A long pole is used to lift a window. If a vertical lift of 80N is needed to raise the window, what force must be exerted along the pole? Assume the pole makes an angle of 34 degrees with the vertical wall.
To find the force that must be exerted along the pole, we can use trigonometry and resolve the force into its vertical and horizontal components.
Since we know the vertical lift force is 80N and the angle between the pole and the vertical wall is 34 degrees, we can start by finding the vertical component of the force. This component will be equal to the lift force, so we have:
Vertical component = Lift force = 80N
Next, we can find the horizontal component of the force. This component will be equal to the force exerted along the pole, and we can use trigonometry to find it. The horizontal component can be found using the equation:
Horizontal component = Force along the pole × cos(angle)
Substituting the given values, we have:
Horizontal component = Force along the pole × cos(34°)
Now, we can rearrange the equation to solve for the force along the pole:
Force along the pole = Horizontal component / cos(34°)
Calculating the horizontal component, we get:
Horizontal component = 80N × cos(34°)
Using a calculator, we find:
Horizontal component ≈ 66.518N
Finally, we can substitute this value into the equation to find the force along the pole:
Force along the pole ≈ 66.518N / cos(34°)
Calculating the final result, we get:
Force along the pole ≈ 78.138N
Therefore, the force that must be exerted along the pole to lift the window is approximately 78.138N.