Final answer:
To find the heavier mass in an Atwood's machine, calculate the total mass using kinetic energy and velocity, then use the acceleration to discriminate between the individual masses m1 and m2, taking into account the acceleration due to gravity.
Step-by-step explanation:
To find the value of the heavier mass in a simple Atwood's machine, we can use the given kinetic energy to determine the total mass, then use the acceleration to find the individual masses. The kinetic energy of the system, which is given as 89 J, is the sum of the kinetic energies of both masses, m1 and m2.
Since each mass moved 15.84 m in 4.4 s from the rest, we can calculate the acceleration (a) by using the formula:
s = 0.5 * a * t2, where s is the distance and t is the time.
The total kinetic energy (K.E. total) is given by the equation:
K.E. total = 0.5 * (m1 + m2) * v2
By rearranging the formula for total mass (m1 + m2) we get:
m1 + m2 = 2 * K.E. total / v2 = 2 * 89 J / (7.2 m/s)2
Using the calculated acceleration and the relationship of forces in an Atwood machine, we can solve for the mass of the heavier object (m2). The forces are m1*g - m2*g = (m1 + m2) * a, where g is the acceleration due to gravity. Rearranging this equation for m2 gives us:
m2 = (m1 * g + (m1 + m2) * a) / g
We can use these equations to calculate m1 and m2, with m2 being the heavier mass.