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Second Law: Motion under Same Acceleration

### 6.4: Second Law: Motion under Same Acceleration

Newton's second law of motion applies to bodies moving under the same acceleration. For example, when a baggage tractor pulls luggage carts, each cart moves at the same acceleration as that of the tractor.

Consider Block 1 of a certain mass on a frictionless, horizontal surface being pulled by a light string that passes over a frictionless and massless pulley. The other end of the string is connected to Block 2 of a different mass over the edge of the surface. Here, Newton's second law is applied to find the acceleration and tension in the string. To do this, a free-body diagram for each mass is drawn separately, and the forces acting on them are identified.

The forces on the block lying on the horizontal surface are gravitational force, the contact force of the surface, and the tension in the string. The hanging block is subjected to gravitational force and the string tension. Note that the tension is the same throughout the string. All forces are either horizontal or vertical, so horizontal/vertical coordinate systems for both objects are used to write component equations for each block. Block 1 has balanced vertical forces, so only the equation relating to the x-components is considered. There are no horizontal forces on Block 2, so only the y-component equation is considered. When Block 1 moves to the right, Block 2 travels an equal distance downward; therefore, they have the same acceleration.

If both these blocks are hung vertically using a massless string over a frictionless pulley, then the acceleration remains the same as one moves upward and the other downward.

This text is adapted from Openstax, University Physics Volume 1, Section 6.1: Solving Problems with Newton's Laws.

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