Consider two charged particles, q1 moving with velocity v1 along the positive x
ID: 2160210 • Letter: C
Question
Consider two charged particles, q1 moving with velocity v1 along the positive x direction q2 and moving with velocity t-2 along the positive y direction. Determine the directions of magnetic forces acting on the charges due to one another, i.e., F12 and F21 and check if they satisfy Newtons third law. We have seen that the validity of the third law implies conservation of total momentum for a multiparticle (two particles in this case) system. Is the total momentum conserved in this case? State your conclusions and explain. Consider a planet orbiting the fixed Sun Take the plane of Planet's orbit to be the x-y plane, with the Sun at the origin, and label the planet's position in the 2D polar Coordinates (r, phi). Show that the planet's angular momentum has magnitude l = mr2omega, where omega = phidot is the Planet's angular velocity about the Sun Show that the rate at which the planet sweeps out area as in Kepler's second law is dA / dt = 1 / 2r2omega and hence that dA / dt = ell / 2m. From your work above deduce Kepler's second law. Show that, provided all the internal forces are central, L vector dot = L vector ext where L vector ext is the net external torque. Consider a mass m on the end of a spring of force constant k and constrained to move along the horizontal x axis. If we place the origin at the Spring's equilibrium position, the potential energy is (1/2)kx2. At time t = 0 the mass is sitting at the origin and is given a sudden kick to the right so that it moves out to a maximum displacement xmax = A and then continues to oscillate about the origin. Write down the equation for conservation of energy and solve it to give the velocity of the mass x in terms of the position x and the total energy E. Show that E = (1/2)kA2 and use this eliminate E from your Expression for x . Use equation t = dx? / x (x?) = m / 2 dx? / E - U(x?) to find the time for the mass to move from the origin to a position x. Solve the result of part (b) to determine x as a function of t and show that the mass executes simple harmonic motion with period 2pi m/k. Instead of a simple pendulum in an accelerated cart that we discussed in class, consider a helium filed balloon that is floating midway inside of an airtight glass bell. Which way is the balloon going to move with respect to the vertical if the cart is accelerating towards the left?Explanation / Answer
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