Question

How much force must be exerted through the wire rope that moves the car in an elevator given that the car masses 501kg and there are 7 people average mass 75 kg and that the friction in the guide along the shaft average 205N. when
a) the car is accelerating upward at 1.00m/s^2?
b) the car is moving upward and slowing down at the equivalent rate?

Answer 1

Point y-axis up, then the force of friction and force of gravity both look down (negative).

a) Here the acceleration is positive (it looks up). According to Newton's second law:

$$Ma=-f-Mg+F,\\ F=Ma+f+Mg=M(g+a)+f=\\=(501+7\cdot75)(9.8+1)+205=11285.8\text{ N}.$$

b) In this case everything's the same, but the acceleration $a$ is directed downward:

$$-Ma=-f-Mg+F,\\ F=f+Mg-Ma=M(g+a)+f=\\=205+(501+7\cdot75)(9.8-1)=92338\text{ N}.$$