Answer to Question #248576 in Civil and Environmental Engineering for bogus

Question

The sketch shows an object of mass 10 kg resting on a smooth plane at 25° to the horizontal. The 10 kg mass is attached to a hanging mass of 1 kg by a light cord passing over a light, frictionless pulley at the top of the plane. Determine the direction of movement when the masses are released and then use Newton’s second law to calculate the acceleration of the system and the tension in the cord.

Answer 1

Newton's second law equation (F_net = m•a) can be applied to both diagrams in order to write two equations for the two unknowns. The F_net will be expressed as the force in the direction of the acceleration minus the one that opposes it. 

$1.960 - F_{tens} = 0.2000(a)$

$F_{tens} - 0.490 = 0.0500(a)$

Now that the acceleration has been found from Equations, its value can be substituted into first Equation in order to determine the tension.

$F_{tens} = 0.0500 \times(5.88)+0.490$

$F_{tens }= 0.784 N$