A 5kg bucket of water is raised from a well with a rope. If the upward acceleration of the bucket is 3m/s/s, find the force exerted on the bucket by the rope.

Apply Newton's second law to the bucket's vertical motion:

F = ma

F = net force, m = mass of the bucket, a = acceleration of the bucket

Let us choose upward force to be positive and downward force to be negative. The net force F is the difference of the tension in the rope lifting the bucket and the weight of the bucket, i. e.:

F = T - W

F = net force, T = tension, W = weight

The weight of the bucket is given by:

W = mg

W = weight, m = mass, g = gravitational acceleration

Make some substitutions:

F = T - mg

T - mg = ma

Isolate T:

T = ma + mg

T = m (a+g)

Given values:

m = 5kg, a = 3m/s², g = 9.81m/s²

Plug in and solve for T:

T = 5 (3+9.81)

T = 64.05N