Question

A 12.6-kg monkey is hanging by one arm from a branch and swinging on a vertical circle. As an approximation, assume a radial distance of 85.3 cm is 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 1.36 m/s. Find (a) the magnitude of the centripetal force acting on the monkey and (b) the magnitude of the tension in the monkey's arm.

Answer 1

a)27.3N

b)150.78N

Step-by-step explanation:

Having in mind the conservation of energy, as the monkey goes up (gaining potential gravitational energy) the kinetic energy must be reduced, so reducing the velocity of the monkey. So the maximum velocity will be at this lower point with a velocity of 1.36m/s

From this velocity and the radius we can calculate the angular velocity for the monkey center of mass:

`w=(1.36m/s)/(0.853m) =1.594 /s`

with this we can calculate the centripetal force magnitude:

`F=m*w^(2) *r=12.6kg*(1.594/s)^(2) *0.853m=27.3N`

On the mokey center of mass we have two opposite forces acting, the tension of the arm and the weight, in order for the monkey to continue swinging the resolt of this two forces must be equal to the centripetal force:

`T-P=F=>T=F+P`

`T=27.3N+12.6kg*9.8m/s^(2)=150.78N`