Question

A solid, frictionless cylinder reel of mass M = 3.13 kg and radius R = 0.437 m is used to draw water from a well (see Figure (a)). A bucket of mass m = 2.04 kg is attached to a cord that is wrapped around the cylinder. (Indicate the direction with the sign of your answer.)

(a) Find the tension T in the cord and acceleration a of the bucket.

T =	N
a =	m/s2

(b) If the bucket starts from rest at the top of the well and falls for 2.84 s before hitting the water, how far does it fall?
m

Answer 1

The tension we calculate as follows:

$T=mg\rightarrow T=(2.04)*(9.8)\rightarrow T=19.99N$

Using Newton's second law, we have the acceleration is:

$\sum F_{y}=mg-T=ma$

$a=\frac{mg-T}{m}\rightarrow (T=mg)\rightarrow a=0$

b)

$s=\frac{1}{2}g(s)^{2}$ $s=\frac{1}{2}(9.8)(2.84)^{2}$ $s=39.52m$