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?

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)

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

step-by-step explanation:

we are given

we have to simplify it

firstly, we will factor it

now, we can cancel like terms

now, we can combine it

so, we get

what are the options.

explanation: