You walk into an elevator, step onto a scale, and push the “up” button. You recall that your normal weight is 625 N. Draw a free-body diagram. (a) When the elevator has an upward acceleration of magnitude 2.50 m/s2, what does the scale read? (b) If you hold a 3.85-kg package by a light vertical string, what will be the tension in this string when the elevator accelerates as in part (a)?
Solution 8E Your normal weight = 625 N Acceleration due to gravity g = 9.80 m/s 2 Therefore, your mass m = 625 N/(9.80 m/s ) 2 m = 63.7 kg 2 (a) The elevator has an upward acceleration of 2.5 m/s . The free body diagram can be drawn as shown below. The elevator has an upward acceleration. Therefore, the net acceleration will be 2 2 2 a net= g + a = 9.80 m/s + 2.50 m/s = 12.3 m/s Your mass is m = 63.7 kg Therefore, when the elevator accelerates up, the scale reading will be R = ma net R = 63.7 kg × 12.3 m/s 2 R = 783.5 N R 784 N The scale will read approximately 784 N for the upward acceleration. (b) The free body diagram for the package is shown below. Mass of the package is p = 3.85 kg Weight of the package w = 3.85 kg × 9.80 m/s 2 p w = 37.7 N p If T be the tension of the string, then T = w + pa p T = 37.7 N + 3.85 × 2.50 N T = 47.3 N Therefore, the tension in the string is approximately 47.3 N .