Final answer:
The magnitude of the centripetal force acting on the monkey is 83.61 N, and the magnitude of the tension in the monkey's arm is 166.55 N.
Step-by-step explanation:
To find the magnitude of the centripetal force acting on the monkey, we can use the equation:
Fc = m * ac
where Fc is the centripetal force, m is the mass of the monkey, and ac is the centripetal acceleration.
From the given information, we know that the mass of the monkey is 8.95 kg and the speed at the lowest point is 2.72 m/s.
Since the monkey is swinging in a vertical circle, the centripetal acceleration is given by:
ac = (v^2) / r
where v is the tangential velocity and r is the radius of the circle.
Plugging in the values, we have
ac = (2.72 m/s)^2 / 0.789 m
Simplifying the equation gives:
ac = 9.348 m/s^2
Now, substituting the values of mass and acceleration into the earlier equation, we get:
Fc = (8.95 kg) * (9.348 m/s^2)
Calculating the product yields:
Fc = 83.61 N
To find the magnitude of the tension in the monkey's arm, we can consider the net force acting on the monkey at the lowest point. The net force is equal to the sum of the centripetal force and the gravitational force:
Net force = Fc + Fg
where Fg is the gravitational force given by:
Fg = m * g
where g is the acceleration due to gravity.
Plugging in the values, we have:
Net force = Fc + (8.95 kg) * (9.8 m/s^2)
Calculating the sum gives:
Net force = 166.55 N
Since the net force is equal to the tension in the monkey's arm, the magnitude of the tension is:
Tension = 166.55 N