Question

As seen from above, a stubborn stump is pulled by a pair of ropes, each with a force of 200 n, but at different angles as shown. from greatest to least, rank the net forces on the stumps.

Answer 1

The net forces on the stubborn stump, ranked from greatest to least, are as follows:

1. The net force when both ropes are pulling vertically (400 N).

2. The net force when one rope is at a 60° angle (173.2 N).

3. The net force when one rope is at a 30° angle (100 N).

Step-by-step explanation

(1)In the scenario where both ropes are pulling vertically, the full force of each rope contributes to the net force. The vertical components add up, resulting in a net force of
`\(F_{\text{net, vertical}} = 200 \, \text{N} + 200 \, \text{N} = 400 \, \text{N}\).`

(2)Similarly, when one rope is at a 60° angle, the vertical component
`(\(F_{\text{vertical}} = 200 \, \text{N} \cdot \sin(60)\))` contributes to the net force, resulting in
`\(F_{\text{net, 60}} \approx 173.2 \, \text{N}\).`

(3)When one rope is at a 30° angle, only the vertical component
`(\(F_{\text{vertical}} = 200 \, \text{N} \cdot \sin(30)\))` contributes to the net force. The calculation yields
`\(F_{\text{net, 30}} \approx 100 \, \text{N}\).`

Therefore, the ranking from greatest to least is 1.
`\(F_{\text{net, vertical}}\),` 2.
`\(F_{\text{net, 60}}\), and 3. \(F_{\text{net, 30}}\).`

Understanding the components of force in each scenario allows us to accurately rank the net forces on the stubborn stump, considering the angles at which the ropes are pulling.