Two perpendicular displacements: 7 m south and 24 m east. Enter the resultant's magnitude in m.
Two ropes tow a cargo sled. One applies 30 N east, and the other applies 40 N north.
The two forces are perpendicular, and the sled responds to their combined effect.
In the vectors topic you combined perpendicular vectors with the Pythagorean theorem and found the resultant. The net force on an object is exactly that: the resultant of the forces acting on it.
Two perpendicular forces combine like any two perpendicular vectors: square each magnitude, add the squares, then square-root.
F_net = √(A² + B²)
For the sled: F_net = √(30² + 40²) = √(900 + 1600) = √2500. So F_net = 50 N.
The direction comes from the same triangle. The angle between the net force and the 30 N force is tan⁻¹(40/30), which is about 53°.
So the net force on the sled is 50 N at about 53° north of east.
The name is the only new thing. The vectors topic calls any vector sum a resultant. For the forces on one object, this course says net force. Same vector, two jobs for the word.
Two perpendicular forces act on a raft: 60 N east and 80 N north. Calculate the net force's magnitude and direction.
Write down the values in the question:
A = 60 N east
B = 80 N north
F_net = ?
Write down the equation:
F_net = √(A² + B²)
Substitute in the values:
F_net = √(60² + 80²)
F_net = √(3600 + 6400)
F_net = √10000
Simplify:
F_net = 100 N
Find the direction from the triangle:
angle north of east = tan⁻¹(80/60)
angle ≈ 53°
The net force is 100 N at about 53° north of east.
Two perpendicular forces act on a barrel: 50 N east and 120 N south. Calculate the net force's magnitude and direction.
Write down the values in the question:
A = 50 N east
B = 120 N south
F_net = ?
Write down the equation:
F_net = √(A² + B²)
Substitute in the values:
F_net = √(50² + 120²)
F_net = √(2500 + 14400)
F_net = √16900
Simplify:
F_net = 130 N
Find the direction from the triangle:
angle south of east = tan⁻¹(120/50)
angle ≈ 67°
The net force is 130 N at about 67° south of east.
Two perpendicular forces act on a crate: 9 N east and 12 N north. Enter the net force's magnitude in N.
Two perpendicular forces act on a canoe: 16 N east and 30 N south. Enter the net force's magnitude in N.
Two perpendicular forces act on a buoy: 40 N east and 9 N north. Enter the angle between the net force and the east direction, in degrees, to the nearest degree. Answers within 1° are accepted.
Two perpendicular forces act on a trailer: 20 N east and 48 N north. Enter the net force's magnitude in N.
A current drives a rowboat with a 36 N force east while the wind drives it with a 77 N force north. The two forces are perpendicular. Enter the net force's magnitude in N.
Two perpendicular forces act on a skiff: 24 N east and 45 N north. Enter the angle between the net force and the east direction, in degrees, to the nearest degree. Answers within 1° are accepted.