1. two ropes are attached to a wagon, one horizontal to the west with a tension force of 20 n, and the other east and at an angle of 30° northward and a tension force of 50 n. find the components of the net force on the cart. show all your work.

The horizontal and vertical components of the net force of the given ropes are;

Horizontal component of Net force = 23.3 i^

Vertical component of net force = 25 j^

We are given;

Tension in Rope 1; T₁ = 20 N

Tension in Rope 2; T₂ = 50 N

      We are told that The tension in Rope 1 is horizontal to the east. Thus;

Horizontal component of T₁ = -20 i^

      The Tension in rope 2 is acting at an angle of 30° northward. Thus;

Horizontal component of T₂ = (50 cos 30)i^

Vertical component of T₂ = (50 sin 30)j^  

Net force = Sum of vertical component + sum of horizontal components

F_net = (50 sin 30)j^  + ((50 cos 30)i^ + (-20 i^)

This will be simplified to get;

F_net = 25 j^ + (43.3 - 20)i^

F_net = 23.3 i^ + 25 j^

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The resultant force of the two ropes on the given cart is 68.1 N.

The given parameters;

The net horizontal component force on the cart is calculated as follows;

∑Fₓ = Fₓ₁  + Fₓ₂

∑Fₓ = 20 x cos(0)  +  50 x cos(30)

∑Fₓ = 20  +  43.3

∑Fₓ = 63.3 N

The net vertical component of the force on the cart;

The resultant force on the cart is calculated as follows;

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