An asymmetrical dumbell consists of two balls of mass m1 = m and m2 = 4m connect

Question

An asymmetrical dumbell consists of two balls of mass m1 = m and m2 = 4m connected by a rod. The distance between the centers of the balls is E. The dumbell is initially at rest on a frictionless surface. At time t = 0, two forces, F1 = Fi + Fj and F2 = 1/2Fi + 1/5Fj are applied and remain constant in magnitude and direction regardless of the dumbell's motion. The quantities m and F are reference mass and force scales respectively. We wish to determine the trajectory of the center of mass, y_bar as a function of x_bar, for the following cases.

A. The rod's mass is negligible

B. The rod's mass is 2m: Treat the bar as a third particle located at x = 1/2E, y = 0

Explanation / Answer

Let the centre of m is at origin a)Resultant Force is 3/2Fi + 6/5Fj = Fr So acceleration is Fr/5m The COM is at 4E/5 So x_bar = 4E/5 + 0.5*(1.5/5m)F*t*t and y_bar = 0.5*(1.2/5m)F*t*t b)Resultant Force is 3/2Fi + 6/5Fj = Fr So acceleration is Fr/7m The COM is at 5E/7 So x_bar = 5E/7 + 0.5*(1.5/7m)F*t*t and y_bar = 0.5*(1.2/7m)F*t*t

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