Consider the charge distribution below. The charge values are q1 = 5 μC, q2 = −4 μC and q3 = −3 μ C. μ stands for micro. q1 and q2 are separated by a distance of 0.3 m, and q2 and q3 are also separated by a distance of 0.3 m. q2 q3 + q1 The goal of this problem is to solve for the magnitude and direction of the net force on q3 due to q1 and q2. The problem is designed to provide for partial credit due from correct process. The magnitude of the force on q3 due to q1 is [ Select ] , which has an x -component of [ Select ] and a y-component of [ Select ] The magnitude of the force on q3 due to q2 is [ Select ], which has an x -component of [ Select ] and a y-component of [ Select ] . The net force on q3 has an x -component of [ Select ] and y-component of [ Select ]. The magnitude of the net force on q3 is [ Select] , with a direction that is [ Select ] degrees as measured counterclockwise from the positive x axis.
Two objects having the same mass, m = 570 g are dropped from rest. Mass m1 is positively charged, Q1 = +750 μC, while m2 is negatively charged, Q2 = −750. μC. Ignore air resistance and the take the electric field near the surface of the Earth to be approximately E→Earth = 150 V/m a. The Electric Force is conservative, use the conservation of energy to derive an equation for the velocity. [3 points] b. Using the derived equation, calculate the final velocities for each mass. [4 points] c. After the masses has fallen a distance of h = 3.50 m, determine the difference in the speed between m1 and m2. [ 2 points]
The current in a single-loop circuit with one resistance R is 4.7 A. When an additional resistance of 2.1 Ω is inserted in series with R, the current drops to 3.8 A. What is R? Number Units
The figure shows a current loop ABCDEFA carrying a current i = 6.69 A. The sides of the loop are parallel to the coordinate axes shown, with AB = 18.5 cm, BC = 25.3 cm, and FA = 10.7 cm. In unit-vector notation, what is the magnetic dipole moment of this loop? (Hint: Imagine equal and opposite currents i in the line segment AD; then treat the two rectangular loops ABCDA and ADEFA.) Number ( i^+ j^+ k) Units
In the figure, a charged particle moves into a region of uniform magnetic field B→, goes through half a circle, and then exits that region. The particle is either a proton or an electron (you must decide which). It spends 113 ns in the region. (a) What is the magnitude of B→? (b) If the particle is sent back through the magnetic field (along the same initial path) but with 3.45 times its previous kinetic energy, how much time does it spend in the field during this trip? (a) Number Units (b) Number Units
A man stands on a platform that is rotating (without friction) with an angular speed of 0.438 rev/s; his arms are outstretched and he holds a brick in each hand. The rotational inertia of the system consisting of the man, bricks, and platform about the central axis is 5.76 kg⋅m2. If by moving the bricks the man decreases the rotational inertia of the system to 2.04 kg⋅m2, (a) what is the resulting angular speed of the platform and (b) what is the ratio of the new kinetic energy of the system to the original kinetic energy? (a) Number Units (b) Number Units
Tyrannosaurus rex may have known from experience not to run particularly fast because of the danger of tripping, in which case its short forearms would have been no help in cushioning the fall. Suppose a T. Rex of mass 4300 kg trips while walking, toppling over, with its center of mass falling freely a distance of 1.4 m. Then its center of mass descends an additional 0.25 m due to compression of its body and the ground. (a) What is the approximate magnitude of the average vertical force on the dinosaur during its collision with the ground (during the descent of 0.25 m)? Now assume that the dinosaur is running at a speed of 19 m/s (fast) when it trips, falls to the ground, and then slides to a stop with a coefficient of kinetic friction of 0.58. Assume also that the average vertical force during the collision and sliding is that in (a). What, approximately, are (b) the magnitude of the average total force on the dinosaur from the ground and (c) the sliding distance? The force magnitudes of (a) and (b) strongly suggest that the collision would injure the torso of the dinosaur. The head, which would fall farther, would suffer even greater injury. (a) Number Units (b) Number Units (c) Number Units
In the figure below, a charged particle moves into a region of uniform magnetic field B→, goes through half a circle, and then exits that region. The particle is either a proton or an electron (you must decide which). It spends 180 ns in the region. (a) What is the magnitude of B→? T (b) If the particle is sent back through the magnetic field (along the same initial path) but with 4.00 times its previous kinetic energy, how much time does it spend in the field during this trip? ns
A 0.00400−kg bullet traveling horizontally with speed 1.00×103 m/s strikes a 16.6 - kg door, embedding itself 10.6 cm from the side opposite the hinges as shown in the figure below. The 1.00−m wide door is free to swing on its frictionless hinges. (a) Before it hits the door, does the bullet have angular momentum relative the door's axis of rotation? Yes No (b) If so, evaluate this angular momentum. (If not, enter zero.) kg⋅m2/s If not, explain why there is no angular momentum. This answer has not been graded yet. (c) Is mechanical energy of the bullet-door system constant in this collision? Answer without doing a calculation. Yes No (d) At what angular speed does the door swing open immediately after the collision? rad/s (e) Calculate the total energy of the bullet-door system and determine whether it is less than or equal to the kinetic energy of the bullet before the collision. KEf = J KEi = J
