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 7.7 m/s at the end of 4.3 s. at that time, the kinetic energy of the system is 96 j and each mass has moved a distance of 16.555 m. find the value of heavier mass. the acceleration due to gravity is 9.81 m/s 2 . answer in units of kg.

Answer 1

1.9 kg First, let's determine the acceleration the masses underwent. That would be the velocity divided by the time, so: 7.7 m/s / 4.3 s = 1.790697674 m/s^2 Now, let's calculate the total mass in motion. The formula for kinetic energy is E = 0.5 M V^2 So solve for M, substitute the known values and calculate. E = 0.5 M V^2 2E = M V^2 2E/V^2 = M 2*96J/(7.7 m/s)^2 = M (192 kg*m^2/s^2)/(59.29 m^2/s^2) = M 3.238320121 kg = M We now need to calculate how many newtons it takes to accelerate 3.238320121 kg of mass at 1.790697674 m/s^2. Since a newton is kg*m/s^2 and we have 2 values, one of kg and the other of m/s^2, that indicates that to get kg*m/s^2 is a simple matter of multiplication. So: 3.238320121 kg * 1.790697674 m/s^2 = 5.798852308 kg*m/s^2 Now how much mass would we need under gravitational acceleration to get 5.798852308 Newtons? That will be a bit of division. So: 5.798852308 kg*m/s^2 / 9.81 m/s^2 = 0.591116443 kg Finally, we simply need to distribute 3.238320121 kg of total mass between m1 and m2 such that m1 has 0.591116443 kg more mass than m2. So: m1 = 3.238320121 kg/2 + 0.591116443 kg/2 m2 = 3.238320121 kg/2 - 0.591116443 kg/2 m1 = 1.619160061 kg + 0.295558222 kg m2 = 1.619160061 kg - 0.295558222 kg m1 = 1.914718282 kg m2 = 1.323601839 kg So m1 masses 1.914718282 kg and m2 masses 1.323601839 kg. To verify. Let's check that their sums and differences are correct. Sum: 1.914718282 kg + 1.323601839 kg = 3.238320121 kg. Correct value Difference: 1.914718282 kg + 1.323601839 kg = 0.591116443 kg. Correct value Rounding to 2 significant figures gives the heavier mass a value of 1.9 kg