A mass is suspended from a string in an airplane. As the plane is in the process of taking off, it is found that the string, instead of being vertical, hangs at an angle of 13 $\degree$ from the vertical. What is the acceleration of the plane at this time? A) 2.3 m/s² B) 3.8 m/s² C) 9.1 m/s² D) 3.5 m/s²

Question

Quizplus · Accepted Answer

The acceleration of the plane is equal to the tension in the string divided by the mass of the object. The tension in the string is equal to the weight of the object times the cosine of the angle between the string and the vertical. The weight of the object is equal to the mass of the object times the acceleration due to gravity. Therefore, the acceleration of the plane is equal to the mass of the object times the acceleration due to gravity times the cosine of the angle between the string and the vertical. In this case, the mass of the object is not given, so we cannot calculate the exact acceleration of the plane. However, we can use the given information to eliminate some of the answer choices.Choice B is incorrect because it is less than the acceleration due to gravity. The acceleration of the plane must be greater than the acceleration due to gravity in order to cause the string to hang at an angle from the vertical.Choice C is incorrect because it is greater than the acceleration due to gravity times the cosine of the angle between the string and the vertical. The acceleration of the plane cannot be greater than this value because the tension in the string cannot be greater than the weight of the object.Choice D is incorrect because it is less than the acceleration due to gravity times the cosine of the angle between the string and the vertical. The acceleration of the plane must be greater than this value in order to cause the string to hang at an angle from the vertical.Therefore, the only correct answer is A.

A Mass Is Suspended from a String in an Airplane °\degree°

A Mass Is Suspended from a String in an Airplane $\degree$