(Newton's Law of Motion) A 60 kg person stands on a scale in an elevator. How many Newtons does the scale read (a) when the elevator is ascending with an acceleration of 1 m/s^2; (b) when it is descending with an acceleration of 1/s^2; (c) when it is ascending at the constant speed of 3m/s; (d) when it is descending at the constant speed of 3m/s?

Question

espex · Answer

Assuming constant acceleration:
At rest the scale would read:$$F=mg, \space 60kg \times 9.8\frac{m}{s^2}=588N$$
If you are accelerating, regardless of direction, you have a net force acting upon you. Since we are asked about the scale, if you are being accelerated upward then an equal force downward is being applied to the scale, which is also the same direction as the force of gravity:$$F_{net}=ma+mg,\space (1\frac{m}{s^2} \times 60kg)+(60kg \times 9.8\frac{m}{s^2})=648N$$ If you are being accelerated downward, again an equal and opposite force is being applied to the scale, the opposite direction of gravity:$$F_{net}=(60kg \times (-1\frac{m}{s^2})) + (60kg \times 9.8\frac{m}{s^2})=528N$$The last two have a velocity as constant, which means your acceleration is 0:$$F_{net}=ma+mg \rightarrow 0+60kg \times 9.8\frac{m}{s^2}=588N$$