Two ropes are attached a wagon one horizontal to the west with a tension force of 75N and other east and at an angle of 38 degrees upward from horizontal with a lension force of 125 N Find the components of the net force on the cart Show your work

The components of the net force on the cart are 23.5 Newton and 76.96 Newton.

Given the following data:

To find the components of the net force on the cart:

First of all, we would determine the horizontal component of the force acting due east.

Next, we would find the resultant horizontal forces:

Therefore, the horizontal component of the net force acts in the opposite direction due east.

Horizontal component of the net force = 23.5 Newton

For the vertical component of the net force:

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The components of the net force acting on the cart are;

Horizontal force, Fₓ ≈ 23.5 N acting east

The vertical force, ≈ 76.96 N

Explanation:

The parameters given in the question are;

The magnitude of the force on the rope acting horizontally to the west = 75 N

The magnitude of the force on the other rope east acting at an angle to the horizontal = 125 N

The angle to the horizontal of the force on the other rope east to the horizontal = 38°

Therefore, we have;

The horizontal component of the force acting east = 125 × cos(38°) ≈ 98.5 N

The net sum of the horizontal forces, ∑Fₓ noting that the horizontal forces are acting in opposite direction is given as follows;

∑Fₓ = 75 - 125 × cos(38°) = 75 - 98.3 = -23.5N

Given that the difference in forces is negative, and hat we took the force acting east as negative, we have that the net horizontal force is acting east with a horizontal component of 23.5N

The net vertical force, ∑F, is given as follows;

∑F = 125 × sin(38°) ≈ 76.96 N

Therefore, the components of the net force acting on the cart are;

Horizontal force, Fₓ ≈ 23.5 N, the vertical force, ≈ 76.96 N