed for one time constant, how much charge (in C) is on the capacitor? C
Two rigid rods are oriented parallel to each other and to the ground. The rods carry the same current in the same direction. The length of each rod is 0.66 m, while the mass of each is 0.097 kg. One rod is held in place above the ground, and the other floats beneath it at a distance of 9.9 mm. Determine the current in the rods. Number Units
A horizontal wire is hung from the ceiling of a room by two massless strings. The wire has a length of 0.11 m and a mass of 0.008 kg. A uniform magnetic field of magnitude 0.050 T is directed from the ceiling to the floor. When a current of I = 38 A exists in the wire, the wire swings upward and, at equilibrium, makes an angle ϕ with respect to the vertical, as the drawing shows. Find (a) the angle and (b) the tension in each of the two strings. (a) ϕ = (b) T =
A torque of 35.0 N⋅m is applied to an initially motionless wheel which rotates around a fixed axis. This torque is the result of a directed force combined with a friction force. As a result of the applied torque the angular speed of the wheel increases from 0 to 9.7 rad/s. After 5.90 s the directed force is removed, and the wheel comes to rest 61.0 s later. (a) What is the wheel's moment of inertia (in kg⋅m2)? kg⋅m2 (b) What is the magnitude of the torque caused by friction (in N⋅m)? N⋅m (c) From the time the directed force is initially applied, how many revolutions does the wheel go through? revolutions
A hanging weight, with a mass of m1 = 0.360 kg, is attached by a cord to a block with mass m2 = 0.850 kg as shown in the figure below. The cord goes over a pulley with a mass of M = 0.350 kg. The pulley can be modeled as a hollow cylinder with an inner radius of R1 = 0.0200 m, and an outer radius of R2 = 0.0300 m; the mass of the spokes is negligible. As the weight falls, the block slides on the table, and the coefficient of kinetic friction between the block and the table is μk = 0.250. At the instant shown, the block is moving with a velocity of vi = 0.820 m/s toward the pulley. Assume that the pulley is free to spin without friction, that the cord does not stretch and does not slip on the pulley, and that the mass of the cord is negligible. (a) Using energy methods, find the speed of the block (in m/s ) after it has moved a distance of 0.700 m away from the initial position shown. m/s (b) What is the angular speed of the pulley (in rad/s) after the block has moved this distance? rad/s
On an essentially frictionless, horizontal ice rink, a skater moving at 6.0 m/s encounters a rough patch that reduces her speed by 40% due to a friction force that is 21% of her weight. Part A Use the work-energy theorem to find the length of this rough patch. Express your answer in meters. s = m
A student sits on a freely rotating stool holding two dumbbells, each of mass 2.99 kg (see figure below). When his arms are extended horizontally (Figure a), the dumbbells are 1.10 m from the axis of rotation and the student rotates with an angular speed of 0.749 rad/s. The moment of inertia of the student plus stool is 2.59 kg⋅m2 and is assumed to be constant. The student pulls the dumbbells inward horizontally to a position 0.301 m from the rotation axis (Figure b). (a) Find the new angular speed of the student. rad/s (b) Find the kinetic energy of the rotating system before and after he pulls the dumbbells inward. Kbefore = J Kafter = J
A counterweight of mass m = 5.20 kg is attached to a light cord that is wound around a pulley as shown in the figure below. The pulley is a thin hoop of radius R = 9.00 cm and mass M = 1.10 kg. The spokes have negligible mass. (a) What is the net torque on the system about the axle of the pulley? magnitude N⋅m direction (b) When the counterweight has a speed v, the pulley has an angular speed ω = v/R. Determine the magnitude of the total angular momentum of the system about the axle of the pulley. ( kg⋅m)v (c) Using your result from (b) and τ→ = dL→/dt, calculate the acceleration of the counterweight. (Enter the magnitude of the acceleration.) m/s2
Starting from rest, a 64.0 kg woman jumps down to the floor from a height of 0.740 m, and immediately jumps back up into the air. While she is in contact with the ground during the time interval 0 < t < 0.800 s, the force she exerts on the floor can be modeled using the function F = 9,200t − 11,500t2 where F is in newtons and t is in seconds. (a) What impulse (in N⋅s) did the woman receive from the floor? (Enter the magnitude. Round your answer to at least three significant figures.) N⋅s (b) With what speed (in m/s ) did she reach the floor? (Round your answer to at least three significant figures.) m/s (c) With what speed (in m/s ) did she leave it? (Round your answer to at least three significant figures.) m/s (d) To what height (in m) did she jump upon leaving the floor? m
A mass of 0.600 kg is attached to a spring and set into oscillation on a horizontal frictionless surface. The simple harmonic motion of the mass is described by x(t) = (0.660 m)cos[(10.0 rad/s)t]. Determine the following. (a) amplitude of oscillation for the oscillating mass m (b) force constant for the spring N/m (c) position of the mass after it has been oscillating for one half a period m (d) position of the mass five-sixths of a period after it has been released m (e) time it takes the mass to get to the position x = −0.100 m after it has been released s
The crate shown in Figure Q1.2 has a mass of m kg and is being raised up a plane at θ degrees by cable parallel to the plane. The coefficient of friction is μ. FIGURE 1.2 Note that values for m, θ and μ are randomly generated. Calculate the magnitude of the tension, T, that will allow an acceleration of a m/s2 up the plane. Note: the value for a is randomly generated. Given that the mass is initially at rest, what is its velocity after it has moved a distance of s m along the plane? Assume that the mass remains on the incline during this motion. Note: the value for s is randomly generated. Note also: constant acceleration can be assumed. What is the work done after the mass has moved a distance of s m?