Answer:
a) T = 58.8 N ( with acceleration a= 0)
b) T= 76.8 N (up ward motion with acc a=3m/s)
c) T = 40.8 N (downward motion with acc -3m/s)
Step-by-step explanation:
The question exact statement is :
A 6kg bucket of water is being pulled straight up by a string at a constant speed. I determined that the tension on the string was F = ma
F = (6kg * 9.8 m/s2) , F = 58.8 N Now its asking At a certain point the speed of the bucket begins to change. The bucket now has an upward constant acceleration of magnitude 3 m/s2. What is the tension in the rope now? The correct answer was "about 78N" then Now assume that the bucket has a downward acceleration, with a constant acceleration of magnitude3 m/s2. Now what is the tension in the rope?
Solution:
a) Motion with constant speed
Mass of bucket= m 6 kg
Weight force of body =mg= 6×9.8=58.8 N
Speed is constant so a=0 m/sec2
So net force is tension
T in the string
and
weight mg of the body!
Net force is;
T-mg =ma (When bucket move up tension will greater than weight - so we subtract small force from bigger force)
==> T-58.8=6×0=0
==> T = 58.8 N
b) When bucket rise up with acceleration a
Here again;
m= 6 kg
g= 9.8 m/sec2
and a= 3 m/sec2
Again net force is
Tension=T
Weight = mg = 538.8N
So, net force is
T-mg = ma
==> T-58.8=6×3
==> T = 18+58.8=76.8 N
c) When bucket comes down with acceleration a
Again
m= 6 kg
g= 9.8 m/sec2
and a= - 3 m/sec2 ( because now acceleration is in opposite direction)
Again net force is
Tension=T
Weight = mg = 58.8N
So, net force is
T-mg = ma
==> T-58.8=6 × (-3)
==> T= -18 +58.8
==> T = 40.8 N