Question

The Atwood machine consists of two masses hanging from the ends of a rope that passes over a pulley. Approximate the pulley as a uniform disk with mass mp = 6.33 kg and radius rp = 0.450 m. The hanging masses are ml = 21.7 kg and mr = 14.5 kg. Calculate the magnitude of the masses' acceleration (a) and the tension in the left and right ends of the rope, tl and tr, respectively.

Answer 1

The acceleration of the masses in the Atwood machine can be calculated using Newton's second law, and the tension in the rope is computed through the individual forces on each mass, with equations adjusted for the mass of the pulley.

Step-by-step explanation:

The problem you've described involves calculating the acceleration of the masses and the tension in the rope of an Atwood machine. To solve this, consider the following:

• Let m1 be the mass on the left (m1 = 21.7 kg) and m2 the mass on the right (m2 = 14.5 kg).
• The acceleration of the system is found using Newton's second law: m1g - m2g = (m1 + m2 + mp)a, where mp is the mass of the pulley and g is the acceleration due to gravity.
• To calculate the tension in the rope, consider the individual forces on each mass: T - m1g = m1a for the heavier mass and m2g - T = m2a for the lighter mass.

To find tl and tr, you need to apply these equations separately to each side of the rope considering the direction of acceleration for each mass.