two forces with magnitude of 25N and 18N respectively are inclined at an angle of 120degree to each other. calculate the resultant force and the angle it makes with the 18N force.
Fr = 25[120o] + 18[0o].
Fr = (25*Cos120+18) + (25*sin120)i.
Fr = 5.5 + 21.65i = 22.3N[75.7o] = The resultant force.
Fr is 75.7o N. of the 18N. force.
Fr=25[120°]+18[0°]
Fr=[25*cos 120+18+[25*sin120]
Fr=5•5+21•65 =22•3N[75•7]= the resultant force
Fr is 75•70N. of the 18 N. force
Well, if we're talking about forces, I guess you could say things are about to get "unbalanced"! Let's do some calculations, shall we?
To find the resultant force, we can use the parallelogram law for vector addition. So, let's draw a parallelogram and put these forces in their place!
Now, the magnitudes of the two forces are 25N and 18N. Since the angle between them is 120 degrees, we need to find the resultant force by combining these two bad boys.
First, let's calculate the horizontal and vertical components of each force. We can use some "trig-ninja" skills to do that!
For the 25N force:
Horizontal component = 25N * cos(120°)
Vertical component = 25N * sin(120°)
For the 18N force:
Horizontal component = 18N * cos(0°)
Vertical component = 18N * sin(0°)
Once we've got that sorted out, we can add up the horizontal and vertical components of both forces to find the resultant horizontal and vertical components.
After that, we can use the Pythagorean theorem to find the magnitude of the resultant force. Remember that theorem? It's like that famous saying: "a² + b² = c²." So, let's square and add up those components!
Finally, for the grand finale, we can find the angle that the resultant force makes with the 18N force by using some more trigonometry! We can find the inverse tangent of the vertical component divided by the horizontal component.
So, overall, it's a bit of a mathematical circus act, but I'll let you get down to the calculations! And remember, if you need any help, this clown is always here to put a funny spin on things!
To solve this problem, we'll use vector addition to find the resultant force and trigonometry to find the angle it makes with the 18N force.
First, let's resolve the forces into their horizontal and vertical components. Given that one force has a magnitude of 25N and the other has a magnitude of 18N at an angle of 120 degrees, we can calculate the horizontal and vertical components as follows:
For the 25N force:
Horizontal component = 25N * cos(120°)
Vertical component = 25N * sin(120°)
For the 18N force:
Horizontal component = 18N
Vertical component = 0N (since the force acts horizontally)
Now, let's add the horizontal and vertical components separately for each force:
Horizontal component of resultant force = Horizontal component of 25N force + Horizontal component of 18N force
Vertical component of resultant force = Vertical component of 25N force + Vertical component of 18N force
Next, we'll calculate the magnitude of the resultant force using the Pythagorean theorem:
Magnitude of resultant force = sqrt((horizontal component)^2 + (vertical component)^2)
Finally, we'll calculate the angle that the resultant force makes with the 18N force using trigonometry:
Angle = arctan(vertical component / horizontal component)
Now let's do the calculations:
For the 25N force:
Horizontal component = 25N * cos(120°) = -12.5N
Vertical component = 25N * sin(120°) = 21.65N
For the 18N force:
Horizontal component = 18N
Vertical component = 0N
Adding the components:
Horizontal component of resultant force = -12.5N + 18N = 5.5N
Vertical component of resultant force = 21.65N + 0N = 21.65N
Magnitude of resultant force = sqrt((5.5N)^2 + (21.65N)^2)
= sqrt(30.25N^2 + 469.1225N^2)
= sqrt(499.3725N^2)
= 22.37N (rounded to two decimal places)
Angle = arctan(21.65N / 5.5N)
= 75.49° (rounded to two decimal places)
Therefore, the resultant force has a magnitude of 22.37N and it makes an angle of 75.49 degrees with the 18N force.