A block is pushed across a horizontal surface by the force shown.If the coefficient of kinetic friction between the block and the surface is 0.30,F = 20 N,θ = 30°,and M = 3.0 kg,what is the magnitude of the acceleration of the block? A)2.8 m/s² B)2.3 m/s² C)1.8 m/s² D)3.3 m/s² E)5.4 m/s²

Question

Quizplus · Accepted Answer

First, we need to resolve the applied force F into its horizontal component: Fcosθ = 20N × cos30° = 17.3N.
Then we need to calculate the force of friction between the block and the surface: Ff = μkN = 0.30 × (3.0kg × 9.81m/s^2) = 8.83N.
The net force acting on the block in the horizontal direction is: Fnet = Fa – Ff = 17.3N – 8.83N = 8.47N.
Finally, we can calculate the acceleration of the block using Newton's second law: Fnet = ma, so a = Fnet/m = 8.47N/3.0kg = 2.8 m/s^2.
Therefore, the correct answer is choice C, 1.8 m/s^2.

A Block Is Pushed Across a Horizontal Surface by the Force