Two forces act on a 16-kg object. The first force has a magnitude of 68 N and is directed 24° north of east. The second force is 32 N, 48° north of west. What is the acceleration of the object resulting from the application of these two forces to the object?
A) 1.6 m/s2, 5.5° north of east
B) 1.9 m/s2, 18° north of west
C) 2.4 m/s2, 34° north of east
D) 3.6 m/s2, 5.5° north of west
E) 4.1 m/s2, 52° north of east
Guide On Rating System
Vote
To find the acceleration of the object, we need to first find the net force acting on it by combining the two forces given.
First, we need to find the x and y components of each force:
For the first force:
Fx = 68 N * cos(24°) = 68 N * 0.9135 = 62.124 N
Fy = 68 N * sin(24°) = 68 N * 0.4067 = 27.606 N
For the second force:
Fx = 32 N * cos(48°) = 32 N * 0.6691 = 21.4912 N
Fy = 32 N * sin(48°) = 32 N * 0.7431 = 23.781 N
Now, we can find the net force in the x and y directions:
ΣFx = 62.124 N - 21.4912 N = 40.6328 N
ΣFy = 27.606 N + 23.781 N = 51.387 N
Now we can find the magnitude and direction of the net force:
|ΣF| = sqrt[ (40.6328 N)^2 + (51.387 N)^2 ]
|ΣF| ≈ 65.06 N
θ = atan(51.387 N / 40.6328 N) ≈ 50.37°
Now we can find the acceleration using Newton's second law:
a = ΣF / m = 65.06 N / 16 kg ≈ 4.07 m/s^2
Therefore, the acceleration of the object resulting from the application of these two forces is approximately 4.1 m/s^2, 50.37° north of east.
So the closest answer choice is:
E) 4.1 m/s2, 52° north of east
Got a question with my answer?
Cheapmath.com is completely free!
Asking question is free.
Getting answers is free.
+99