A 3.18 kg. bucket of water is being lowered into a well. It is accelerating downwards at -0.54 m/s2. What is the upwards tension in the rope

ma=mg-T

T=m(g-a)

T=3.18(9.8-0.54)=29.45 N

160n

To find the upwards tension in the rope, we need to consider the forces acting on the bucket.

First, we need to calculate the gravitational force acting on the bucket, which is given by the formula:

Gravitational force = mass * acceleration due to gravity

Given that the mass of the bucket is 3.18 kg and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate:

Gravitational force = 3.18 kg * 9.8 m/s^2

Next, we know that the bucket is accelerating downwards at -0.54 m/s^2. This means there must be an additional force acting on the bucket in the upward direction. This force is provided by the tension in the rope.

So, by using Newton's second law of motion, which states that the net force on an object is equal to the mass of the object multiplied by its acceleration, we can determine the net force acting on the bucket:

Net force = mass * acceleration

Since the acceleration is negative (-0.54 m/s^2) and the mass is positive (3.18 kg), the net force will be negative as well, indicating that it acts in the opposite direction of the acceleration.

Now we can set up an equation:

Net force = gravitational force - tension

Plugging in the values we have:

-3.18 kg * -0.54 m/s^2 = (3.18 kg * 9.8 m/s^2) - tension

Simplifying the equation:

1.7172 N = 31.764 N - tension

Rearranging the equation to isolate tension:

tension = 31.764 N - 1.7172 N

tension = 30.0468 N

Therefore, the upwards tension in the rope is approximately 30.0468 Newtons.