Multiple Concept Example 9 reviews the concepts that play a role in this problem. As an aid in working this problem, consult Concept Simulation 1.1. Two forces are applied to a tree stump to pull it out of the ground. Force F→ A has a magnitude of 1820 newtons (N) and points 38.0∘ south of east, while force F→ B has a magnitude of 2760 N and points due south. Using the component method, find the (a) magnitude and (b) direction of the resultant force F→A + F→ B that is applied to the stump. Specify the direction as a positive angle with respect to due east. (a) Number Units (b) Number Units
A charge of 15.0 μC is to be split into two parts that are then separated by 25.0 mm. What is the maximum possible magnitude of the electrostatic force between those two parts? Number Units
Calculate the number of coulombs of positive charge in 338 cm3 of (neutral) water. (Hint: A hydrogen atom contains one proton; an oxygen atom contains eight protons.) Number Units
(a) A physics lab instructor is working on a new demonstration. She attaches two identical iron spheres with mass m = 0.180 g to strings of length L as shown in the figure. Both spheres have the same charge of 6.80 nC, and are in static equilibrium when θ = 5.25∘. What is L (in m)? Assume the strings are massless. m (b) What If? The charge on both spheres is increased until each string makes an angle of θ = 10.5∘ with the vertical. If both spheres have the same electric charge, what is the charge (in nC) on each sphere in this case? nC
(a) A ball is attached to a string of length L = 15.2 cm and suspended from the ceiling, as shown in the figure. A uniform electric field points to the right in the figure. When θ = 14.9∘, the ball is in equilibrium. Find the net charge on the ball (in μC). μC (b) What If? If the electric field is suddenly turned off, what is the speed of the ball at the bottom of its swing (in m/s)? m/s
A positively charged particle of mass m and charge q is released from rest in a uniform electric field, E→ = (10i^) V/m. The particle, after travelling 2 s in this electric field, enters a region that is free from electric field but has a steady and uniform magnetic field, B→ = (−4k^) T. What will be the radius of the circular path (in meters) and the direction of angular velocity of the particle in this region? (Select the closest number among the following choices.) (Note: an incorrect answer will be penalized 2 pts.) a) 5.0; k^ b) 0.2; k^ c) 0.2; −k^ d) 2.0; k^ e) 5.0; −k^
Charges Q1 = 7.2 C and Q2 = −8.5 C are at adjacent corners of a square of side 0.5 m. There is no charge at point A, which is the midpoint along its side. The potential is chosen so that V approaches O very far from the charges. The electric potential energy in this system is ____ ×1011 J.
Consider the two small, equal-mass, charged balls shown in the figure. The top ball is suspended from the ceiling by a filament, and has a charge of q1 = 31.1 nC. The bottom ball has a charge of q2 = −58.0 nC, and is directly below the top ball. Assume d = 2.00 cm and m = 6.70 g. (a) Calculate the tension (in N) in the filament. N (b) If the filament can withstand a maximum tension of 0.180 N, what is the smallest value d can have before the filament breaks? (Give your answer in cm.) cm
The 10-kg block A is connected to the 20-kg block B by a rigid lightweight link with pin connections at both ends (which means the link is a two-force member). Both blocks are on rollers. A 200 N horizontal force is pushing block A as shown. Determine the acceleration (m/s2) of block A. 65.4 9.81 6.667 32.2 10 20
Two identical conducting spheres, fixed in place, attract each other with an electrostatic force of 0.147 N when their center-to-center separation is 61.1 cm. The spheres are then connected by a thin conducting wire. When the wire is removed, the spheres repel each other with an electrostatic force of 0.0539 N. Of the initial charges on the spheres, with a positive net charge, what was (a) the negative charge on one of them and (b) the positive charge on the other? (Assume the negative charge has smaller magnitude.) (a) Number Units (b) Number Units
A particle of charge +1.8 μC is released from rest at the point x = 94 cm on an x axis. The particle begins to move due to the presence of a charge Q that remains fixed at the origin. What is the kinetic energy of the particle at the instant it has moved 29 cm if (a)Q = +46 μC and (b) Q = −46 μC? (a) Number Units (b) Number Units
A particle of charge Q is fixed at the origin of an xy coordinate system. At t = 0 a particle (m = 0.910 g, q = 5.53 μC) is located on the x axis at x = 19.2 cm, moving with a speed of 26.7 m/s in the positive y direction. For what value of Q will the moving particle execute circular motion? (Neglect the gravitational force on the particle.) Number Units
A +8.30 μC charge is placed at the origin, as in the figure below. (a) What is the magnitude and direction of the electric field due to the +8.30 μC charge at the point marked P? (b) What is the magnitude and direction of the electric force on a −1.50 μC charge placed at point P due to the +8.30 μC charge? (c) What is the magnitude and direction of the electric field due to the +8.30 μC charge at the point marked R? (d) What is the magnitude and direction of the electric force on a −1.50 μC charge placed at point R due to the +8.30 μC charge?
Two tiny conducting spheres are identical and carry charges of −21.9 μC and +42.1 μC. They are separated by a distance of 2.01 cm. (a) What is the magnitude of the force that each sphere experiences? (b) The spheres are brought into contact and then separated to a distance of 2.01 cm. Determine the magnitude of the force that each sphere now experiences. (a) Number Units (b) Number Units
A first charge, q1 = 15.1 μC, is located at r→1 = (3.03 m)i^ + (−3.74 m)j^ A second charge, q2 = −45.2 μC, is located at r→2 = (9.15 m)i^ + (7.86 m)j^ The force on the first charge due to the second charge can be written, using Cartesian unit vectors, as follows: F→ = Fxi^ + Fyj^ Part (a) What is the of the x component of the force on the first charge due to the second charge in newtons? Part (b) What is the y component of the force on the first charge due to the second charge in newtons? Part (c) What is the magnitude, in newtons, of the force on the first charge due to the second charge?
A simple harmonic oscillator consists of a block of mass 4.30 kg attached to a spring of spring constant 210 N/m. When t = 1.60 s, the position and velocity of the block are x = 0.104 m and v = 3.580 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