# the maximum and minimum magnitude of the resultant of two forces are 16 N and 4N.calculate t he magnitude of individual force.

chukkaiwar rohit
14 Points
11 years ago

max resultant of two forces x and yy is x+y and min of the two forces is x-y

x+y=16

x-y=4

=>x=10N y=6N

Saurabh Anand
38 Points
11 years ago

let the two vector be a and b then maxm resultant would be a+b=16 and minm resultant would be a-b=4...solve these two eqns and u will get the answer i.e. 10 and 6...

Akash Kumar Dutta
98 Points
11 years ago

10,6

larisha sharma
18 Points
11 years ago

but for adding 2 vector ..formula is[ a2 + b2 +2abcos thetA]^1/2    OVER HERE WE DO NOT KNOW THETA

Saurabh Anand
38 Points
11 years ago

??but for adding 2 vector ..formula is[ a2 + b2 +2abcos thetA]^1/2    OVER HERE WE DO NOT KNOW THETA...

see in case of maxm resultant we take theta equals to 0degree i.e. cos(theta)=1

n in case of minm resultant we take theta = 180 degree i.e. cos(theta)=-1

SOURAV MISHRA
37 Points
11 years ago

CLEARLY YOU HAVE TO SOLVE A SYSTEM OF SIMULTANEOUS EQUATIONS. THIS IS VERY EASY AND I WILL MENTION THE ANSWER DIRECTLY.

THE GREATER ONE IS 10N AND THE SMALLER ONE IS 6N.

Suraj Tamang
14 Points
9 years ago
See, maximum resultant will be produced when angle between the two forces are 0o so cos 0 = 1
therefore, the resultant equation will give you (a + b)2 i.e R = a + b
and mimimum resultatn  will be produced when the two forces are actining  on the opposite direction ie angle between them is 180o, so cos 180 = – cos 0 = -1 that gives you R = a – b then solve the simple simultanius equation a + b = 16 and a – b = 4.
Suraj Tamang
14 Points
9 years ago
See, maximum resultant will be produced when angle between the two forces are 0o so cos 0 = 1
therefore, the resultant equation will give you (a + b)2 i.e R = a + b
and mimimum resultatn  will be produced when the two forces are actining  on the opposite direction ie angle between them is 180o, so cos 180 = – cos 0 = -1 that gives you R = a – b then solve the simple simultanius equation a + b = 16 and a – b = 4.
4 years ago
Dear student,

Let the forces be F1 and F2, where F1 > F2
Now the maximum resultant is possible when both the forces act in the same direction, i.e. Fres = F1 + F2
Hence, F1 + F2 = 16
Now the minimum resultant force is possible when forces act in opposite direction, i.e. Fres = F1 – F2
Hence, F1 – F2 = 4
Solving the two equations, we get
F1 = 10 N
F2 = 6 N

Thanks and regards,
Kushagra