Five small washers are taped to a uniform meter stick that lies along the x-axis

PHYSICS · Multi-part · CBSE · Physics · System of Particles and Rotational Motion · System of Particles and Rotational Motion

Problem

Five small washers are taped to a uniform meter stick that lies along the x-axis. Each washer has mass

0.20\,\text{kg}

and is fixed at the following positions measured from the left end of the stick:

0.10\,\text{m}

0.30\,\text{m}

0.50\,\text{m}

0.70\,\text{m}

, and

0.90\,\text{m}

. An additional mass

M

is to be attached somewhere along the stick so that the overall center of mass of the stick-washer-mass system is at

x = 0.60\,\text{m}

. (Treat the mass of the meter stick itself as negligible.) (1) Part 1: Derive an algebraic expression for the

x

-coordinate of the center of mass of the complete system in terms of

M

and the unknown position

d

of the additional mass. Clearly indicate all contributing terms. (2) Part 2: Using the requirement that the center of mass be at

x = 0.60\,\text{m}

, solve symbolically for

d

in terms of the given numerical values and the mass

M

. (3) Part 3: For

M = 0.80\,\text{kg}

, compute the numerical value of

d

and state whether the additional mass must be placed between the

0.50\,\text{m}

and

0.70\,\text{m}

washers or outside that interval. (4) Part 4: Provide a brief explanation of why your answer in Part 3 is consistent with the distribution of mass along the stick.

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