The length a spring stretches is directly proportional to the force applied. If a force of 7 pounds stretches a spring 8 inches, how much force is necessary to stretch the same spring 3 inches?
Well, springs can be so stretchy! In this case, we can use a little math to figure it out. So, if a force of 7 pounds stretches the spring 8 inches, we can say that the force is directly proportional to the stretch.
To find out how much force is necessary to stretch the spring 3 inches, we can set up a proportion. If 7 pounds stretches the spring 8 inches, then x pounds (our unknown) would stretch it 3 inches.
So, we have the proportion 7 pounds / 8 inches = x pounds / 3 inches.
Now we can solve for x. Cross-multiplying, we get x pounds = (7 pounds * 3 inches) / 8 inches.
Calculating that out, we have x pounds = 2.625 pounds.
Therefore, approximately 2.625 pounds of force would be necessary to stretch the same spring 3 inches. Just remember, springs can be quite moody, so don't push them too hard!
To find out how much force is necessary to stretch the spring 3 inches, we can set up a proportion using the given information.
Let x be the force needed to stretch the spring 3 inches.
According to the given information:
Force1/Spring Length1 = Force2/Spring Length2
Plugging in the values:
7 pounds/8 inches = x/3 inches
To solve for x, we can cross-multiply and divide:
(7 pounds * 3 inches) = (8 inches * x)
21 pounds = 8 inches * x
Dividing both sides of the equation by 8 inches:
x = 21 pounds / 8 inches
Therefore, the force necessary to stretch the same spring 3 inches is approximately 2.625 pounds.
To find the force necessary to stretch the spring 3 inches, we need to apply the concept of proportionality.
We know that the length a spring stretches is directly proportional to the force applied. In mathematical terms, this can be expressed as:
Force = k * Length
where k is the proportionality constant.
To find the value of k, we can use the given information that a force of 7 pounds stretches the spring 8 inches. Plugging these values into the equation, we have:
7 = k * 8
Now, let's solve for k:
k = 7 / 8
k = 0.875
So the value of k is 0.875.
Now that we have the value of k, we can find the force necessary to stretch the spring 3 inches:
Force = k * Length
Force = 0.875 * 3
Force = 2.625
Therefore, the force necessary to stretch the same spring 3 inches is approximately 2.625 pounds.
force = stretch distance * spring constant
same spring ... same constant