A man of mass 70 kg, stands on a weighing machine in a lift, which is moving (a) upwards with a uniform speed of 10 ms-1. (b) downwards with a uniform acceleration of 5 ms-2. (c) upwards with a uniform acceleration of 5 ms-2. What would be the readings on the scale in each case? (d) What would be the reading if the lift mechanism failed and it hurtled down freely under gravity?
(a). As the lift is moving at a uniform speed, acceleration a=0 R=mg=70×10⇒700N Reading on the weighing scale =700/g=700/10=70kg (b) Mass of the man, m=70kg Acceleration, a=5m/s2 downward Using Newtons second law of motion, we can write the equation of motion as: R+mg=maR=m(g−a)=70(10−5)=70×5=350N Reading on the weighing scale ⇒350g=350/10=35kg (c) Mass of the man, m=70kg Acceleration, a=5m/s2 upward Using Newtons second law of motion, we can write the equation of motion as: R−mg=maR=m(g+a)=70(10+5)=70×15=1050N Reading on the weighing scale ⇒1050/g=1050/10=105kg (d) When the lift moves freely under gravity, acceleration a=g Using Newtons second law of motion, we can write the equation of motion as: R+mg=ma =m(g−g)=0 Reading on the weighing scale =0/g=0kg The man will be in a state of weightlessness.
