Question

A simple Atwood's machine uses a massless pulley and two masses m1 and m2. Starting from rest, the speed of the two masses is 5.3 m/s at the end of 4.4 s. At that time, the kinetic energy of the system is 42 J and each mass has moved a distance of 11.66 m. Find the value of the heavier mass m2. The acceleration due to gravity is 9.81 m/s². Answer in units of kg.

Answer 1

To find the value of the heavier mass in an Atwood machine, you can use the equations for acceleration and tension, as well as the kinetic energy equation. Rearrange the equations to isolate the unknown mass and solve for its value.

Step-by-step explanation:

In an Atwood's machine, the acceleration of the system can be found using the equation:

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

where a is the acceleration, m1 is the mass of one object, m2 is the mass of the other object, and g is the acceleration due to gravity.

To find the tension in the string, we can use the equation:

T = m1(a + g)

where T is the tension in the string.

In this case, we are given the values of a, m1, and the kinetic energy of the system. We can use the kinetic energy equation (KE = (1/2)(m1 + m2)v^2) to find the value of m2. Rearranging the equation, we have:

m2 = (2KE / v^2) - m1