Final answer:
To find the tension in a string connected to two objects with different masses, one on a table and one hanging, free-body diagrams and Newton's second law are used to set up equations for both masses. However, the calculated tension of approximately 11.664 N doesn't match the provided options, so there may be an error in the options given or in the question's assumptions.
Step-by-step explanation:
To calculate the magnitude of the tension in the string holding a 3.6 kg object on a table and a 1.8 kg hanging object over a pulley with negligible friction, we will first use a free-body diagram (FBD) for each mass to identify the forces acting on them. Next, we'll apply Newton's second law (F = ma), where F stands for force, m for mass, and a for acceleration.
- For the hanging mass, we have the gravitational force (weight) Fg = m * g, where g is the acceleration due to gravity (9.8 m/s2), and the tension in the string, T. The net force Fnet = m * a = m * g - T.
- For the mass on the table, since friction is negligible, the only horizontal force is tension, so Fnet = m * a = T.
Because the system is connected by the same string, the acceleration and tension are the same for both masses.
Using these relations, we can set up the equations:
1.8 kg * a = 1.8 kg * 9.8 m/s2 - T
3.6 kg * a = T
Adding these two equations gives us:
1.8 kg * a + 3.6 kg * a = 1.8 kg * 9.8 m/s2
5.4 kg * a = 1.8 kg * 9.8 m/s2
a ≈ 3.24 m/s2
Now we can solve for T using the acceleration we just calculated:
3.6 kg * 3.24 m/s2 = T
T ≈ 11.664 N
However, since this result is not one of the options provided, it seems there may have been a miscalculation or the provided options may be incorrect. Without knowing the exact context or premise of the question, it's difficult to provide a strictly correct answer. If the question includes any additional information or constraints not considered here, they could significantly affect the result.