> restart;

> eq1:= F - mu*m2*g - T = m1*a;

> eq2:= T - mu*m2*g = m2*a;

> solve({eq1, eq2}, {a,T});

Do these formulas have the right behavior for reasonable assumptions of m1, m2, and mu.
For example, are the units correct? The answer here is yes, T has units of Newtons and
a has units of m/s^2 if standard units are used for F, m1, m2, and g. What happens if mu is
decreased to zero? or if m2 becomes very massive compared to m1? or m1 becomes very
massive compared to m2? For mu decreasing, the frictional force goes to zero so our solutions
should reflect that.

> assign(%);

> limit(T, mu=0);

> limit(a, mu=0);

These are indeed the correct limits for no friction. Without friction, the change in motion is just the external
force divided by the sum of the masses in the system.

> limit(a, m1=infinity);

As m1 gets very massive, the acceleration of the system tends toward 0.

> limit(a, F=2*mu*m2*g);

As the external force F approaches the same value as the frictional forces opposing it, the
acceleration slows until the system eventually stops. Since the frictional force depends on
m2, letting m2 get massive also eventually brings the acceleration to zero when F = 2*mu*m2*g.