Question

What is the tension in string number 1 if the mass of m1 is 4.0 kg and the mass of m2 is 1.0 kg?

Answer 1

The tension in string number 1 when the mass of
`\(m_1\)` is 4.0 kg and the mass of
`\(m_2\)` is 1.0 kg is 39.2 N.

Step-by-step explanation:

To determine the tension in string number 1, we need to consider the forces acting on the system. In this setup, two masses
`\(m_1\) and \(m_2\)`are connected by a string passing over a pulley. When solving for tension, we take into account the gravitational force acting on each mass.

The tension in the string can be calculated using the formula:

`\[T = m_1 \cdot g - m_2 \cdot g\]`

where
`\(T\)` is the tension,
`\(m_1\)` is the mass of the first object,
`\(m_2\)` is the mass of the second object, and
`\(g\)` is the acceleration due to gravity (approximately 9.8 m/s²).

For the given masses, with
`\(m_1\) as 4.0 kg and \(m_2\)` as 1.0 kg, substituting the values into the formula:

`\[T = (4.0 \, \text{kg} * 9.8 \, \text{m/s}^2) - (1.0 \, \text{kg} * 9.8 \, \text{m/s}^2)\]`

`\[T = 39.2 \, \text{N} - 9.8 \, \text{N}\]`

`\[T = 29.4 \, \text{N}\]`

However, this is the tension in string number 2. To find the tension in string number 1, the value of tension is the same due to the nature of the pulley system. Therefore, the tension in string number 1 is also 39.2 N.