Question

A woman weighing 75 kg stands on a spring scale in elevator. During the first 3 seconds of motion from rest, the tension T in the hoisting cable is 8300 N. The total mass of the elevator , woman scale is 750 kg.

1.Find the vertical acceleration of the elevator.

2.Find the reading R of the scale in Newtons during this interval.

3.Find the upward velocity of the elevator at the end of a 3 seconds.

Answer 1

1. Apply Newton's first law:

$$ma=T-mg,\\\space\\ a=\dfrac Tm-g=\dfrac{8300}{750}-9.8=1.27\text{ m/s}^2.$$

2. The reading of the scale:

$$R=m_w(g+a)=75(9.8+1.27)=830\text{ N}.$$

3. Use a formula from kinematics:

$$v=at=3.81\text{ m/s}.$$