find by calculation,the resultant two equal forces of 6N each acting at a 4N point at an angle of (a) 60 degree (b)120 degree with each other{hint cos120= -cos60 =1 and half or 1/2
a. F1 = 6N @ 0o, F2 = 6N @ 60o.
X = 6 + 6*Cos60 = 9.0 N.
Y = 0 + 4*sin60 = 3.46 N.
F1+F2 = X+Yi = 9 + 3.46i
Fr = 9 + 3.46i + 4 = 13 + 3.46i = 13.5 N
@ 14.9o
To find the resultant of two equal forces, we can use the concept of vector addition. The resultant can be calculated using the following formula:
Resultant = 2 * Force * cos(angle/2)
Let's calculate the resultant for both cases:
(a) When the angle is 60 degrees:
Resultant = 2 * 6N * cos(60/2)
= 2 * 6N * cos(30)
= 2 * 6N * (√3/2)
= 6N * √3
Therefore, the resultant of two equal forces of 6N each acting at a 4N point at a 60-degree angle is 6N * √3.
(b) When the angle is 120 degrees:
Resultant = 2 * 6N * cos(120/2)
= 2 * 6N * cos(60)
= 2 * 6N * (-1/2)
= 6N * (-1)
Therefore, the resultant of two equal forces of 6N each acting at a 4N point at a 120-degree angle is -6N.
So, the resultant is 6N * √3 when the angle is 60 degrees, and it is -6N when the angle is 120 degrees.