Three small magnetic carts sit on a frictionless air track

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

Problem

Three small magnetic carts sit on a frictionless air track. Cart A has mass

0.40\,\text{kg}

and is at

x=0.00\,\text{m}

. Cart B has mass

0.60\,\text{kg}

and is at

x=0.80\,\text{m}

. Cart C, originally identical to Cart A (

0.40\,\text{kg}

), is at

x=1.60\,\text{m}

. All positions lie along the

x

-axis. A technician replaces Cart C with a new cart of mass

1.20\,\text{kg}

, placing the new cart at the same position

x=1.60\,\text{m}

. No external horizontal forces act during the replacement (the technician lifts the old cart vertically and lowers the new one vertically). (1) Determine the initial

x

-coordinate of the center of mass of the three-cart system before Cart C is removed. (2) Determine the

x

-coordinate of the center of mass after the heavier replacement cart is placed at

x=1.60\,\text{m}

. (3) Calculate the horizontal displacement of the system’s center of mass that results from the replacement. State whether the center of mass moved toward the positive or negative

x

direction.

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