Question

Two forces with magnitudes of 150 and 100 pounds act on an object at angles of 30° and 120°, respectively. Find the direction and magnitude of the resultant force. Round to two decimal places in all intermediate steps and in your final answer.

Answer 1

Explanation:

Fx = 150cos30 +100cos120

= 150(0.866)+100(-0.5) =129.9-50=79.9 pounds

and

Fy= 150sin30+100sin120

= 150(0.5) +100(0.866)= 75+ 86.6 =161.6 pounds

The magnitude of the resultant is sqrt of (Fx^2 +Fy^2) which is equal to the sqrt of (79.9)^2+(161.6)^2 = 180.27 lbs

the direction of the resultant is by the given arctan Fy/Fx =arctan 161.6/79.9= 63.69 deg

Answer 2

Resultant = 180.27 pounds

direction is 63.69 degrees

Explanation:

We have to resolve the x and y component of both forces with respect to given angles

Fx = 150cos30 +100cos120

= 150(0.866)+100(-0.5) =129.9-50=79.9 pounds

and

Fy= 150sin30+100sin120

= 150(0.5) +100(0.866)= 75+ 86.6 =161.6 pounds

Magnitude of the resultant is =
`√(Fx^2+Fy^2)`

=
`√((79.9)^2+(161.6)^2)`

= 180. 27 pounds

Direction of the resultant is given by arctan(
`(Fy)/(Fx)`

arctan(
`(161.6)/(79.9)`

=63.69 degrees