Question

Find the resultant R of the following forces all acting on the same point in the given directions: 30lb northeast; 70 lb to the south; and 50 lb 20 degrees north of west.

Answer 1

net force is 40.8 Lb in direction 50.8 degree South of West

Step-by-step explanation:

As we know that the three forces are given as

F1 = 30 lb North East

F2 = 70 lb South

F3 = 50 lb at 20 degree North of West

Now we can write in vector form as

`F_1 = 30 sin45 \hat i + 30 cos45 \hat j`

`F_1 = 21.2 \hat i + 21.2 \hat j`

`F_2 = -70 \hat j`

`F_3 = -50 cos20\hat i + 50 sin20 \hat j`

`F_3 = -47\hat i + 17.1 \hat j`

now the net force due to above all

`F = F_1 + F_2 + F_3`

`F = (21.2 - 47)\hat i + (21.2 - 70 + 17.1)\hat j`

`F = -25.8 \hat i - 31.7 \hat j`

magnitude of net resultant force is

`F = √(25.8^2 + 31.7^2)`

`F = 40.8 Lb`

direction of the force is along

`\theta = tan^(-1)((31.7)/(25.8))`

`\theta = 50.8 degree`

So net force is 40.8 Lb in direction 50.8 degree South of West