Question

A fisherman yanks a fish out of the water with an acceleration of

a = 2.4 m/s² using a very light fishing line that has a test value of 100 N. The fisherman, unfortunately, loses the fish as the line snaps. Find the mass that the fishing line of 100 N can support.

Answer 1

To determine the mass that a 100 N fishing line can support, we use Newton's second law of motion and find that it can support up to 41.67 kg before breaking when subjected to an acceleration of 2.4 m/s².

Step-by-step explanation:

To find the mass that a fishing line of 100 N can support, we can use the relationship between force, mass, and acceleration given by Newton's second law of motion, F = ma. Since the fishing line snaps at 100 N, this is the maximum force it can exert before breaking. We are given the acceleration as 2.4 m/s². To find the mass, we simply rearrange the equation to solve for m (mass), which equals F (force) divided by a (acceleration).

Step 1: Write down Newton's second law of motion: F = ma.
Step 2: Rearrange the equation to solve for m: m = F/a.

Step 3: Insert the known values into the equation: m = 100 N / 2.4 m/s².

Step 4: Calculate the mass: m = 41.67 kg (rounded to two decimal places).

Therefore, the fishing line of 100 N can support a mass of up to 41.67 kg before it reaches its breaking point and snaps.