An Electric Pendulum and a Uniform Magnetic Field *NO CORRECT ANSWER*
The figure shows an electric pendulum consisting of a wire of length L = 1m connected to a sphere of mass m = 5kg and positive charge q = 2C in a region containing a uniform gravitational field g = 10m/s² and a uniform magnetic field B = 15T perpendicular to the plane of the paper. The maximum traction supported by the wire is T = 240N. The ball is abandoned from rest from position 1. Find the maximum
HEIGHT
h traveled by the sphere until the wire breaks.
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1 solution
Let θ be the angle that the wire forms with the vertical, after the sphere has dropped a height h relative to position 1. At that time, the sphere has already reached a speed v = √2gh.
From Newton's second law, in the radial direction, we have:
T - mgcosθ - qvB = mv² / L
T - mgcosθ - qB√2gh = 2mgh / L
cosθ = h / L
T = 3mgh / L + qB√2gh
240 = 150h + 30√20h
8 = 5h + √20h
25h² - 100h + 64
h < L
h = 0.4m
(NO ANSWERS) SORRY!!!