Please explain thoroughly and please don\'t skip any steps Consider this Atwood
ID: 1528874 • Letter: P
Question
Please explain thoroughly and please don't skip any steps
Consider this Atwood machine (two masses M1 = 5 kg, M2 = 7 kg and g = 9.80 m/s2 and a simple pulley). The masses begin at the same height, at rest. They are released and allowed to move distances d = 1.5 m, one up, one down, after which time their speeds are vf .
Find vf , the speed of the pair of comoving masses at the instant that the they have displaced as described.
Find the string tension on M1 by computing the work that it does on M1.
M. M,Explanation / Answer
acceleration of the atwood machine is given as
a = (M2 - M1) g /(M2 + M1)
a = (7 - 5) (9.8) /(7 + 5)
a = 1.6 m/s2
consider the motion for block of mass M2 going down
Y = displacement = 1.5 m
Vo = initial speed = 0 m/s
Vf = final speed
using the equation
Vf2 = Vo2 + 2 a Y
Vf2 = 02 + 2 x 1.6 x 1.5
Vf = 2.2 m/s
work done by tension force = change in kinetic energy + potential energy gained
T d = (0.5) M1 Vf2 + M1 gd
T (1.5) = (0.5) (5) (2.2)2 + 5 x 9.8 x 1.5
T = 57.2 N