Newton's second law: The following four forces act on a 4.00 kg object: ₁ = 300 N east ₂ = 700 N north ₃ = 500 N west ₄ = 600 N south What is the acceleration of the object? A) 224 N in a direction 63.4° north of west B) 300 N in a direction 63.4° north of west C) 300 N in a direction 26.6° north of west D) 224 N in a direction 26.6° north of west E) 2100 N in a direction 26.6° north of west

Question

Quizplus · Accepted Answer

To find the acceleration of the object, we need to use Newton's second law which states that the net force on an object is equal to its mass times its acceleration, or F_net = ma.

First, we need to find the net force on the object by adding up all the given forces:

F_net = 300 N east + 700 N north + (-500 N west) + (-600 N south)
F_net = 500 N north

Note that we chose a northward direction to be positive, so the negative forces in the westward and southward directions subtract from the positive forces in the eastward and northward directions.

Now, we can use F_net = ma to solve for the acceleration:

a = F_net/m
a = (500 N north)/(4.00 kg)
a = 125 m/s^2 north

Finally, to express the answer in the given format, we need to find the magnitude and direction of the acceleration:

magnitude = |a| = 125 m/s^2
direction = arctan(a_y/a_x) = arctan(500 N/0 N) = 90° north of west

We can convert this to a direction angle north of due west by subtracting 90°:

direction angle = 90° - 90° = 0° west of north

Since we're looking for a direction angle north of west, we need to subtract this from 90°:

direction angle = 90° - 0° = 90° north of west

This is equivalent to a direction angle of 26.6° west of north, which is choice D.

Newton's Second Law: the Following Four Forces Act on a 4.00