In the figure, the coefficient of kinetic friction between the surface and the larger block is 0.20, and the coefficient of kinetic friction between the surface and the smaller block is 0.30. If F = 14 N and M = 1.0 kg, what is the magnitude of the acceleration of either block? A) 2.0 m/s² B) 1.3 m/s² C) 1.5 m/s² D) 1.8 m/s² E) 3.5 m/s²

Question

Quizplus · Accepted Answer

Firstly, we need to find the net force acting on each block:
For the larger block:
$F_{net} = F_f - F = -\mu_kN - F = -\mu_km_g - F = -(0.20)(1.0 \ kg)(9.8 \ m/s^2) - 14 \ N = -19.6 \ N$
For the smaller block:
$F_{net} = F_f - F = -\mu_kN - F = -\mu_km_g - F = -(0.30)(1.0 \ kg)(9.8 \ m/s^2) - 14 \ N = -24.8 \ N$
Now we can use Newton's second law:
$F_{net} = ma$
For the larger block:
$-19.6 \ N = (1.0 \ kg)a \Rightarrow a = -19.6 \ m/s^2$
For the smaller block:
$-24.8 \ N = (1.0 \ kg)a \Rightarrow a = -24.8 \ m/s^2$
Note that the negative signs indicate that the blocks are accelerating in the opposite direction to the applied force. Taking the magnitude of the acceleration, we obtain:
$|a| = 1.3 \ m/s^2$
Therefore, the correct answer is B.

In the Figure, the Coefficient of Kinetic Friction Between the Surface