Two forces are simultaneously acting on a 4.0 kg object on top of a frictionless surface. The forces are 12 N upward and 16 N to the right, yielding a net force as shown in the figure. What is the magnitude of the net force F?
F = sqrt(F1^2+F2^2).
To find the magnitude of the net force, we can use the Pythagorean theorem since the forces are perpendicular to each other.
Let's label the upward force as F1 = 12 N and the rightward force as F2 = 16 N.
The net force F can be found using the equation:
F^2 = F1^2 + F2^2
Substituting the values:
F^2 = (12 N)^2 + (16 N)^2
F^2 = 144 N^2 + 256 N^2
F^2 = 400 N^2
Taking the square root of both sides:
F = √400 N^2
F = 20 N
Therefore, the magnitude of the net force F is 20 N.
To find the magnitude of the net force, we can use the Pythagorean theorem. The net force vector is the resultant of the two given forces, one going upward and the other going to the right.
Let's label the upward force as F1 and the force to the right as F2. We have F1 = 12 N and F2 = 16 N.
Using the Pythagorean theorem, the magnitude of the net force (F) is given by:
F = sqrt(F1^2 + F2^2)
Substituting the values of F1 and F2 into the equation:
F = sqrt((12 N)^2 + (16 N)^2)
Simplifying:
F = sqrt(144 N^2 + 256 N^2)
F = sqrt(400 N^2)
F = 20 N
Therefore, the magnitude of the net force F is 20 Newtons.