The tension at which a fishing line snaps is commonly called the line's "strength." What minimum strength is needed for a line that is to stop a salmon of weight 85 N in 11.0 cm if the fish is initially drifting at 2.8 m/s? Assume a constant deceleration.
At initial velocity u=2.8 m/s the fish is stopped in a distance of S=0.11m. The acceleration a is therefore:
2aS = u²-0²
Solve for a (negative).
Use F=ma to find the required strength.
In practice, you would double that value to give a factor of safety of 2 if you don't want the big fish to go away.
tension= mass*acceleartion=85/g *a
now, to find a.
Vf^2=Vi^2+2ad
0=2.8^2+2a*.11
solve for a.
To find the minimum strength needed for a fishing line to stop a salmon, we need to determine the force required to bring the salmon to a stop.
First, let's calculate the deceleration using the initial velocity, final velocity (which is zero as the fish comes to a stop), and displacement. We can use the equation:
\(v^2 = u^2 + 2as\),
where
\(v\) = final velocity (0 m/s),
\(u\) = initial velocity (2.8 m/s),
\(a\) = acceleration (deceleration),
\(s\) = displacement (0.11 m).
Rearranging the equation to solve for deceleration (a):
\(0 = (2.8 \, m/s)^2 + 2a(0.11 \, m)\),
\(0 = 7.84 \, m^2/s^2 + 0.22a\).
Now, let's find the deceleration (a):
\(0.22a = -7.84 \, m^2/s^2\),
\(a = \frac{-7.84 \, m^2/s^2}{0.22} \approx -35.64 \, m/s^2\).
The negative sign indicates that the acceleration is in the opposite direction of the initial velocity, causing the fish to decelerate.
Next, we can calculate the force required to bring the fish to a stop using Newton's second law of motion:
\(F = ma\),
where
\(F\) = force,
\(m\) = mass (weight/gravity),
\(a\) = acceleration (deceleration).
Given that the weight of the fish is 85 N, we can find the mass using Newton's second law:
\(85 \, N = m \cdot 9.8 \, m/s^2\) (assuming the acceleration due to gravity is approximately \(9.8 \, m/s^2\)),
\(m = \frac{85 \, N}{9.8 \, m/s^2} \approx 8.67 \, kg\).
Finally, we can calculate the force required:
\(F = 8.67 \, kg \cdot (-35.64 \, m/s^2)\),
\(F \approx -303.15 \, N\).
The negative sign indicates that the force needed is in the opposite direction of the fish's motion.
Therefore, the minimum strength needed for the fishing line to stop the salmon is approximately 303.15 N.