How Does the Tension Compare to the Weight of the Hanging Block?

August 19, 2023
David Sunnyside

In this article we will answer the question, “How does the tension compare to the weight of the hanging block?” We are dealing with a classic mechanics problem relating motion (acceleration) to force (tension in the rope) using Newton’s second law.

A block of mass m is attached over a pulley to another hanging mass m, as shown above. The surface on which the blocks rest is frictionless. The system is given an initial velocity to the left and then released. The acceleration of the hanging mass m is given by the equation (a = mg). What is the direction of the tension force in the rope?

The answer to this question involves the free-body diagrams of both systems. However, since the two blocks are connected by a cord that passes over a single, frictionless massless pulley, they must be treated as a single system for the purposes of this analysis.

Tension is a pulling force exerted by each end of a string, cable, chain, rod, or similar one-dimensional continuous object to restore the string/rod to its stretched length. It should be noted that the force of gravity acting on the block also has a tangential effect on the string, which is to say that it has a pull on the rope in the same direction as the gravitational force. Therefore, at any point along the string, the tension force exerted by each end of the rope is identical to the gravitational force, and therefore cancels out.

David Sunnyside
Co-founder of Urban Splatter • Digital Marketer • Engineer • Meditator
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