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

To solve this problem, we need to resolve the force F into two components: one parallel to the incline and one perpendicular to the incline. The force perpendicular to the incline will be cancelled out by the normal force of the incline on the block, since the surface is frictionless. The force parallel to the incline will cause the block to accelerate.

We can use trigonometry to find the parallel component of F: F_parallel = F * sin(30°) = 12.5 N

We can then use Newton's second law (F = ma) to find the acceleration: 
F_parallel = ma 
12.5 N = 3.0 kg * a 
a = 4.17 m/s^2

However, we need to make sure to take the component of acceleration parallel to the incline, since the total acceleration will have a component perpendicular to the incline (due to gravity) which does not contribute to the motion of the block up the incline.

The component of acceleration parallel to the incline can be found using trigonometry: 
a_parallel = a * sin(30°) = 2.5 m/s^2

Therefore, the magnitude of the resulting acceleration of the block is 2.5 m/s^2, which is closest to choice A (2.3 m/s^2).

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