Answer:
Step-by-step explanation:
Graphic Method:
To solve this problem graphically, you will need to draw a vector diagram. Draw the two forces 10N and 20N as vectors originating from the same point, with the angle between the vectors being 60°. Then, draw the resultant vector that joins the tail of the first vector to the head of the second vector. The magnitude of the resultant vector is the magnitude of the resultant force.
Mathematical Method:
To solve this problem mathematically, you will need to use the law of cosines. The law of cosines states that:
R² = A² + B² - 2ABcosϴ
Where R is the magnitude of the resultant vector, A and B are the magnitudes of the two vectors, and ϴ is the angle between the two vectors.
So, in this case, R² = 10² + 20² - 2(10)(20)cos60°
R² = 100 + 400 - 400cos60°
R² = 500 - 200
R = √300
Therefore, the magnitude of the resultant vector is √300N.
If the two forces are now made to be inclined at 120° to each other, the law of cosines states that:
R² = A² + B² - 2ABcosϴ
Where R is the magnitude of the resultant vector, A and B are the magnitudes of the two vectors, and ϴ is the angle between the two vectors.
So, in this case, R² = 10² + 20² - 2(10)(20)cos120°
R² = 100 + 400 - 400cos120°
R² = 500 + 200
R = √700
Therefore, the magnitude of the new resultant vector is √700N.