1-kg salmon is hooked by fishermen and it swims off at 2m/s. The fishermen stops the salmon in 50cm by breaking his reel. How muchfroce does the fishing line exert on the fish?
To determine the force exerted by the fishing line on the fish, we can use Newton's second law of motion, which states that force (F) is equal to the mass (m) of an object multiplied by its acceleration (a). In this case, the acceleration of the fish can be calculated using the given information.
Given:
- Mass of the fish (m) = 1 kg
- Initial velocity (u) = 2 m/s
- Final velocity (v) = 0 m/s (since it stops)
- Distance (s) = 50 cm = 0.5 m
We need to find the force exerted by the fishing line, which can be calculated as:
F = m * a
To determine the acceleration (a), we can use the kinematic equation:
v^2 = u^2 + 2as
Rearranging the equation to solve for acceleration (a):
a = (v^2 - u^2) / (2s)
Now, let's substitute the values:
a = (0^2 - 2^2) / (2 * 0.5)
a = (-4) / 1
a = -4 m/s^2
Notice that the acceleration is negative because the fish is decelerating or slowing down.
Finally, we can calculate the force exerted by the fishing line:
F = m * a
F = 1 kg * (-4 m/s^2)
F = -4 N
Therefore, the fishing line exerts a force of -4 Newtons on the fish. The negative sign indicates that the force acts in the opposite direction of the fish's motion.