When a 40-N force, parallel to the incline and directed up the incline, is applied to a crate on a frictionless incline that is 30° above the horizontal, the acceleration of the crate is 2.0 m / s 2 ,

Question

When a 40-N force, parallel to the incline and directed up the incline, is applied to a crate on a frictionless incline that is 30° above the horizontal, the acceleration of the crate is 2.0 m / s 2 , up the incline. The mass of the crate is

TestHub · Accepted Answer

Forces along the frictionless incline: the 40 N pull up the incline and the component mg sin $θ$ down the incline. Net force = ma:

$40 - mg sin 3 0^{\circ} = m \times 2.0$

$40 = m (2.0 + 9.8 \times \frac{1}{2}) = m (2.0 + 4.9) = 6.9 m$

$m = \frac{40}{6.9} \approx 5.8 kg$

Correct option: (C).

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