Dynamics

Dynamics

Blocks of mass mA=6 kg and mB=4 kg subjected to a force of 25 N.
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.

Solution
Blocks A of 0.35 kg and B of 1.15 kg connected by rope and drawn by force of 15 N.
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 \( g=10\;{\text{m/s}}^{2} \).

Solution
Block A on a horizontal surface connected by a rope through a pulley to a suspended block B.
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 \( g=10\;\text{m/s}^{2} \).

Solution
Block B of mass 2 kg connected on both sides to a block A of mass 5 kg and to a block C of mass 3 kg.

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 \( g=10\;\text{m/s}^{2} \),

Solution
Atwood machine with block A of mass 6.25 kg and block B with mass of 6.75 kg.
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) \( F=1200\;\text{N} \).

Solution
Atwood machine subjected to force F with masses of mA=24 kg and mB=40 kg.