Need help working this problem. Thanks in advance!
1) A 50-m tape is used to measure between two points. The average weight of the tape per meter is 0.320 N. If the measured distance is 48.888 m, with the tape supported at the ends only and with a tension of 100 N, find the corrected distance.
See:
http://www.jiskha.com/display.cgi?id=1285538020
To solve this problem, we need to take into account the weight and tension of the tape to determine the corrected distance.
Let's break down the problem step by step:
1) Find the weight of the tape:
The problem states that the average weight of the tape per meter is 0.320 N. Since the measured distance is 48.888 m, we can calculate the weight of the tape using the formula Weight = Average Weight per meter x Distance. So, the weight of the tape is 0.320 N/m x 48.888 m = 15.555 N.
2) Find the net force acting on the tape:
The net force acting on the tape can be found by subtracting the tension from the weight. In this case, the tension is given as 100 N, so the net force is 15.555 N - 100 N = - 84.445 N. Note that the negative sign indicates that the direction of the force is opposite to the tension.
3) Find the corrected distance:
To find the corrected distance, we need to account for the change in length of the tape due to the net force. The change in length can be calculated using Hooke's Law: Change in Length = (Net Force x Original Length) / (Tensile Modulus). However, since the equation is not given in the problem, we need to assume a value for the tape's tensile modulus.
Assuming the tensile modulus of the tape is 10^9 N/m^2 (a common value for materials like steel), we can calculate the change in length as follows:
Change in Length = (- 84.445 N x 50 m) / (10^9 N/m^2)
Calculating this expression gives us the change in length of the tape. To find the corrected distance, we subtract this change from the measured distance:
Corrected Distance = Measured Distance - Change in Length
By plugging in the values, the final equation would look like this:
Corrected Distance = 48.888 m - (result of the change in length calculation)
So, you can compute the corrected distance by substituting the values and solving the equation.