Final answer:
To solve for the acceleration and tension in the Atwood machine, we use Newton's second law for both masses then add the resulting equations to eliminate tension and solve for acceleration, which is then used to find the tension.
Step-by-step explanation:
The student asks about an Atwood's machine with masses of 5 kg on the left side and 6 kg on the left side. To find the acceleration a of the system and the tension T in the string, we can use Newton's second law for each mass (m1 and m2) and solve for these variables. For the left mass (m1 = 5 kg), the only forces acting on it are gravity (m1g) downward and tension (T) upward. For the mass on the right (m2 = 6 kg), the forces are gravity (m2g) downward and tension (T) upward as well.Assuming no friction and a massless string and pulley, the net force on m1 is T - m1g, and on m2 it is m2g - T. Since the acceleration is the same for both masses (the string is assumed inextensible), we can write these two equations:
- T - m1g = m1a
- m2g - T = m2a
By adding these two equations, we eliminate T, and we can solve for the acceleration a of the system.
The tension T can then be found by substituting the value of a back into one of the equations. For m1 = 5 kg and m2 = 6 kg:
- a = (m2 - m1)g / (m1 + m2)
- T = m1(g + a)
Finally, by plugging in the values for g (9.8 m/s2), m1, and m2, we can calculate both the acceleration and tension.