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

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.

Quizplus · Accepted Answer

Since the floor is frictionless, the only force acting on the box is the tension force T.

The weight of the box acts vertically down, and we can resolve it into two components - one along the horizontal direction (mg sin 15°) and the other along the vertical direction (mg cos 15°).

By Newton's second law, the horizontal component of the weight force is balanced by the tension force T. Thus, T = mg sin 15°.

The acceleration of the box in the horizontal direction is given by a = T/m, and substituting T = mg sin 15° gives a = g sin 15°.

Comparing with the given constant acceleration a, we can see that g sin 15° (which is greater than a) is the actual acceleration of the box.

Therefore, T = ma/g sin 15° > ma.

A Box of Mass M Is Pulled with a Constant