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 9.0 cm if the fish is initially drifting at 2.5 m/s? Assume a constant deceleration and that the fishing line is horizontal.
To determine the minimum strength needed for the fishing line, we need to calculate the acceleration of the salmon when it stops.
First, we need to determine the time it takes for the salmon to stop. We can use the equation of motion:
v^2 = u^2 + 2as
Where:
- v is the final velocity (0 m/s since the salmon stops)
- u is the initial velocity (2.5 m/s)
- a is the acceleration
- s is the distance (9.0 cm or 0.09 m)
Rearranging the equation, we have:
a = (v^2 - u^2) / (2s)
Substituting the values:
a = (0^2 - 2.5^2) / (2 * 0.09)
a = -6.94 m/s^2
The negative sign indicates that the salmon is decelerating. Now, we can calculate the force needed to stop the salmon using Newton's second law:
F = ma
Where:
- F is the force (strength of the fishing line) we want to find
- m is the mass of the salmon
- a is the acceleration
The weight of the salmon is given as 85 N, so we can use Newton's second law to find the mass:
m = F_g / g
m = 85 N / 9.8 m/s^2
m ≈ 8.67 kg
Substituting the values:
F = (8.67 kg) * (-6.94 m/s^2)
F ≈ -59.96 N
The negative sign indicates that the force should act in the opposite direction to the motion of the salmon.
Therefore, the minimum strength needed for the fishing line is approximately 59.96 N.
To determine the minimum strength required for the fishing line to stop the salmon, we need to consider the physics involved in stopping the fish.
First, we need to calculate the initial velocity of the fish. Since the fish is initially drifting at 2.5 m/s and the fishing line is horizontal, the initial velocity is also 2.5 m/s.
Using the equation of motion: vf^2 = vi^2 + 2ad
where vf is the final velocity (which is zero since the fish stops), vi is the initial velocity, a is the acceleration, and d is the distance traveled.
Rearranging the equation to solve for acceleration (a):
a = (vf^2 - vi^2) / (2d)
Substituting the given values:
a = (0 - (2.5 m/s)^2) / (2 * 0.09 m)
Calculating the acceleration:
a = -6.94 m/s^2
Now, we can use Newton's second law of motion, F = ma, to determine the force required to stop the fish. The force needed is equal to the weight of the salmon since it is being acted upon by gravity.
F = m * a
Substituting the given values:
F = (85 N) * (-6.94 m/s^2)
Calculating the force:
F = -590.9 N
Since the force and tension in the fishing line should be in the opposite direction to stop the fish, the minimum strength needed for the line would be approximately 590.9 N.