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 A) T = ma. B) T > ma. C) T < ma.

Answer 1

Answer:

B) T > ma

Explanation:

To solve the problem, we have to apply Newton's second law, which states that the resultant of the forces acting on the box is equal to the product between the mass of the box (m) and its acceleration (a):

$\sum F = ma$ (1)

We are only interested in the forces acting along the horizontal direction (because there is no acceleration along the vertical axis, since the box is sliding along the floor). There are only two forces acting along the horizontal direction:

- The component of the tension of the wire parallel to the floor, $T cos 15^{\circ}$

- The force of friction, $F_f$, acting in the opposite direction (against the motion)

So, eq.(1) becomes

$T cos 15^{\circ} - F_f = ma$

which can be rewritten as

$T = \frac{ma+F_f}{cos 15^{\circ}}$

We can notice that:

$ma + F_f > ma$ by definition

$cos 15^{\circ} < 1$

This means that the tension T is greater than the product (ma), so the correct answer is B.