Final answer:
The tension in the cable is equal to the weight of the hanging mass. Since the system is moving at a constant velocity, this tension matches the weight of the 5 kg mass on the table, which leads to the conclusion that the mass of the hanging block is also 5 kg.
Step-by-step explanation:
Given that the system is moving at a constant velocity, this indicates that the forces on the system are balanced. In the case of the 5 kg mass on a frictionless table connected to a cable and a hanging mass, the tension in the cable is equal to the weight of the hanging mass, as there is no acceleration (Newton's first law).
If we let m represent the mass of the hanging block and using the earth’s gravitational acceleration (g = 9.8 m/s²), the tension T in the rope will equal the weight of the hanging mass, which is m*g.
Since the system is moving at a constant velocity, the tension is also equal to the weight of the 5 kg mass on the table, which is 5 kg * 9.8 m/s².
Therefore, we have the equation m*g = 5 kg * 9.8 m/s².
To find the mass of the hanging block, we rearrange the equation to solve for m: m = (5 kg * 9.8 m/s²) / 9.8 m/s².
This simplifies to m = 5 kg.
Therefore, the mass of the hanging block must also be 5 kg.