Question
A man weighs 70 kg. He stands on a weighing scale in a lift which is moving:
(a) upwards with uniform speed of 10m/s,
(b) downwards with uniform acceleration of 5 m/s2 and
(c) upwards with uniform acceleration of 5 m/s2.
What would be the reading on the scale in each case?
(d) What would be the reading, if the lift mechanism failed and it hurtled down freely under gravity?
Solution
We know the apparent weight of body in the lift is given by,
W = m(g+a)
where the positive sign stands for lift acceleration in vertically upward direction and the negative sign stands, if lift accelerates in vertically downward direction.
(a) Since lift moves with uniform velocity,
therefore a = 0
∴ W = 70(9.8+0) = 686N
(b) Since lift accelerates in downward direction with acceleration
∴ W = 70 (9.8 - 5) = 336 N
(c) Since lift accelerates in vertically upward direction with acceleration
∴ W = 70 (9.8 - 5) = 1036 N
When lift falls freely, the acceleration of lift in verticlly downward direction is![<pre>uncaught exception: <b>mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied</b><br /><br />in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56<br />#0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array)
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∴ W = 70(9.8 - 9.8) = 0 N
W = m(g+a)
where the positive sign stands for lift acceleration in vertically upward direction and the negative sign stands, if lift accelerates in vertically downward direction.
(a) Since lift moves with uniform velocity,
therefore a = 0
∴ W = 70(9.8+0) = 686N
(b) Since lift accelerates in downward direction with acceleration
∴ W = 70 (9.8 - 5) = 336 N
(c) Since lift accelerates in vertically upward direction with acceleration
∴ W = 70 (9.8 - 5) = 1036 N
When lift falls freely, the acceleration of lift in verticlly downward direction is
∴ W = 70(9.8 - 9.8) = 0 N