A helicopter lifts a 61 kg astronaut 19 m vertically from the ocean by means of a cable. The acceleration of the astronaut is g/14. How much work is done on the astronaut by (a) the force from the helicopter and (b) the gravitational force on her? Just before she reaches the helicopter, what are her (c) kinetic energy and (d) speed? (a) Number Units (b) Number Units (c) Number Units (d) Number Units
The figure shows a cold package of hot dogs sliding rightward across a frictionless floor through a distance d = 21.0 cm while three forces act on the package. Two of them are horizontal and have the magnitudes F1 = 9.0 N and F2 = 2.0 N; the third is angled down by Θ = 60.0∘ and has the magnitude F3 = 7.0 N. (a) For the 21.0 cm displacement, what is the net work done on the package by the three applied forces, the gravitational force on the package, and the normal force on the package? (b) If the package has a mass of 3.0 kg and an initial kinetic energy of 0, what is its speed (in m/s) at the end of the displacement? (a) Number Units (b) Number Units
Point charges of 6.50 μC and −2.25 μC are placed 0.350 m apart. (Assume the negative charge is located to the right of the positive charge. Include the sign of the value in your answers.) (a) Where can a third charge be placed so that the net force on it is zero? m to the right of the −2.25 μC charge (b) What if both charges are positive? m to the right of the 2.25 μC charge
A pulsar is a rapidly rotating neutron star that emits a radio beam the way a lighthouse emits a light beam. We receive a radio pulse for each rotation of the star. The period T of rotation is found by measuring the time between pulses. Suppose a pulsar has a period of rotation of T = 0.0526 s that is increasing at the rate of 3.81 x 10−5 s/y. (a) What is the pulsar's angular acceleration α? (b) If α is constant, how many years from now will the pulsar stop rotating? (c) Suppose the pulsar originated in a supernova explosion seen 632 years ago. Assuming constant α, find the initial T. (a) Number Units (b) Number Units (c) Number Units
The figure shows a current loop ABCDEFA carrying a current i = 3.95 A. The sides of the loop are parallel to the coordinate axes shown, with AB = 21.7 cm, BC = 30.1 cm, and FA = 12.0 cm. In unit-vector notation, what is the magnetic dipole moment of this loop? (Hint: Imagine equal and opposite currents i in the line segment AD; then treat the two rectangular loops ABCDA and ADEFA.) Number ( i^+ j^+ k) Units
Point charges of 6.75 μC and −3.75 μC are placed 0.350 m apart. (Assume the negative charge is located to the right of the positive charge. Include the sign of the value in your answers.) (a) Where can a third charge be placed so that the net force on it is zero? m to the right of the −3.75 μC charge (b) What if both charges are positive? m to the right of the 3.75 μC charge
A 8.0 μF capacitor is charged by a 155 V battery (see the figure (Figure 1) a) and then is disconnected from the battery. When this capacitor (C1) is then connected (see the figure b) to a second (initially uncharged) capacitor, C2, the final voltage on each capacitor is 25 V. Figure 1 of 1 V (a) (b) Part A What is the value of C2? [Hint. Charge is conserved. ] Express your answer using two significant figures. C2 =
A circuit contains an emf produced by a moving metal rod of charge 15.5 μC across a magnetic field of 0.28 T, shown in the diagram. This allows a 367 Ω light bulb to turn on. If the force on the metal rod is 4 N, what would be the current running across the circuit? The length of the rod L = 2.9 mm. The rails and rod have a negligible electrical resistance. (Hint: This is a 3 to 4 step problem. Start by working backwards. Try using the equation for what you're solving for, and then use equations to sub in missing info) Answer to 3 sig figs.
A particle of mass 11.2 g and charge 71.3 μC moves through a uniform magnetic field, in a region where the free-fall acceleration is −9.8 j^ m/s2 without falling. The velocity of the particle is a constant 19.2 i^ km/s, which is perpendicular to the magnetic field. What, then, is the magnetic field? Number ( i^+ j^+ k^) Units
A rigid, vertical rod with a mass of 2.9 kg simply rests on the floor and is held in place by static friction. The coefficient of static friction between the rod and the floor is 1/7. The rod also has a wire connected between its top end and the floor, as shown in the figure. A horizontal force F is applied at the midpoint of the rod. Find the greatest force F that can be applied at the midpoint of the rod without causing it to slip. N
A penguin of mass m moving at speed V0 has an initial height of H. She slides with no friction through the dip and up the other side to a height of h. What is her final velocity at height h? Consider the case where H = 3.2 m, h = 1.7 m and V0 = 1.8 m/s. Enter your answer in m/s.
A hanging weight, with a mass of m1 = 0.375 kg, is attached by a rope to a block with mass m2 = 0.835 kg as shown in the figure below. The rope 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 rope does not stretch and does not slip on the pulley, and that the mass of the rope 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
A torque of 35.6 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 10.5 rad/s. After 5.80 s the directed force is removed, and the wheel comes to rest 60.6 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
The Mars Pathfinder spacecraft used large airbags to cushion its impact with the planet's surface when landing. Assuming the spacecraft had an impact velocity of vO = 22.00 m/s at an angle of 45∘ with respect to the horizontal, the coefficient of restitution is 0.85. The friction is neglected and the acceleration due to gravity on Mars is 3.73 m/s2. Problem 13.170. b Mars pathfinder length of bounce Determine the length of the first bounce. The length of the first bounce is m. ! Required information Problem 13.170 Mars pathfinder cushioned landing Dependet Multi -part- assign all parts NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part.