Hooke's law states that the distance, d, a string is stretched varies directly with the force, F, applied to the spring. If a force
of 12 pounds stretches a spring 3 inches, how far will the spring stretch when a force of 30 pounds is applied?
d = (30Lbs/12Lbs) * 3in. = 7.5 In.
To solve this problem, we can use Hooke's Law, which states that the distance a string is stretched varies directly with the force applied.
According to Hooke's Law, we can set up a proportion to solve for the unknown distance. We have the following information:
Force 1 (F1) = 12 pounds
Distance 1 (d1) = 3 inches
Force 2 (F2) = 30 pounds
Distance 2 (d2) = ?
We can set up the proportion as:
F1 / d1 = F2 / d2
Plugging in the known values, we get:
12 / 3 = 30 / d2
To solve for d2, we can cross multiply:
12 * d2 = 3 * 30
Simplifying:
12 * d2 = 90
To find the value of d2, we divide both sides of the equation by 12:
d2 = 90 / 12
Calculating:
d2 = 7.5 inches
Therefore, when a force of 30 pounds is applied, the spring will stretch 7.5 inches.
To solve this problem using Hooke's law, we can set up a proportion using the given information.
According to Hooke's law:
d₁ / F₁ = d₂ / F₂
Where:
d₁ = initial distance (3 inches)
F₁ = initial force (12 pounds)
d₂ = unknown distance
F₂ = new force (30 pounds)
Plugging in the values:
3 / 12 = d₂ / 30
To solve for d₂, we can cross-multiply and solve for it:
3 × 30 = 12 × d₂
90 = 12 × d₂
Now, divide both sides of the equation by 12 to isolate d₂:
90 / 12 = d₂
7.5 = d₂
Therefore, when a force of 30 pounds is applied, the spring will stretch approximately 7.5 inches.