The force required to stretch a spring varies directly with the amount the spring is stretched. A force of 29 pounds is needed to stretch a spring 39 inches.
How much force is required to stretch the spring 27 inches?
Answer in units of lb
F = 27in/39in * 29Lbs = 20.1 Lbs.
Well, torturing a spring doesn't sound very funny to me, but I'll give it a shot anyway!
If a force of 29 pounds is needed to stretch the spring 39 inches, and the force varies directly with the amount the spring is stretched, we can set up the proportion:
29 pounds / 39 inches = x pounds / 27 inches
To solve for x, we cross-multiply and get:
29 * 27 = 39 * x
Then we divide both sides by 39 to isolate x:
x = (29 * 27) / 39
Now, let's bring in the clown calculator to do the math!
Calculating...drum roll, please...and...
*beep beep beep*
The force required to stretch the spring 27 inches is approximately 19.76923076923077 pounds.
I hope the spring isn't too "sprung" after all that stretching!
To find the amount of force required to stretch the spring 27 inches, we can use the concept of direct variation.
Given that the force required to stretch the spring varies directly with the amount the spring is stretched, we can set up a proportion:
Force1 / Stretch1 = Force2 / Stretch2
29 lb / 39 in = Force2 / 27 in
To solve for Force2, we can cross-multiply and then divide:
29 lb * 27 in = 39 in * Force2
783 lb*in = 39 in * Force2
783 lb*in / 39 in = Force2
20 lb = Force2
Therefore, the force required to stretch the spring 27 inches is 20 pounds.
To solve this problem, we can use the concept of direct variation between force and the amount the spring is stretched.
First, let's set up the direct variation equation:
Force = k * stretch
where "Force" is the force required to stretch the spring, "k" is the constant of variation, and "stretch" is the amount the spring is stretched.
We are given that a force of 29 pounds is needed to stretch the spring 39 inches. Let's use this information to find the value of "k".
29 = k * 39
To solve for "k", we divide both sides of the equation by 39:
k = 29 / 39
Now we know the value of "k". To find out how much force is required to stretch the spring 27 inches, we can use the direct variation equation:
Force = k * stretch
Force = (29 / 39) * 27
Calculating this expression, we get:
Force ≈ 20.2308 lb
Therefore, approximately 20.2308 pounds of force is required to stretch the spring 27 inches.