How long will it take for the heavier mass to reach the floor? What will be the speed of the two masses when the heavier mass hits the floor?

Question

An Atwood’s machine has masses of 100 g and 110 g. The lighter mass is on the floor and the heavier mass is 75 cm above the floor.

Julia Aguilar · Accepted Answer

#t approx 1.83s#

#v approx 0.82 ms^(-1)# If we say that the heavier mass is #m_2# and the lighter is #m_1#, and we idealise so that, for instance the pulley has no inertia, then the magnitude of the acceleration of the masses is: #a = g cdot (m_2 - m_1)/(m_2 + m_1) =g /22# In terms of tile, the relevant equation of motion for the heavier mass (at constant acceleration) is: #x = ut + 1/2 a t^2# #t = sqrt((2x)/a)# #t = sqrt((2 cdot 0.75)/(g/22)) approx 1.83s# In terms of velocity, the relevant equation of motion for the heavier mass (at constant acceleration) is: #v^2 = u^2 + 2 ax# #v= sqrt(2 ax)# #= sqrt(2 (g/22) 0.75) approx 0.82 ms^(-1)#

Carson Alexander · Answer

undefined The time it takes for the heavier mass to reach the floor depends on the specifics of the situation, such as the height from which the masses are dropped and the gravitational acceleration. However, assuming both masses are dropped simultaneously from the same height, they will reach the floor at the same time, regardless of their mass.

When the heavier mass hits the floor, both masses will have the same speed, assuming there is no air resistance. This is because they experience the same gravitational acceleration and fall the same distance in the same amount of time, resulting in identical final speeds.