Two packing crates of masses [tex]m_1 = 10.0 \, \text{kg}[/tex] and [tex]m_2 = 5.00 \, \text{kg}[/tex] are connected by a light string that passes over a frictionless pulley. The 5.00 kg crate lies on a smooth incline of angle [tex]43.0^\circ[/tex].

Find the acceleration of the 5.00 kg crate and the tension in the string.

To find the acceleration of the 5.00 kg crate and the tension in the string, we need to apply Newton's second law and consider the forces acting on the system.

The gravitational force acting on the 5.00 kg crate can be resolved into two components: one perpendicular to the incline (mg*cos(43.0°)) and one parallel to the incline (mg*sin(43.0°)).

The tension in the string is in the same direction as the force parallel to the incline.

Since the system is connected by a light string, the tension in the string is the same on both sides. Therefore, the tension in the string can be considered as the force accelerating the 5.00 kg crate.

Using Newton's second law, we can set up equations for the acceleration of the system and the tension in the string. Considering the net force along the incline, we have: m2*g*sin(43.0°) - T = m2*a.

Considering the net force perpendicular to the incline, we have: m2*g*cos(43.0°) = m2*g.

By solving these equations simultaneously, we can find the values of acceleration (a) and tension (T). Plugging in the given values, we find that the acceleration of the 5.00 kg crate is 4.22 m/s² and the tension in the string is 46.9 N.

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