Question

A 100-kg block being released from rest from a height of 1.0 m. It then takes it 1.40 s to reach the floor. What is the mass m of the other block

Answer 1

Complete Question

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Answer:

The mass of the other block is  $m_1 = 81.14 \ kg$

Explanation:

From the question we are told that

   Mass of the first block is  $m_1 = 100 \ kg$

   The height is  $s = 1.0 \ m$

   The time it takes it is  $t = 1.40 \ s$

 Generally from kinematic equation

       $s = ut + \frac{1}{2} at^2$

Here u  is the initial velocity which zero given that it was at rest initially

So

     $s = 0 * t + \frac{1}{2} at^2$

=>  $s = \frac{1}{2} at^2$

=> $1 = \frac{1}{2}* a * (1.40 )^2$

=>  $a = 1.0204 \ m/s^2$

Generally from the diagram the resultant force due to the weight of the first object and the tension on the string is  mathematically represented as

      $mg - T = ma$

=>   $T = m g - ma$

=>   $T = m(g - a)$

=>   $T = 877.96 \ N$

Generally from the diagram the resultant force due to the weight of the second object and the tension on the string is  mathematically represented as  

     $T - m_1g = m_1 a$

=>   $877.96 = m_1 (a + g)$

=>   $877.96 = m_1 (1.0204 + 9.8 )$

=>   $m_1 = 81.14 \ kg$