Tension in a fishing line
1. 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 8.0 cm if the fish is initially drifting at 2.5 m/s? Assume a constant deceleration.
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Weight of the salmon=w= 85 N
Acceleration due to gravity g= 9.81 m/s^2
Mass of the salmon=w/g= 8.66 Kg =85/9.81
v1= 2.5 m/s
v2= 0 m/s
x=distance travelled= 8 cm= 0.08 m
v^2=v1^2+2ax, assuming constant accelearion/deceleration
where a is the acceleration
Rearranging terms a=(v2^2-v1^2)/2x
Calculating the value of a using the values of v1,v2 and x given
a= -39.06 m/s^2
Force exerted on the fish= -(ma) (negative sign since force in opposite direction to the direction of movement)
m= 8.66 Kg
a= -39.06 m/s^2
F=-ma= 338.26 N
Minimum strength needed for a line to stop the salmon of weight 85 N in 8.0 cm= 338.26 N Answer
We can check the answer
m= 8.66 Kg
v= 2.5 m/s
Initial Kinetic energy=1/2 m v ^2= 27.06 Joules
This should be equal to the work done on the fish=Force x distance
Force= 338.26 N
distance=x= 0.08 m
Therefore work done= 27.06 Joules
These two are indeed equal