Apparent Weight. A $550$ N physics student stands on a bath$-$ room scale in an elevator that is supported by a cable. The combined mass of student plus elevator is $850$ kg$.$ As the elevator starts moving, the scale reads $450$ N$.($a$)$ Find the acceleration of the elevator $($magni$-$ tude and direction$).($b$)$ What is the acceleration if the scale reads $670$ N$?($c$)$ If the scale reads zero, should the student worry? Explain. $($d$)$ What is the tension in the cable in parts $($a$)$ and $($c$)?$