A string of length 4m is extended by 0.02m when a load of 0.4kg is suspended at its end. What will be the length of the string when the applied force is 15N...
A string of length 4m is extended by 0.02m when a load of 0.4kg is suspended at its end. What will be the length of the string when the applied force is 15N?
Answer Details
The problem involves finding the final length of a string when a certain force is applied to it, given its initial length and how much it extends under a certain load. To solve the problem, we can use Hooke's law, which states that the extension of an elastic object is directly proportional to the applied force, provided the elastic limit is not exceeded. In this case, we know that the string of length 4m extends by 0.02m when a load of 0.4kg is suspended at its end. This means that the spring constant k is: k = F/x = (0.4 kg * 9.81 m/s^2)/0.02 m = 196.2 N/m where F is the force, x is the extension, and 9.81 m/s^2 is the acceleration due to gravity. To find the length of the string when a force of 15N is applied, we can use Hooke's law again: F = kΔL where ΔL is the change in length of the string. Rearranging the equation to solve for ΔL, we get: ΔL = F/k = 15 N/196.2 N/m = 0.0764 m Therefore, the final length of the string is: L = 4m + ΔL = 4m + 0.0764m = 4.0764m So the answer is 4.08m.