Answer :
(a) The magnitude of the centripetal force acting on the monkey is approximately 188.784 N. (b) The magnitude of the tension in the monkey's arm is also approximately 188.784 N.
In this problem, we are given the mass of a monkey, its radial distance from a branch, and its speed at the lowest point on a vertical circle. We need to find the magnitude of the centripetal force acting on the monkey and the tension in its arm.
(a) To find the magnitude of the centripetal force, we can use the equation F = m * v^2 / r, where F is the force, m is the mass, v is the velocity, and r is the radius. Plugging in the given values, the mass of the monkey is 10.8 kg, the speed is 1.73 m/s, and the radius is 97.9 cm (or 0.979 m). Calculating the force using this equation gives us approximately 188.784 N.
(b) The tension in the monkey's arm is equal to the centripetal force acting on it. Therefore, the magnitude of the tension in the monkey's arm is also approximately 188.784 N.
In summary, the magnitude of the centripetal force acting on the monkey is approximately 188.784 N, and the magnitude of the tension in the monkey's arm is also approximately 188.784 N.
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