Two ropes are attached to a wagon, one horizontal to the west with a tension force of 40 N and the other east at an angle of 23° northward and a tension force of 50 N. Find the components of the net force on the cart

F = -40 + 50[23o]

X = -40 + 50*Cos23 = 6.02 N.
Y = 50*sin23 = 19.5 N.

To find the components of the net force on the cart, we need to break down the forces into their horizontal and vertical components.

1. Horizontal component:
The force acting horizontally to the west is 40 N. This force points in the negative x-direction.

2. Vertical component:
The force acting at an angle of 23° northward has a tension force of 50 N. We need to resolve this force into its vertical component.

The vertical component (Fv) can be found using the formula:
Fv = F * sin(θ)

Where F is the given force and θ is the angle.

Fv = 50 N * sin(23°)
Fv = 50 N * 0.3907
Fv ≈ 19.54 N

Therefore, the vertical component of the net force on the cart is approximately 19.54 N upwards.

So, the components of the net force on the cart are:
Horizontal component: 40 N (to the west)
Vertical component: 19.54 N (upwards)

To find the components of the net force on the cart, we need to break down the forces acting on the cart into their horizontal and vertical components.

Let's start by representing the horizontal force as Fx, and the vertical force as Fy.

Given:
- The horizontal force (west) = 40 N (acting to the left)
- The angled force (east at an angle of 23° northward) = 50 N

To find the horizontal component of the angled force (Fxa), we can use trigonometry. The horizontal component can be calculated using the formula: Fxa = F * cos(theta), where F is the magnitude of the force and theta is the angle it makes with the horizontal.

Fxa = 50 N * cos(23°)
Fxa ≈ 45.77 N (acting to the right)

To find the vertical component of the angled force (Fya), we can also use trigonometry. The vertical component can be calculated using the formula: Fya = F * sin(theta), where F is the magnitude of the force and theta is the angle it makes with the horizontal.

Fya = 50 N * sin(23°)
Fya ≈ 21.21 N (upward)

Combining the horizontal forces:
Net horizontal force (Fx) = Fx1 + Fxa = 40 N - 45.77 N
Net horizontal force (Fx) ≈ -5.77 N (acting to the left)

Combining the vertical forces:
Net vertical force (Fy) = Fy1 + Fya = 0 N + 21.21 N
Net vertical force (Fy) ≈ 21.21 N (upward)

Therefore, the components of the net force on the cart are approximately -5.77 N horizontally (to the left) and 21.21 N vertically (upward).