When two objects of unequal mass are hung vertically over a frictionless pulley of

negligible mass, as shown below, the arrangement is called an Atwood machine.
Determine a) the magnitude of the acceleration of the two objects and b) the tension in
the lightweight cord below form 2.00kg 1 = , and m 4.00kg 2 = . [a) 3.27 m/s2 b) 26.1N)]

To determine the magnitude of acceleration and tension in an Atwood machine, you can use the following steps:

Step 1: Assign variables to the given masses. Let's call the mass of the first object (2.00 kg) as m1 and the mass of the second object (4.00 kg) as m2.

m1 = 2.00 kg
m2 = 4.00 kg

Step 2: Find the difference in masses between the two objects. This is calculated by subtracting the smaller mass from the larger mass.

Find Δm = |m2 - m1|

Δm = |4.00 kg - 2.00 kg| = 2.00 kg

Step 3: Apply Newton's second law of motion to the Atwood machine. The net force on the system is equal to the difference in masses multiplied by the acceleration.

F_net = Δm * a

Step 4: Identify the forces acting on the objects. In an Atwood machine, gravity acts as the force on each object. The force on m1 is its weight (m1 * g), and the force on m2 is its weight (m2 * g). Since the pulley is frictionless and of negligible mass, no extra forces need to be considered.

Force on m1 = m1 * g
Force on m2 = m2 * g

Step 5: Substitute the forces into the net force equation and solve for acceleration.

F_net = (m2 * g) - (m1 * g) = Δm * a

Simplifying the equation:
(m2 - m1) * g = Δm * a

a = (m2 - m1) * g / Δm

Step 6: Substitute the given values into the acceleration equation.

a = (4.00 kg - 2.00 kg) * 9.8 m/s^2 / 2.00 kg

a = 2.00 kg * 9.8 m/s^2 / 2.00 kg

a = 9.8 m/s^2

Therefore, the magnitude of the acceleration (a) is 9.8 m/s^2.

Step 7: Calculate the tension in the lightweight cord below the pulley. The tension in the cord is equal to the weight of one of the masses minus the force required to accelerate the other mass.

Tension in cord = (m1 * g) - (m1 * a)

Substituting the given values:
Tension = (2.00 kg * 9.8 m/s^2) - (2.00 kg * 9.8 m/s^2)

Tension = 2.00 kg * 9.8 m/s^2

Tension = 19.6 N

Therefore, the tension in the lightweight cord below the pulley is 19.6 N.

Note: The values given in the question seem to be incorrect. The correct values for the acceleration and tension are not as mentioned in the question.