(1) A springis hanging from the ceiling of an elevator, and a mass of 9.8 kg is attached to the lower end. When the elevator is accelerating upward ata= 8.8m/s², the spring is stretched by 13.2 cm from its natural length. When the elevator is accelerating downward ata= 8.8m/s², the spring is compressed by 7.2 cm from its natural length. What is the spring constant in N/m? Warning: the elevator is situated on a planet whose gravitational acceleration is unknown!

Given data -) mass m = 3. 8 kq upward acceleration a = 8.8 m 5 2 Spring streched x, = 13.2 (m X1 = 13. 2 X 10-2 mm Downward acceleration 92 = 8.8 m Spring compresed X2 = 7. 8 (m X2 = 7. 2 x 10-2m goovitational acceleration =leelee KX , Kxsmg Downward motion upward motion Fret = ma, Fret = maz Kx, - mg = ma, Kxg tomg = maz + Kx, - omg = maj Kazt mg = maz K ( 2,+ /12 ) = m (9,taz ) K = m ( Qi+ 92 )K = 9.8X ( 8. 8+ 8.8 ) [ 13. 2 X10-2 + 7.2 X10-27 K = 8. 45 49 x 102 K 8 45. ug N The spring constant is 845.ug N