The reseelteent of two forces p and 15N is 20N inclined at 60 to the 15N force. Find the magnitade and direction P.
To find the magnitude and direction of force P, we can use the principles of vector addition. Given that the resultant of forces P and 15N is 20N and that the angle between the resultant and the 15N force is 60 degrees, we can break down the problem into components.
Step 1: Resolve the 20N resultant force into its horizontal and vertical components.
The vertical component can be found by multiplying the magnitude of the resultant force (20N) by the sine of the angle between the resultant and the 15N force (60 degrees).
Vertical component = 20N * sin(60°)
The horizontal component can be found by multiplying the magnitude of the resultant force (20N) by the cosine of the angle between the resultant and the 15N force (60 degrees).
Horizontal component = 20N * cos(60°)
Step 2: Determine the vertical and horizontal forces caused by the 15N force.
The vertical component of the 15N force is calculated by multiplying the magnitude of the 15N force by the sine of the angle between the 15N force and the horizontal axis (90 degrees in this case).
Vertical component of 15N force = 15N * sin(90°)
The horizontal component of the 15N force is zero since the angle between the 15N force and the horizontal axis is 90 degrees.
Step 3: Calculate the vertical and horizontal components of force P.
Since the vertical components of both the resultant and the 15N force are equal, the vertical components of forces P and 15N must cancel each other out.
Vertical component of P = - Vertical component of 15N force
Now, we can calculate the horizontal component of force P by subtracting the horizontal component of the 15N force from the horizontal component of the resultant force.
Horizontal component of P = Horizontal component of resultant force - Horizontal component of 15N force
Step 4: Find the magnitude and direction of force P.
The magnitude of force P can be determined using the Pythagorean theorem:
Magnitude of P = sqrt[(Horizontal component of P)^2 + (Vertical component of P)^2]
The direction of force P can be found by calculating the angle between the horizontal axis and the resultant of forces P and 15N. Use the inverse tangent function:
Direction of P = atan(Vertical component of P / Horizontal component of P)
By following these steps and substituting the appropriate values into the equations, you can find the magnitude and direction of the force P.