Question

A fisherman is using a very light fishing line that breaks when the tension exceeds 20N. He lifts a fish vertically out of the water with an upwards acceleration of 2 m/s^2. What is the largest mass of the fish for which the line will hold?

Answer 1

The largest mass of the fish for which the line will hold is approximately 1.74 kg.

Step-by-step explanation:

To calculate the largest mass of the fish for which the line will hold, we need to determine the tension in the line when it exceeds 20N.

Using Newton's second law, we can find the tension in the line as follows:

Tension = mass of the fish × acceleration due to gravity + mass of the fish × acceleration

Since the tension should not exceed 20N, we can solve the equation for mass of the fish:

Tension > 20N

mass of the fish × 9.8 m/s^2 + mass of the fish × 2 m/s^2 > 20N

mass of the fish × (9.8 m/s^2 + 2 m/s^2) > 20N

mass of the fish > 20N / (9.8 m/s^2 + 2 m/s^2)

mass of the fish > 1.74 kg

Therefore, the largest mass of the fish for which the line will hold is approximately 1.74 kg.

Answer 2

1.695 kg

Step-by-step explanation:

maximum tension, T = 20 N

acceleration, a = 2 m/s^2

acceleration due to gravity, g = 9.8 m/s^2

Let the mass of fish is m.

Use Newton's second law

T - mg = ma

T = m (g + a)

20 = m (9.8 +2 )

m = 1.695 kg

Thus, the largest mass of the fish is 1.695 kg.