A child of mass m runs on ice with velocity v0 and steps on the end of a plank of length 1 and mass M that is perpendicular to the child's path, as shown. a. Describe quantitatively the motion of the system after the child is on the plank. Neglect friction with the ice. b. One point on the plank is at rest immediately after the collision. Where is it?
Given that circuit C2 has a current-voltage response of I = 10∗V+(−100), I in mA, V in volts, what is the maximum voltage VB for which the voltage source is not supplying power when the voltage source is connected to circuit C2? maximum VS = number (rtol = 0.01, atol = 1 e−05) V
In the figure particles 1 and 2 are fixed in place on an x axis, at a separation of L = 8.40 cm. Their charges are q1 = +e and q2 = −64e. Particle 3 with charge q3 = +4e is to be placed on the line between particles 1 and 2, so that they produce a net electrostatic force F→3, net on it. (a) At what coordinate should particle 3 be placed to minimize the magnitude of that force? (b) What is that minimum magnitude?
Two line-charges with line charge density of ρ1 = +1 μC/m and ρ2 = −1 μC/m are placed in parallel to the x-axis, as shown in Fig. Q2. Find (a) the electric field strength at the point R(0, 5, 0) cm. (4 marks) (b) The potential difference between point R and point P(0, 7, 0) cm. (4 marks) (c) The potential difference between point R and point Q(5, 5, 0) cm. (2 marks) Fig. Q2
An 820 turn wire coil of resistance 24.0 Ω is placed around a 12500 turn solenoid, 7.60 cm long, as shown in the figure below. Both coil and solenoid have cross-sectional areas of 1.60×10−4 m2. (a) How long does it take the solenoid current to reach 63.2% of its maximum value? ms (b) Determine the average back emf caused by the self-inductance of the solenoid during this interval. V (c) Determine the average rate of change in magnetic flux through the coil during this interval. V (d) Determine the magnitude of the average induced current in the coil. A
3- (25 pts) As shown in the figure, a positively charged particle (q0, mass m0) is moving with a velocity V0 in the presence of both an electric field and a magnetic field. Electric field is generated by very large parallel plates. The potential difference between the two plates is 100 V. The particle is following a straight trajectory. Calculate the magnitude and the direction of the magnetic field between the plates. (Ignore gravitational interactions).
4- (25 pts) a) Calculate the magnitude and the direction of the magnetic field generated by a straight current (I) -carrying wire of length L at point P. b) As shown in the figure, the second identical current (I) carrying wire is placed above the first wire. Calculate magnitude and direction of the magnetic force between the two wires. (Do not try to calculate the integral, clearly identify the boundaries). F =
Q2-(25 pts) A variable resistor, R, whose value ranges from 0 to ∞ is connected between the terminals of a battery that has an emf ε = 18.0 V, and an internal resistance of 4.00 Ω. The ammeter and voltmeter are idealized meters. a) (8 pts.) As R varies over its full range of values, what will be the largest and smallest readings of the voltmeter and ammeter? Justify each answer with statement and/or direct calculation below. b) (8 pts.) The power dissipated at the variable resistor is 18.0 W. What can be the maximum reading on the voltmeter in this case? c) (9 pts.) Suppose we replace the variable resistor with a cylindrical wire of length 8.0 cm and cross section diameter 0.5 cm. The voltmeter reads 15.0 V. Calculate resistivity of the cylindrical wire, the magnitudes of the current density and the electric field through the wire. V18W = J = E = ρ =
A +13.0 C charge is located at the origin. A -5.0 C charge is placed at x = 1.0 m. At what finite location(s) on the x axis will the electric field be equal to zero? A) at 0 < x < 0.5 m C) at x < 0 E) It can never be zero B) at 0.5, < x < 1.0 m D) at x > 1.0 m
Refer to the figure below, positive charge Q is distributed uniformly along the positive y-axis between y = 0 and y = a. A negative point charge −q lies on the positive x-axis, at a distance x from the origin. (a) Calculate the x - and y-components of the electric field produced by the charge distribution Q at points on the positive x-axis. (b) Calculate the x - and y-components of the force that the charge distribution Q exerts on −q. (c) Show that if x≫a, Fx ≈ −Qq/4πε0x2 and Fy ≈ +Qqa/8πε0x3
The magnetic field of a plane EM wave is given by: B→ = B0 sin(kx−ωt)k^ This wave is traveling in the +x direction. The electric field of the wave would be given by: E→ = −cB0 sin(kx−ωt)j^ E→ = cB0 cos(kx−ωt)i^ E→ = −cB0 cos(kx−ωt)j^ E→ = cB0 sin(kx−ωt)j^ E→ = −cB0 sin(kx−ωt)k^
An object undergoing simple harmonic motion takes 0.17 s to travel from one point of zero velocity to the next such point. The distance between those points is 31 cm. Calculate (a) the period, (b) the frequency, and (c) the amplitude of the motion. (a) Number Units (b) Number Units (c) Number Units
A bullet is fired horizontally and embeds itself in a block of wood as shown in the figure below. After the impact, the block and embedded bullet slide 12 mm and come to a stop. The mass of the bullet is 30 g, the mass of the wooden block is 10 kg, and the coefficient of kinetic friction between the block and the surface is μk = 0.4. a. Determine the velocity of the block and embedded bullet just after the impact. b. Determine the velocity of the bullet just before the impact.