Answer to Question #115458 in Classical Mechanics for Lizwi

Question

A box of inertia 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 T compared to ma? Is T=ma? Is T<ma? Is T>ma?

Answer 1

Let's investigate forces, acting on a box. It's a gravity force, reaction force and tension force of the rope. Writing equation of motion in horizontal projection, we have: $T\cos{15^o}=m a$. From this equation we obtain: $T=\dfrac{1}{\cos{15^o}}ma$. As $\cos{15^o}<1$, so $\dfrac{1}{\cos{15^o}}>1$, thus $T>ma$