A simple Atwood machine consists of two
masses m1 and m2 that
are connected by a string wound over a pulley, as seen in the
figure below. Assume m2 is larger
than m1. Motion in the upward direction is
positive. On a piece of paper, draw two free body diagrams; one for
each of the masses, showing all forces acting on each mass. Then
answer the following questions
(e) Write Newton's Second Law equation (in the
form Fnet = ma)
for m1 in
the y-direction. It is important to use the correct
signs for each of the forces. Motion in the upward direction is
positive and motion in the downward direction is negative. (Be sure
to enter your answer in the above form with the sum of the forces
in the left hand side answer box. The right hand side answer box
should have the appropriate form of ma. Use the
following as
necessary: a, f, FN, g, m1,
and T.)
Fnet
=
ma
_
=
_
(f) Write Newton's Second Law equation (in the
form Fnet = ma)
for m2 in
the y-direction. It is important to use the correct
signs for each of the forces. Motion in the upward direction is
positive and motion in the downward direction is negative. (Be sure
to enter your answer in the above form with the sum of the forces
in the left hand side answer box. The right hand side answer box
should have the appropriate form of ma. Use the
following as
necessary: a, f, FN, g, m2,
and T.)
Fnet
=
ma
_
=
_
(g) Use your answers from parts (e) and (f) to get an expression
for the magnitude of the tension T. (Use the
following as
necessary: m1, m2,
and g.)
T =
(h) Use your answers from parts (e), (f), and (g) to find the
magnitude of a, the acceleration of the system. (Use
the following as
necessary: m1, m2,
and g.)
a =
(j) Suppose m1 = 7 kg
and m2 = 11 kg. What is the
tension in the string?
T =
(k) Suppose m1 = 7 kg
and m2 = 11 kg. What is the
value of the acceleration?
a =
(l) Suppose that m2 starts from rest
at a height of 7 m. Use the kinematic equations to
determine how long it takes for m2 to
hit the ground.