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A fisherman in a boat is using a “10–lb test” fishing line. this means that the line can exert a force of 45 n without breaking (1 lb = 4.45 n). (a) how heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) if he accelerates the fish upward at 2.0 m/s2, what maximum weight fish can he land? (c) is it possible to land a 15–lb trout on 10–lb test line? why or why not?

Respuesta :

As we know that boat will have maximum limit as 45 N

So here we can not apply force more than 45 N

So here we can say

Part 1)

when fishes are pulled upwards with constant speed

so here

[tex]F = mg[/tex]

[tex]45 = m* 9.8[/tex]

[tex]m = 4.6 kg[/tex]

so in first case the weight of fish lifted up will be 4.6 kg

Part 2)

When it is pulled upwards with acceleration 2 m/s^2

[tex]F - mg = ma[/tex]

[tex]F = m*(g + a)[/tex]

[tex]45 = m*(9.8 + 2)[/tex]

[tex]m = 3.81 kg[/tex]

so in this case we can pull up total mass of 3.81 kg

Part 3)

It is not possible to land more weight because in that case the weight will exceed the limit of breaking force in each case either accelerating upwards or moving up with constant speed.

The maximum mass of the fish that the fisherman can hold is 3.81 kg, also the line can not hold a 15–lb trout on 10–lb test line.

How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed?

We know that the fisherman boat is using the 10-lb test, therefore, we will use Newton's second law of motion,

[tex]Force= mass \times accleration[/tex]

The acceleration is will be equal to the acceleration due to gravity, substitute the values,

[tex]Force= mass \times accleration = weight\\\\[/tex]

Hence, the weight of the fish that fishermen can catch is 10 lbs.

If he accelerates the fish upward at 2.0 m/s2, what maximum weight fish can he land?

We know that fisherman is accelerating the fish upwards but a resisting force will also be applied to the fish due to the gravity.

[tex]Force - (m\times g ) = (m\times a)\\\\Force - weight = (m\times a)\\\\[/tex]

Given to us

Force = 45 N

g = 9.81 m/s²

a = 2.0 m/s²

Substitute the values,

[tex]45 - (9.81m) = (2 m )\\\\45= 2m+9.81m\\\\m = 3.81\rm\ kg[/tex]

Hence, the maximum mass of the fish that the fisherman can hold is 3.81 kg.

Is it possible to land a 15–lb trout on 10–lb test line?

We know that the maximum force that the line can exert is 45 N, if we convert 10 lb to Newton we get,

10 lb = 44.5 N

while if we convert 15 lb,

15 lb = 66.75 N

which will exceed the limit of the line.

Hence, we can not land a 15–lb trout on 10–lb test line.

Learn more about Weight and Mass:

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