Question

Given two forces P and Q with magnitudes of 22 N and 17 N, and the angle between force Q and the resultant R is 30°, you need to:

1) Find the angle between force P and the resultant R.
2) Determine the magnitude of the resultant force R.

Answer 1

To find the angle between force P and the resultant R, we can use the trigonometric relationships between the forces. The angle between force Q and the resultant R is given as 30°. The angle between force P and the resultant R is found to be 210°. To determine the magnitude of the resultant force R, we can use the law of cosines. The magnitude of the resultant force R is found to be 11.14 N.

Step-by-step explanation:

To find the angle between force P and the resultant R, we can use the trigonometric relationships between the forces. The angle between force Q and the resultant R is given as 30°. Since the forces P and Q are added to give the resultant force, the angle between force P and resultant R can be found using the formula:

angle(P, R) = angle(Q, R) + angle(Q, P)

Substituting given values:

angle(P, R) = 30° + 180°

angle(P, R) = 210°

Therefore, the angle between force P and the resultant R is 210°.

To determine the magnitude of the resultant force R, we can use the law of cosines. The law of cosines states that the magnitude of the resultant force R is equal to:

|R| = sqrt(|P|^2 + |Q|^2 - 2|P||Q|cos(angle(P, Q)))

Substituting given values:

|R| = sqrt((22 N)^2 + (17 N)^2 - 2(22 N)(17 N)cos(30°))

|R| = sqrt(484 N^2 + 289 N^2 - 748 N^2 cos(30°))

|R| = sqrt(773 N^2 - 748 N^2 cos(30°))

|R| = sqrt(773 N^2 - 748 N^2 * 0.866)

|R| = sqrt(773 N^2 - 648.968 N^2)

|R| = sqrt(124.032 N^2)

|R| = 11.14 N

Therefore, the magnitude of the resultant force R is 11.14 N.