The force F (in pounds) needed on a wrench handle to loosen a certain bolt varies inversely with the length L (in inches) of the handle. A force of 30 pounds is needed when the handle is 9 inches long. If the handle of the wrench is 6 inches long, approximately how much force is needed to loosen the bolt? Round answer to two decimal places if necessary.

9 * 30 = 6 * ?

Did you know?

Did you know that the force required to loosen a bolt using a wrench handle varies inversely with the length of the handle? This means that as the length of the handle decreases, the force needed increases. In a specific example, if a force of 30 pounds is needed when the handle is 9 inches long, we can determine the force needed when the handle is 6 inches long. To do so, we use the inverse variation formula: F = k/L, where F is the force, L is the length of the handle, and k is the constant of variation. In this case, we can let F1 and L1 represent the initial force and length, respectively, and F2 and L2 represent the force and length we are trying to find. Using the given information, we have F1 = 30 and L1 = 9. Plugging these values into the formula, we get 30 = k/9. Solving for k, we find that k = 270. Now, we can use the formula to find F2 when L2 = 6: F2 = k/L2 = 270/6 = 45. Therefore, approximately 45 pounds of force is needed to loosen the bolt when the handle is 6 inches long.