Question

Two ropes are attached to a wagon, one horizontal to the left with a tension force of 30 n, and the other right and at an angle of 30° above the horizontal and a tension force of 40 n. the cart moves directly to the right. find the horizontal component of the net force on the cart. show all your work.

Answer 1

The horizontal component of the net force on the cart is approximately 4.64 N to the right, calculated by subtracting the 30 N leftward force from the horizontal component of the 40 N force that is acting at a 30° angle above the horizontal.

Step-by-step explanation:

To find the horizontal component of the net force on the cart, we need to consider both the horizontal tension of 30 N to the left and the horizontal component of the 40 N force acting at a 30° angle above the horizontal to the right. For the second rope, we use trigonometry to find the horizontal component:

Horizontal component of the 40 N force = 40 N × cos(30°)

If we calculate this, we get:

40 N × cos(30°) = 40 N × (\(√3\)/2) ≈ 34.64 N

Now, we subtract the leftward force from the rightward horizontal component to find the net horizontal force:

Net horizontal force = 34.64 N - 30 N = 4.64 N to the right

Therefore, the horizontal component of the net force on the cart is approximately 4.64 N to the right.