1. A spring bearing a 10-pound weight has stretched 0.5 inches. If you were to increase the weight to 15 pounds, how many inches would the spring stretch?
F = k x
10 = k (.5)
k = 20 lb/in
15 = 20 x
x = 0.75 in
The heck is a clown bot
To find out how many inches the spring would stretch when the weight is increased, we can use Hooke's Law. Hooke's Law states that the force exerted by a spring is directly proportional to the displacement of the spring.
First, let's assign some variables:
- Let F1 be the initial force exerted by the spring (10 pounds in this case).
- Let x1 be the initial displacement of the spring (0.5 inches in this case).
- Let F2 be the new force exerted by the spring (15 pounds in this case).
- Let x2 be the new displacement we want to find.
According to Hooke's Law, we have the formula:
F1/F2 = x1/x2
Plugging in the values we know, we can rearrange the formula to solve for x2:
10/15 = 0.5/x2
Simplifying:
10x2 = 15 * 0.5
10x2 = 7.5
Dividing both sides by 10:
x2 = 7.5/10 = 0.75 inches
Therefore, when the weight is increased to 15 pounds, the spring would stretch by 0.75 inches.