Question

Three blocks of masses 1.0, 2.0, and 4.0 kilograms are connected by massless strings, one of which passes over a frictionless pulley of negligible mass. What is the complete question?

Answer 1

The acceleration of the blocks can be found by setting up and solving equations using the concept of tension in strings. The tension in the rope can be determined by substituting the acceleration value into one of the tension equations. The hanging mass does not hit the floor in this scenario.​

Step-by-step explanation:

In this question, we have three blocks of masses 1.0 kg, 2.0 kg, and 4.0 kg connected by massless strings over a frictionless pulley. The system is in equilibrium, which means the net force on each block is zero. We can use Newton's second law and the concept of tension in strings to determine the tension and acceleration of the blocks.

1. The acceleration of the system can be found by comparing the forces acting on the blocks. Taking the downward direction as positive, the equations for the two blocks are:
   (1.0 kg block):
   T - 1.0 kg * g = (1.0 kg * a) => T = 1.0 kg * g + 1.0 kg * a
   (4.0 kg block):
   T - 4.0 kg * g = (4.0 kg * a) => T = 4.0 kg * g + 4.0 kg * a
   Since both equations are equal to tension (T), we can equate them: 1.0 kg * g + 1.0 kg * a = 4.0 kg * g + 4.0 kg * a. Solving for acceleration (a), we get a = (4.0 kg * g - 1.0 kg * g) / (1.0 kg + 4.0 kg).
2. To find the tension in the rope, we can substitute the acceleration value obtained in the previous step into one of the equations for tension:
   T = 1.0 kg * g + 1.0 kg * a.
3. Since the system is in equilibrium, the hanging mass will not hit the floor as it starts from rest. Hence, the speed with which the hanging mass hits the floor is 0 m/s.