Two kids are on a beach pulling an inner tube. One is pulling at a force of 45N[N] and the other one pulling at 60N[SW]. What is the net force? (I tried to do it by taking the 60N and making a right angled triangle with it, i got 42.43N north and west, then I tried to combine those results with the 45N north, i ended up with 42, but I'm not sure if it's right, or if i even did it right.)

Question

Two kids are on a beach pulling an inner tube. One is pulling at a force of 45N[N] and the other one pulling at 60N[SW]. What is the net force? (I tried to do it by taking the 60N and making a right angled triangle with it, i got 42.43N north and west, then I tried to combine those results with the 45N north, i ended up with 42, but I'm not sure if it's right, or if i even did it right.)

Answer 1

You basically have it right. Just perhaps not too clear about the direction and how to combine the two x- and y- components. Here's how it can be worked out:

Resolve all forces in the x- (east) and y- (north) directions.

F1=45N due north
=(0,45)
F2=60N due SW
=(-60cos(45°),-60sin(45°))
=(-42.4264,-42.4264) (approx.)

Net force
= F1+F2
= (0,45) + (-42.4264,-42.4264)
=(-42.4264,2.5736)
=√(-42.4264²+2.5736²) in the direction of atan2(2.5736,-42.4264)
=42.5N at S86.53°W

Answer 2

To find the net force, you need to break down the forces into their horizontal and vertical components. Let's break down each force separately.

For the 45N[N] force, since it acts vertically in the north direction, its vertical component is 45N.

For the 60N[SW] force, first, we need to find its horizontal and vertical components. To do that, you can use trigonometry. The force is acting in the southwest direction, which forms a 45-degree angle with the horizontal.

Using trigonometric ratios, we can determine that the horizontal component is 60N * cos(45°) ≈ 42.43N, and the vertical component is 60N * sin(45°) ≈ 42.43N.

Now, let's add up the horizontal and vertical components separately:

Horizontal Component:
45N + 42.43N = 87.43N (We don't need to specify the direction since the forces are acting in the same direction horizontally.)

Vertical Component:
45N + 42.43N = 87.43N (Since both forces are acting vertically in the same direction, the signs add up.)

Now, to find the net force, we can use the Pythagorean theorem. The net force is the vector sum of the horizontal and vertical components:

Net Force = √(87.43N)² + (87.43N)² ≈ √(7620.6549N² + 7620.6549N²) ≈ √(15241.3098N²) ≈ 123.35N

So, the net force is approximately 123.35N, which is the magnitude of the resultant force acting on the inner tube.