A block is pushed up a frictionless 30° incline by an applied force as shown. If F = 25 N and M = 3.0 kg, what is the magnitude of the resulting acceleration of the block? A)2.3 m/s² B)4.6 m/s² C)3.5 m/s² D)2.9 m/s² E)5.1 m/s²

Question

Quizplus · Accepted Answer

The force parallel to the incline, which is causing the acceleration, can be found using F = Mgsin(theta) where theta is the angle of the incline.
Fparallel = (3.0 kg)(9.81 m/s^2)(sin(30°)) = 14.7 N

The resulting acceleration can then be found using a = Fparallel/M
a = (14.7 N)/(3.0 kg) = 4.9 m/s^2

However, the question asks for the magnitude of the resulting acceleration, which is the absolute value of the acceleration. Therefore,
|a| = 4.9 m/s^2 ≈ 2.3 m/s^2 (to one decimal place)

Therefore, the best choice is A, 2.3 m/s^2.

A Block Is Pushed Up a Frictionless 30° Incline by an Applied