Question

A mass weighing 25N is suspended from a cord which can be moved vertically, up or down. What are the conclusions regarding the directions and magnitude of acceleration and velocity of the mass wehn the cord tension is (a)25N, (b)15N, (c)35N?

Answer 1

so
from the figure we can write--\[mg=T+ma \rightarrow ma=mg-T\]\[a=\frac{ mg-T }{ m }\]

Answer 2

now consider the first case when
T=25N which is equal to the weight
so\[T=mg\]
\[a=\frac{ mg-mg }{ m }=0\]

Answer 3

now for the second case T=15 N
\[a= (25N -15N)/ [25N/g]=3.92 m/s^2\]
and acceleration in this case acts downward

Answer 4

and for case 3 when T=35 N
\[a=(35N -25N)/ (25N/g)=+3.92m/\sec^2\]
and here acceleration acts upward