5.13 A man of mass 70 kg stands on a weighing scale in a lift which is moving

(a) Upwards with a uniform speed of 10 m s^-1

 

(b) Downwards with a uniform acceleration of 5 m s^-2

 

(c) Upwards with a uniform acceleration of 5 m s^-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?

<p>The mass of the man, m = 70 kg, g = 10 m/s2, Let W be the reading on the weighing scale</p><p><strong> (a)</strong> When the lift is moving upward with uniform speed of 10 m/s, the acceleration = 0</p><p>The value of W is given by W = mg = 70&nbsp;<span title="Click to copy mathml"><math><mo>*</mo><mn>10</mn></math></span>&nbsp;= 700 N</p><p>&nbsp;</p><p><strong> (b)</strong> The lift is moving downward with acceleration, a = 5m/s²Using Newton's 2nd law of motion, the equation of motion can be written as W + MA = mg or W = m (g-a)</p><p>= 70&nbsp;<span title="Click to copy mathml"><math><mo>*</mo></math></span>&nbsp; (10-5) = 350 N</p><p>&nbsp;</p><p><strong> (c)</strong> The lift is moving upward with acceleration of a =5m/s². Using Newton's 2nd law</p><p>W = m (g+a) = 70&nbsp;<span title="Click to copy mathml"><math><mo>*</mo><mo> (</mo><mi></mi><mn>10</mn><mo>+</mo><mn>5</mn><mo>)</mo></math></span>&nbsp;= 1050 N</p><p>&nbsp;</p><p><strong> (d)</strong> If the lift mechanism fails, the lift will come down with acceleration due to gravity, a = g</p><p>W = m (g –a) = 0. This is the state of weightlessness</p>

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