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Jacob has a mass of 54.4 kg. He is swinging from a rope that is 3.7 m long, and the rope is exerting a centripetal force of 115 N. What is Jacob's tangential speed?

Answer :

Final answer:

Jacob's tangential speed can be calculated from the centripetal force using the formula v = sqrt(Fc × r / m), by substituting the given values for mass, radius (rope length), and centripetal force.

Explanation:

To determine Jacob's tangential speed while swinging, we can use the formula for centripetal force:

Fc = (mv2) / r, where Fc is the centripetal force, m is the mass, v is the tangential speed, and r is the radius of the circle (in this case, the length of the rope).

Rearranging the formula to solve for v gives us:
v = sqrt(Fc × r / m). Plug in the given values: Jacob's mass m = 54.4 kg, the rope's length (and thus the radius) r = 3.7 m, and the centripetal force Fc = 115 N.

Let's calculate the tangential speed:
v = sqrt(115 N × 3.7 m / 54.4 kg)

Performing the calculation gives us Jacob's tangential speed. This formula accounts for the centripetal acceleration that is required to keep Jacob moving in a circular path while swinging from the rope.

Learn more about Centripetal Force here:

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