### Dynamics

*Dynamics*

Two blocks of masses
\( m_{\text{A}}=0.35\;\text{kg} \)
and
\( m_{\text{B}}=1.15\;\text{kg} \)
are on a frictionles horizontal surface, the blocks are connected by a rope with negligible mass. A horizontal
force of constant intensity equal to 15 N is applied by pulling the two blocks. Find the magnitude acceleration
acquired by the system and the tension in the rope connecting the blocks.

In the system of the figure, the body

*A*slides on a horizontal surface without friction, dragged by body*B*that moves downward. Bodies*A*and*B*are attached to each other by a rope of negligible mass parallel to the surfacee and passing through a frictionless pulley of negligible mass. The masses of*A*and*B*are respectively 32 kg and 8 kg. Find the acceleration of the system and the tension on the cord. Assume \( g=10\;{\text{m/s}}^{2} \).
In the system of the figure, the body

*B*slides on a horizontal surfacee without friction, it is connected through by ropes and pulleys, lightweight and frictionless, with two bodies*A*and*C*that move vertically. The masses of*A*,*B*and*C*are respectively 5 kg, 2 kg and 3 kg. Find the acceleration of the system and the tension on the cord. Assume \( g=10\;\text{m/s}^{2} \).*Atwood Machine*

An Atwood machine has masses of
\( m_{\text{A}}=6.25\;\text{kg} \)
and
\( m_{\text{B}}=6.75\;\text{kg} \)
are connected by an weightless cord, through an pulley frictionless. Find:

a) The acceleration of the system;

b) The tension in the rope connecting the masses;

c) The tension in the rope that holds the system to the ceiling.

Assume the free-fall acceleration \( g=10\;\text{m/s}^{2} \),

a) The acceleration of the system;

b) The tension in the rope connecting the masses;

c) The tension in the rope that holds the system to the ceiling.

Assume the free-fall acceleration \( g=10\;\text{m/s}^{2} \),

In an Atwood machine the two bodies, at rest on a horizontal surface, are connected by a cord, of negligible
mass, that passes over a frictionless pulley of negligible mass. The masses are
\( m_{\text{A}}=24\;\text{kg} \)
and
\( m_{\text{B}}=40\;\text{kg} \)
and the free fall acceleration
\( g=10\;\text{m/s}^{2} \).
Find body accelerations when:

a) \( F=400\;\text{N} \);

b) \( F=720\;\text{N} \);

c) \( F=1200\;\text{N} \).

a) \( F=400\;\text{N} \);

b) \( F=720\;\text{N} \);

c) \( F=1200\;\text{N} \).