Three identical point masses

PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Force and Translational Dynamics · Force and Translational Dynamics

Problem

Three identical point masses, each of mass

2.0\,\text{kg}

, are connected by light rods to form a rigid triangular frame that lies in the

xy

-plane of an inertial coordinate system. • Mass 1 is located at

(+0.40\,\text{m},\,0.00\,\text{m})

and has instantaneous velocity

(+2.0\,\text{m/s},\,+1.2\,\text{m/s})

. • Mass 2 is located at

(-0.20\,\text{m},\,+0.35\,\text{m})

and has instantaneous velocity

(+0.95\,\text{m/s},\,-0.60\,\text{m/s})

. • Mass 3 is located at

(-0.20\,\text{m},\,-0.35\,\text{m})

and has instantaneous velocity

(+3.05\,\text{m/s},\,-0.60\,\text{m/s})

. All velocities are measured in the same inertial frame. Treat the rods as massless so that only the point masses contribute to the kinetic energy. (a) Determine the instantaneous position of the center of mass and its speed. (b) Compute the total kinetic energy of the system directly from the given velocities of the three masses. (c) Calculate the kinetic energy associated with the translational motion of the center of mass. (d) For each mass, find its velocity relative to the center of mass. Use these relative velocities to evaluate the kinetic energy associated with rotation about the center of mass. (e) Compare your results from parts (b), (c), and (d). Discuss the significance of any agreement you observe.

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