Question

Two forces act at a point in the plane. The angle between the two forces is given. Find the magnitude of the resultant force. forces of and ​newtons, forming an angle of

Answer 1

Answer:

F = 44.22 N

Explanation:

Let force 1, $F_1=19\ N$

Force 2, $F_2=32\ N$

The angle between forces, $\theta=118^{\circ}$

We need to find the magnitude of the resultant force. It is based on the law of cosines. The formula is given by :

$F^2=F_1^2+F_2^2-2AB\cos\theta\\\\F^2=(19)^2+(32)^2-2\times 19\times 32\times \cos(118)\\\\F=\sqrt{(19)^{2}+(32)^{2}-2\times19\times32\times\cos(118)}\\\\F=44.22\ N$

So, the magnitude of resultant force is 44.22 N.

Answer 2

Correct question: Two forces act on a point on the plane. The angle between the two forces is given. Find the magnitude of the resultant force. forces of 19 and 32 newtons, forming an angle of 118 degrees.

the magnitude of the resultant force is 28.53 N.

The resultant of the two vectors can be calculated using parallelogram theorem.

parallelogram theorem states that if two vectors are represented by the adjacent side of a parallelogram, the resultant of the vectors is the diagonal of the parallelogram drawn from the point of intersection of the vectors.

This can be expressed mathematically as

R² = P²+Q²-2PQcos(180-∅).............. Equation 1

Where R = resultant of the vectors, P and Q = the two vectors respectively, ∅ = angle between the vectors.

From the question,

Given: P = 19 N, Q = 32 N, ∅ = 118°

Substitute these values into equation 2

R² = 19²+32²-2×19×32cos(180-118)

R² = 361+1024-1216cos62°

R² = 1385-1216(0.4695)

R² = 1385-570.878

R² = 814.122

R = √(814.122)

R = 28.53 N

Hence, the magnitude of the resultant force is 28.53 N

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