An 800 N gorilla swings from vine to vine. As the gorilla grabs a new vine, both vines form an angle of 30o with the vertical. What is the net force on each vine?

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To find the net force exerted on each vine, we need to split the force into its horizontal and vertical components.

Since both vines form an angle of 30 degrees with the vertical, this means that the angle between the force and the vertical is also 30 degrees.

We can start by finding the vertical component of the force. To do this, we can use the formula:

Vertical Component = Force * sin(θ)

Where:
- Force is the magnitude of the force exerted on the vine
- θ is the angle between the force and the vertical

Plugging the values into the formula, we get:

Vertical Component = 800 N * sin(30°)

Using a scientific calculator, we find that sin(30°) is approximately 0.5.

Vertical Component = 800 N * 0.5 = 400 N

Therefore, the vertical component (net force) exerted on each vine is 400 N.

Next, we can find the horizontal component of the force. Following a similar process, we can use the formula:

Horizontal Component = Force * cos(θ)

Plugging the values into the formula, we get:

Horizontal Component = 800 N * cos(30°)

Using a scientific calculator, we find that cos(30°) is approximately 0.87.

Horizontal Component = 800 N * 0.87 ≈ 696 N

Therefore, the horizontal component (net force) exerted on each vine is approximately 696 N.

To summarize:
- The net force exerted vertically on each vine is 400 N.
- The net force exerted horizontally on each vine is approximately 696 N.