Only two forces act on a 3.0-kg mass. One of the forces is 9.0 N east, and the other is 8.0 N in the direction of 62° north of west. What is the magnitude of the acceleration of the mass? A) 2.0 m/s² B) 2.4 m/s² C) 3.3 m/s² D) 2.9 m/s² E) 5.7 m/s²

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Quizplus · Accepted Answer

To find the magnitude of the acceleration, we first need to find the resultant force acting on the mass. The forces can be broken down into their components:- The 9.0 N force is entirely in the east direction (x-axis).- The 8.0 N force at 62° north of west can be broken down into x and y components:  - $F_x = 8.0 \cos(62°)$ (west direction, so it will be negative when combined with the eastward force)  - $F_y = 8.0 \sin(62°)$ (north direction)Calculating these components:- $F_x = -8.0 \cos(62°) \approx -3.8$ N (west)- $F_y = 8.0 \sin(62°) \approx 7.1$ N (north)The net force in the x-direction (east-west) is:- $F_{net,x} = 9.0 - 3.8 = 5.2$ N (east)Since there's no other force in the y-direction in the problem statement, the net force in the y-direction is just $F_y = 7.1$ N (north).The magnitude of the net force is found using Pythagoras' theorem:- $F_{net} = \sqrt{F_{net,x}^2 + F_{y}^2} = \sqrt{5.2^2 + 7.1^2} \approx 8.7$ NFinally, using Newton's second law ($F = ma$), the magnitude of the acceleration ($a$) can be found by dividing the net force by the mass:- $a = \frac{F_{net}}{m} = \frac{8.7}{3.0} \approx 2.9$ m/s$^2$Therefore, the correct answer is D) 2.9 m/s$^2$.

Only Two Forces Act on a 3