Tension: Force + Velocity. Breaking Strength.

[nj_phy]

[SOLVED] Tension: Force + Velocity. Breaking Strength.

Homework Statement

The tension at which a fishing line breaks is commonly called the ``breaking strength''. What minimum breaking strength is needed for a fishing line to stop a salmon that weighs 90.0 N in 18.0 cm if the fish is moving horizontally with an initial velocity of 2.5 m/s? Assume the acceleration is constant.

Homework Equations

F=mg, F=ma, V^2 = Vo^2 + 2a(X-Xo)

The Attempt at a Solution

I'm not really sure how to tackle this problem. At first I simply assumed the minimum breaking strength of the string would have to be at least > 90N. However the fact that it's moving at 2.5m/s says to me that the 18cm of distance traveled increases the force created by the fish. But I'm not sure, algebraically, how to relate Force to Velocity. Also, since the fish weighs 90N, that implies its weight in relation to gravity. How would this translate when analyzing only movement in the X direction?

 

[nj_phy]

Solved

Ok. This problem is trivial and I apologize for wasting space on your forum, but maybe some day it will help someone else who gets caught up on the details...

I neglected to notice that final Velocity would be 0. Once I realized this I saw I could use one of the kinematics equations to derive acceleration.

Here's what I did...

(Vf^2-Vi^2)/(X-Xo) = 2a
--> 0m/s - (2.5^2m/s)/(0m - .18m) = 2a
--> a = 17.361m/s^2

Now I can derive the mass of the fish by using F in the y-direction (since we know gravity is 9.8m/s^2)...

F=mg
--> 90N = m(9.8m/s^2)
--> m = 9.18kg

Now, put it all together for the x-direction...

F = (9.18kg)(17.361m/s^2) = 159.443 N

 

[ogb p]

I would approach this problem by first defining the variables and their relationships. In this case, the tension (T) is equal to the force (F) applied to the fishing line, which is a combination of the weight of the fish (mg) and the force of acceleration (ma). The velocity (V) of the fish also plays a role in determining the breaking strength.

We can use the equation F=ma to calculate the force of acceleration. The fish has an initial velocity (Vo) of 2.5 m/s and travels a distance of 18.0 cm (0.18 m) before being stopped by the fishing line. We can use the equation V^2 = Vo^2 + 2a(X-Xo) to solve for the acceleration (a) of the fish.

Plugging in the values, we get:

0^2 = (2.5)^2 + 2a(0.18-0)

a = -31.25 m/s^2

Since the fish is moving horizontally, the force of acceleration is in the opposite direction of the fish's initial velocity. This means that the total force (F) applied to the fishing line is the sum of the weight of the fish and the force of acceleration, which are acting in opposite directions.

F = mg + ma

F = (90 N) + (-31.25 m/s^2)(90 N)

F = 562.5 N

Therefore, the minimum breaking strength of the fishing line must be at least 562.5 N in order to stop the salmon with a weight of 90.0 N moving at an initial velocity of 2.5 m/s over a distance of 18.0 cm.