Lauren is pulling on a trunk with a 15-N force. Wayne pulls at right angles to Lauren. With how much force must Wayne pull to make the resultant force on the trunk 22 N? Round answer to one decimal place.
X^2 + Y^2 = R^2,
(15)^2 + Y^2 = (22)^2,
Y^2 = (22)^2 - (15)^2 =259,
Y = 16.1N.
To find out how much force Wayne must pull to make the resultant force on the trunk 22 N, we can use the Pythagorean theorem.
Let's assume that Wayne's force is represented by the variable F. Since Wayne is pulling at right angles to Lauren, his force will be perpendicular to hers. Therefore, we can form a right triangle using the 15 N force and Wayne's force.
According to the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the hypotenuse represents the resultant force on the trunk, which is 22 N.
So our equation becomes:
(15 N)^2 + F^2 = (22 N)^2
Simplifying the equation:
225 N^2 + F^2 = 484 N^2
Rearranging the equation to solve for F:
F^2 = 484 N^2 - 225 N^2
F^2 = 259 N^2
Taking the square root of both sides:
F = √259 N
Rounding the answer to one decimal place:
F ≈ 16.1 N
Therefore, Wayne must pull with approximately 16.1 N of force to make the resultant force on the trunk 22 N.
To find the force with which Wayne must pull to make the resultant force on the trunk 22 N, we can use vector addition.
Let's assume Lauren's force is acting in the positive x-direction (horizontally) with a magnitude of 15 N. Since Wayne is pulling at a right angle to Lauren, his force will be acting in the positive y-direction (vertically). We'll denote Wayne's force as Fy.
Since the two forces are acting at right angles, we can use the Pythagorean theorem to find the magnitude of the resultant force:
Resultant force (Fr) = √(Fx^2 + Fy^2)
We know that the resultant force is 22 N, so we have:
22 N = √(15 N^2 + Fy^2)
Simplifying the equation, we get:
484 N^2 = 225 N^2 + Fy^2
Subtracting 225 N^2 from both sides, we have:
Fy^2 = 484 N^2 - 225 N^2
Fy^2 = 259 N^2
Taking the square root of both sides, we find:
Fy ≈ √259 N ≈ 16.1 N
Wayne must pull with a force of approximately 16.1 N to make the resultant force on the trunk equal to 22 N.