Two forces 5N and 10N act on a body in the direction due North and east respectively at an angle 75 degree. Calculate the resultant force of the inclined angle.
Hmmm. Due north and east respecdtively at an angle of 75deg? N and E are at 90 deg
5N+10N= 15N
F=ma
15N=m10kg
15/10kg=m10kg/10kg
1.5kg=0
1.5kg=m
Using parallelogram law:
R2=p2+r2-2pq cos 180-ø
=25+100-2*5*10 cos 180-75=105
=125-100(-0.2588)
=125+25.88
R2=150.88
R=√150.88=12.3
To calculate the resultant force of the inclined angle, we need to use vector addition. Here are the steps to find the resultant force:
Step 1: Represent each force as a vector.
The force of 5N acting due North can be represented as a vector with a magnitude of 5N pointing upward.
The force of 10N acting due East can be represented as a vector with a magnitude of 10N pointing to the right.
Step 2: Resolve the vectors into their horizontal and vertical components.
To find the horizontal and vertical components of the 5N vector, we can use trigonometry. Since the angle is 75 degrees and the force is acting due North, the vertical component (Vy) will be 5N * sin(75°) and the horizontal component (Vx) will be 5N * cos(75°).
Similarly, the horizontal component (Hx) of the 10N vector will be 10N * cos(0°) and the vertical component (Hy) will be 10N * sin(0°).
Step 3: Add the horizontal and vertical components separately.
Add the horizontal components: Hx + Vx = 10N * cos(0°) + 5N * cos(75°).
Add the vertical components: Hy + Vy = 10N * sin(0°) + 5N * sin(75°).
Step 4: Calculate the magnitude of the resultant force.
The magnitude of the resultant force (R) can be found using the Pythagorean theorem:
R = √(Rx^2 + Ry^2), where Rx is the sum of the horizontal components and Ry is the sum of the vertical components.
Step 5: Calculate the direction of the resultant force.
The direction of the resultant force can be found using the inverse tangent function:
θ = tan^(-1)(Ry/Rx).
Using these steps, you can calculate the resultant force and its inclined angle.