Question

1. draw a force diagram for the bucket of water that is being raised from the well at a constant velocity.

force diagram:
sign conventions:
sum of forces equation(s):
\\(\sum f_x =\\)
\\(\sum f_y =\\)
system schema:
( bucket )
subscript definitions:

Explanation:

Step1: Analyze horizontal forces

Since the bucket is moving vertically (raised from the well), there are no horizontal forces acting on it. So, \(\sum F_{x}=0\)

Step2: Analyze vertical forces

The bucket is moving at a constant velocity. According to Newton's first law (\(F = ma\), and \(a = 0\) for constant velocity), the net force in the vertical direction is zero. The upward force \(T\) (tension in the rope) and the downward force \(mg\) (weight of the bucket - water system) act on the bucket. So, \(\sum F_{y}=T - mg=0\)

Answer:

\(\sum F_{x}=0\)
\(\sum F_{y}=T - mg = 0\)