Combined Lifting Force

[nycmathguy]

Section 1.10
68

An overhead garage door has two springs, one on each side of the door. A force of 15 pounds is required to stretch each spring 1 foot. Because of a pulley system, the springs stretch only one-half the distance the door travels. The door moves a total of 8 feet, and the springs are at their natural lengths when the door is open. Find the combined lifting force applied to the door by the springs when the door is closed.

Let L = length
Let k = constant of proportionality
Let f = applied force

L = fk

1 = 15k

1/15 = k

L = (1/2)(8)

L = 4

4 = (1/15)f

4 ÷ (1/15) = f

4 • 15 = f

60 pounds = f

You say?

 

[MathLover1]

question was: Find the combined lifting force applied to the door by the springs when the door is closed.
thus, for 2 springs combined force applied = 2 × 60 pounds = 120 pounds

 

[nycmathguy]

question was: Find the combined lifting force applied to the door by the springs when the door is closed.
thus, for 2 springs combined force applied = 2 × 60 pounds = 120 pounds

I almost got it right. I felt that combine means to add f + f or 60 + 60 or 2f = 2(60) = 120 pounds. I give myself credit for this effort. You recently met me online. For me to go this far when endeavoring to solve a word problem is pure magic.