In order to get up and down the wall in Game of thrones, a mechanical elevator m

Question

In order to get up and down the wall in Game of thrones, a mechanical elevator
must be used. Suppose that Samwise hops into the elevator with John Snow. John
snow who knows nothing, cannot gure out how much counter weight they need
to put-on the other side of the elevator to make their side move. Samwise however
gets motion sickness, and will vomit if the elevator accelerates any faster than 2.0
m=s2. If John Snow has a mass of 75kg and Samwise has a mass of 140 kg, how
much mass must they put on the other side to make the elevator accelerate at the
desired maximum rate. Note that the acceleration due to gravity is the same in the
seven kingdoms.

Explanation / Answer

Let the Counter mass they need to add = mc
Weight of Samwise, M = 140 Kg
Weight of Jonsnow, m = 75 Kg

Max Acceleration, a = 2 m/s^2

T - (M+m)*g = (M+m)*a
T - (140+75)*g = (140 + 75)*2
T = 215* (2+9.8) N
T = 2537 N

mc*g - T = mc*a
mc (g - a) = T
mc = 2537 /(9.8 - 2)
mc = 325.25 Kg
Mass = 325.25 Kg
Counter Weight they need to add, = 325.25 * 9.8 N = 3187.5 N

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