Question

4 caroline is on an airplane. at one point in the flight, she measures that her luggage has an apparent weight of 135 n. the actual weight of her luggage is 115 n. which of the following best describes the vertical motion of the airplane?
the airplane is accelerating upwards at 1.71 m/s²
the airplane is accelerating upwards at 21.3 m/s²
the airplane is accelerating downwards at 1.71 m/s²
the airplane is accelerating downwards at 21.3 m/s²

Explanation:

Step1: Calculate the mass of the luggage

We know that weight \(W = mg\). Given the actual weight \(W = 115\space N\) and \(g=9.8\space m/s^{2}\). Using the formula \(m=\frac{W}{g}\), we have \(m=\frac{115}{9.8}\space kg\approx 11.73\space kg\).

Step2: Use the formula for apparent weight

The formula for apparent weight \(W_{apparent}=m(g + a)\) (when accelerating upwards) or \(W_{apparent}=m(g - a)\) (when accelerating downwards). Since \(W_{apparent}=135\space N>115\space N\), the plane is accelerating upwards.
Substitute \(W_{apparent}=135\space N\), \(m = 11.73\space kg\) and \(g = 9.8\space m/s^{2}\) into \(W_{apparent}=m(g + a)\).

$$135=11.73\times(9.8 + a)$$

$$9.8 + a=\frac{135}{11.73}$$

$$9.8+a\approx11.51$$

$$a=11.51 - 9.8=1.71\space m/s^{2}$$

Answer:

The airplane is accelerating upwards at \(1.71\space m/s^{2}\)