Question

A 5.0 kg block hangs from the ceiling by a mass-less rope. A Second block with a mass of 10.0 kg is attached to the first block and hands below it on another piece of mass-less rope. What is the tension in the first rope? And what is the tension in the second rope?

Answer 1

The first rope's tension supports both masses:

T - (5.0 kg + 10.0 kg) g = 0   ===>   T = 147 N

The second rope's tension supports the second mass:

T - (10.0 kg) g = 0   ===>   T = 98 N

Answer 2

The tension in the first and second rope are; 147 Newton and 98 Newton respectively.

Given the data in the question

• Mass of first block; $m_1 = 5.0kg$

• Mass of second block, $m_2 =10kg$

• Tension on first rope; $T_1 =\ ?$

• Tension on second rope; $T_2 =\ ?$

To find the Tension in each of the ropes, we make use of the equation from Newton's Second Laws of Motion:

$F = m\ *\ a$

Where F is the force, m is the mass of the object and a is the acceleration ( In this case the block is under gravity. Hence ''a" becomes acceleration due to gravity  $g = 9.8m/s^2$ )

For the First Rope

Total mass hanging on it; $m_T = m_1 + m_2 = 5.0kg + 10.0kg = 15.0kg$

So Tension of the rope;

$F = m\ * \ g\\\\F = 15.0kg \ * 9.8m/s^2\\\\F = 147 kg.m/s^2\\\\F = 147N$

Therefore, the tension in the first rope is 147 Newton

For the Second Rope

Since only the block of mass 10kg is hang from the second, the tension in the second rope will be;

$F = m\ * \ g\\\\F = 10.0kg \ * 9.8m/s^2\\\\F = 98 kg.m/s^2\\\\F = 98N$

Therefore, the tension in the second rope is 98 Newton

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