In the figure below, two blocks are connected by a lightweight, flexible cord that passes over a frictionless pulley. If m1 = 2.97 kg and m2 = 5.48 kg, what are the accelerations of each block?

The problem involves two blocks connected by a cord and a pulley, with given masses m1 and m2. We can solve this problem using Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.

Step 1: Identify the forces acting on each block.

For m1, the forces are:

• The gravitational force (downwards): F1 = m1 * g
• The tension in the cord (upwards): T

For m2, the forces are:

• The gravitational force (downwards): F2 = m2 * g
• The tension in the cord (upwards): T

Step 2: Apply Newton's second law to each block.

For m1 (assuming upwards is positive):

• Net force = m1 * a1 = T - m1 * g

For m2 (assuming downwards is positive):

• Net force = m2 * a2 = m2 * g - T

Step 3: Since the cord is lightweight and flexible and the pulley is frictionless, the tension is the same throughout the cord and the accelerations of the two blocks are equal in magnitude but opposite in direction. Therefore, we can set a1 = -a2 = a.

Substitute these into the equations from step 2:

For m1:

• m1 * a = T - m1 * g

For m2:

• m2 * a = m2 * g - T

Step 4: Solve these two equations simultaneously to find a and T.

Add the two equations to eliminate T:

m1 * a + m2 * a = m2 * g - m1 * g a = (m2 * g - m1 * g) / (m1 + m2)

Substitute the given values m1 = 2.97 kg, m2 = 5.48 kg, and g = 9.8 m/s² (approximate value of the acceleration due to gravity on the surface of the Earth) into this equation to find the acceleration a.

Step 5: The acceleration of m1 is -a (upwards) and the acceleration of m2 is a (downwards).