A 9.5 kg monkey is hanging by one arm from a branch and is swinging on a vertical circle. As an approximation, assume a radial distance of 90 cm between the branch and the point where the monkey's mass is located. As the monkey swings through the lowest point on the circle, it has a speed of 3.4 m/s.
(a) Find the magnitude of the centripetal force acting on the monkey.
(b) Find the magnitude of the tension in the monkey's arm.
To find the magnitude of the centripetal force acting on the monkey, we can use the formula for centripetal force:
F = m * a
where F is the centripetal force, m is the mass of the monkey, and a is the centripetal acceleration.
The centripetal acceleration can be calculated using the formula:
a = v² / r
where v is the velocity of the monkey and r is the radius of the circle.
(a) Find the magnitude of the centripetal force:
First, convert the radius from centimeters to meters:
r = 90 cm = 0.9 m
Then, substitute the given values into the formula:
a = (3.4 m/s)² / 0.9 m
a ≈ 12.62 m/s²
Now, plug the acceleration into the formula for centripetal force:
F = (9.5 kg) * (12.62 m/s²)
F ≈ 119.99 N
Therefore, the magnitude of the centripetal force acting on the monkey is approximately 119.99 N.
(b) Find the magnitude of the tension in the monkey's arm:
The tension in the arm of the monkey is equal in magnitude but opposite in direction to the centripetal force.
So, the magnitude of the tension is also approximately 119.99 N.