Question

two masses are connected at two ends of a light inextensible string that passes over a frictionless pulley. the difference in their mass is 0.5kg. the system moves 10m in 2s starting from rest. what are the masses?

Answer 1

The masses of the two objects connected by a string passing over a frictionless pulley are approximately 0.52 kg and 1.02 kg, with the lighter being 0.52 kg and the heavier being 1.02 kg.

Step-by-step explanation:

To find the masses of the two objects connected by a light inextensible string passing over a frictionless pulley, we need to use the laws of motion and the relationship between acceleration, distance, and time. Given that one mass is heavier than the other by 0.5 kg and the system moves 10 m in 2 s starting from rest, we can apply the equations of motion to determine the acceleration:

a = 2s/t2 = (2*10 m) / (2 s)2 = 5 m/s2

Let m be the mass of the lighter object. Then, the mass of the heavier object is (m + 0.5) kg. Using Newton's second law (F = ma) and the fact that tension is equal on both sides of the pulley, we can set up the following equation:

(m + 0.5)g - mg = (m + m + 0.5)a

Solving for m yields:

m(g - a) = 0.5a

m = 0.5a / (g - a)

m = 0.5*5 / (9.8 - 5) = 2.5 / 4.8 ≈ 0.52 kg

Therefore, the lighter mass is approximately 0.52 kg, and the heavier mass is 1.02 kg.