The force required to compress a spring varies directly as the change in the length of the spring. If a force of 30 pounds is required to compress a certain spring 6 inches, how much force is required to compress the spring 8 inches?

Question

The force required to compress a spring varies directly as the change in the length of the spring. If a force of 30 pounds is required to compress a certain spring 6 inches, how much force is required to compress the spring 8 inches?

Answer 1

To solve this problem, we need to use the concept of direct variation. In direct variation, two variables are directly proportional to each other. In this case, the force required to compress the spring and the change in the length of the spring are directly proportional.

We can set up a proportion to find the answer. Let's denote the force required to compress the spring as F and the change in length as x:

F/6 = 30/8

To solve for F, we can cross-multiply and solve for the unknown variable:

8F = 180

F = 180/8

F = 22.5

Therefore, the force required to compress the spring 8 inches is 22.5 pounds.

Answer 2

We are given that the force required to compress the spring is directly proportional to the change in length of the spring. This means that the ratio of force to change in length is constant.

Let's call this constant k.

So, we have the equation:

force = k * change in length

We are given that a force of 30 pounds is required to compress the spring 6 inches. Plugging these values into the equation, we get:

30 = k * 6

To find the value of k, we can divide both sides of the equation by 6:

k = 30/6 = 5

Now, we need to find the force required to compress the spring 8 inches. Plugging this value and the value of k into the equation, we get:

force = 5 * 8

Simplifying, we find:

force = 40

Therefore, the force required to compress the spring 8 inches is 40 pounds.

Answer 3

To find the force required to compress the spring 8 inches, we can use the concept of direct variation.

The force required to compress the spring is directly proportional to the change in the length of the spring. This means that if we double the change in length, the force required will also double.

Let's set up a proportion to solve for the force:

Force1 / Length1 = Force2 / Length2

Where Force1 is the force required to compress the spring 6 inches, Length1 is the initial length of the spring (in this case, 6 inches), Force2 is the force required to compress the spring 8 inches (which we want to find), and Length2 is the new length of the spring (in this case, 8 inches).

Plugging in the values we know:

30 pounds / 6 inches = Force2 / 8 inches

Now we can solve for Force2:

(30 pounds * 8 inches) / 6 inches = Force2

240 pounds / 6 inches = Force2

40 pounds = Force2

Therefore, the force required to compress the spring 8 inches is 40 pounds.

The force required to compress a spring varies directly as the change in the length of the spring. If a force of 30 pounds is required to compress a certain spring 6 ​inches, how much force is required to compress the spring 8 ​inches?

To solve this problem, we need to use the concept of direct variation. In direct variation, two variables are directly proportional to each other. In this case, the force required to compress the spring and the change in the length of the spring are directly proportional.

We are given that the force required to compress the spring is directly proportional to the change in length of the spring. This means that the ratio of force to change in length is constant.

To find the force required to compress the spring 8 inches, we can use the concept of direct variation.

The force required to compress a spring varies directly as the change in the length of the spring. If a force of 30 pounds is required to compress a certain spring 6 inches, how much force is required to compress the spring 8 inches?