Question

A spring scale reads in kg. Two masses are at rest. The string is massless and the pulley is frictionless. Assume that m = 3 kg. Calculate the tension in the string connecting the two masses. Include the forces acting on each mass and how they contribute to the tension.

Answer 1

The tension in a string connecting two masses in a system with a frictionless pulley and massless string is equivalent to the weight of the hanging mass when in static equilibrium, calculated as T = m2g.

Step-by-step explanation:

To calculate the tension in a string connecting two masses in a system consisting of a frictionless pulley, we apply Newton's second law. If we have masses m1 and m2, and m2 is hanging while m1 rests on a surface then:

• For mass m1 (on a surface), the forces are tension T and friction (which is zero).
• For mass m2 (hanging), the forces are tension T and the weight of the mass (m2g).

In static equilibrium, the tension T will equal the weight of the hanging mass because there's no acceleration, so T = m2g.

For example, if m1 = 5.00 kg, m2 = 3.00 kg, and g = 9.8 m/s2, the tension T in the string would be T = m2g = 3.00 kg * 9.8 m/s2 = 29.4 N. Thus, the tension in the string connecting two masses in static equilibrium is equivalent to the weight of the hanging mass alone.