Shark Swimming in Circular Pool: Calculating Centripetal Force

What is the centripetal force of the 681kg shark if the pool has a diameter of 14m and it is swimming 1 lap in 80s?

To calculate the centripetal force of the shark swimming in a circular pool, we will use the equation for centripetal force, which is F = MV^2/R. Given that the shark's mass (M) is 681 kg, the radius (R) of the pool is half of the diameter, which is 14m / 2 = 7m, and the time taken to swim 1 lap is 80 seconds, we can determine the velocity (V) of the shark and then substitute the values into the equation to find the centripetal force.

Calculating Velocity of the Shark:

The circumference of the circular pool is calculated by pi * diameter = pi * 14m ≈ 43.98229715 m. Since velocity is defined as distance divided by time, the velocity of the shark is 43.98229715 m / 80 s = 0.549778714 m/s.

Calculating Centripetal Force:

Substitute the known values into the centripetal force equation:

F = MV^2/R

F = 681 kg * (0.549778714 m/s)^2 / 7m

F = 681 kg * 0.302256635 m^2/s^2 / 7m

F = 205.8367683 kg*m^2/s^2 / 7m

F = 29.40525261 kg*m/s^2

Rounded to 2 significant figures, the centripetal force of the shark swimming in the circular pool is approximately 29 Newtons.

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