Question

7. A cable it attached to a motor in order to open a large airplane hangar door. If the angle of depression of the cable from the motor to the door is 10%, and the force that the motor pulls is 450 lbs, find the work done by the motor in pulling the door 35 ft.

Answer 1

To find the work done by the motor in pulling the door, we need to calculate the force applied by the motor and the displacement of the door. The angle of depression of the cable is given as 10%. We can use the Pythagorean theorem to find the horizontal distance between the motor and the door.

Step-by-step explanation:

To find the work done by the motor in pulling the door, we need to calculate the force applied by the motor and the displacement of the door. The angle of depression of the cable is given as 10%, which means that the vertical distance between the motor and the door is 10% of the horizontal distance. Let's assume the horizontal distance between the motor and the door is x. Since the angle of depression is 10%, the vertical distance would be 0.1x.

So, we have a right triangle with the horizontal distance x and the vertical distance 0.1x. The hypotenuse of this triangle is the length of the cable, which we'll call L. Using the Pythagorean theorem, we can find the value of x.

Once we have the value of x, we can calculate the displacement of the door by subtracting the initial position of the door from the final position. Finally, we can calculate the work done by the motor using the formula work = force × displacement.

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