Three carts, ,

PHYSICS · Multi-part · CBSE · Physics · Laws of Motion · Laws of Motion

Problem

Three carts,

C_1

C_2

, and

C_3

, of masses

0.40\,\text{kg}

0.60\,\text{kg}

, and

0.80\,\text{kg}

respectively, are aligned on a nearly frictionless horizontal track. The carts are connected in series by two light strings. A constant horizontal force of

6.0\,\text{N}

is applied to

C_1

toward

C_2

and

C_3

, causing the three-cart system to accelerate together. (1) Part 1: (a) Draw separate free-body diagrams for each cart, clearly labeling every force acting on each cart while they accelerate. (2) Part 2: (b) Using the free-body diagrams, derive an expression for the common acceleration of the system. (3) Part 3: (c) Determine the numerical value of the acceleration, including units. (4) Part 4: (d) Calculate the tension in the string between

C_1

and

C_2

and the tension in the string between

C_2

and

C_3

. Explain any differences between these two tensions in terms of the forces identified in part (a).

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