Question

A box of mass m is pulled with a constant acceleration a along a horizontal frictionless floor by a wire that makes an angle of 15° above the horizontal. If t is the tension in this wire, then what is the relationship between t, m, and a?

Answer 1

The relationship between the tension, mass, and acceleration for a box pulled on a frictionless surface is given by the equation t = ma / cos(15°), where t is the tension, m is the mass, and a is the acceleration.

Step-by-step explanation:

The relationship between the tension t, mass m, and acceleration a for a box being pulled on a frictionless horizontal surface can be found using Newton's second law of motion. The horizontal component of the tension provides the force which equals mass times acceleration, or F = ma. Since the wire makes an angle of 15° above the horizontal, the horizontal component of tension is t * cos(15°), and thus we have the equation t * cos(15°) = ma, which can be rearranged to find t as a function of m and a: t = ma / cos(15°).