Question

Little confused on this?:

Two paramedics are carrying a person on a stretcher. Paramedics 1 exerts a force of 350.0 N at 58° above the horizontal and Paramedic 2 exerts a force of 299.9 N, upward. Find the magnitude of the net force acting on the stretcher.

Answer 1

The magnitude of the net force acting on the stretcher, considering forces exerted by Paramedics 1 and 2, is approximately 619.86 N, combining both horizontal and vertical components.

To find the magnitude of the net force acting on the stretcher, we need to consider both the horizontal and vertical components of the forces exerted by the paramedics. We can break down the forces into their horizontal (x) and vertical (y) components using trigonometric functions.

Let's denote:

-
`\( F_(1x) \) and \( F_(1y) \)` as the horizontal and vertical components of the force exerted by Paramedic 1,

-
`\( F_(2x) \) and \( F_(2y) \)` as the horizontal and vertical components of the force exerted by Paramedic 2.

For Paramedic 1:

`\[ F_(1x) = 350.0 \, \text{N} \cdot \cos(58^\circ) \]\[ F_(1y) = 350.0 \, \text{N} \cdot \sin(58^\circ) \]`

For Paramedic 2:

`\[ F_(2x) = 0 \, \text{N} \]` (since the force is directly upward)

`\[ F_(2y) = 299.9 \, \text{N} \]`

Now, to find the net force:

`\[ F_{\text{net, x}} = F_(1x) + F_(2x) \]\[ F_{\text{net, y}} = F_(1y) + F_(2y) \]`

Finally, the magnitude of the net force
`(\( F_{\text{net}} \))` can be calculated using the Pythagorean theorem:

`\[ F_{\text{net}} = \sqrt{F_{\text{net, x}}^2 + F_{\text{net, y}}^2} \]`

Let's calculate this:

`\[ F_(1x) = 350.0 \, \text{N} \cdot \cos(58^\circ) \approx 181.22 \, \text{N} \]\[ F_(1y) = 350.0 \, \text{N} \cdot \sin(58^\circ) \approx 297.07 \, \text{N} \]\[ F_{\text{net, x}} = 181.22 \, \text{N} + 0 \, \text{N} = 181.22 \, \text{N} \]\[ F_{\text{net, y}} = 297.07 \, \text{N} + 299.9 \, \text{N} = 596.97 \, \text{N} \]\[ F_{\text{net}} = √(181.22^2 + 596.97^2) \approx 619.86 \, \text{N} \]`

Therefore, the magnitude of the net force acting on the stretcher is approximately
`\( 619.86 \, \text{N} \)`.