Monkeys#

(https://makeagif.com/gif/gibbon-brachiation-a5VJFW) sourced from this original YouTube video (https://www.youtube.com/watch?v=acy–k7Qww0)

Brachiation is a form of locomotion (movement) where primates swing from tree limb to tree limb using only their arms. During brachiation, the body is alternately supported under each forelimb. Source: https://en.wikipedia.org/wiki/Brachiation

Part 1#

In brachiation, monkeys move from tree branch to tree branch by swinging from their arms. In the position shown in the figure (left), draw a free body diagram on the provided axes in the figure (right) for the monkey, assuming that it is momentarily at rest. (Label the forces $$\vec{F}$$ and $$\vec{W}$$ with subscripts on each, and include the angle).

Let the mass of the monkey be 10 kg, $$\theta$$ = 30 $$^{\circ}$$ , and the centre of mass of the monkey to be 50 cm from its centre of mass as shown in the figure.

File upload box will be shown here.

Part 2#

Calculate the torque exerted by $$\vec{F\_{m\ on\ b}}$$ about the branch.

Please enter in a numeric value in m.

Part 3#

Calculate the torque exerted by the mass of the monkey about the branch.

Please enter in a numeric value in m.

Part 4#

The moment of inertia of a solid sphere about its centre is $$\frac{2}{5}$$ $$M$$$$R^{2}$$ . If the the mass of the monkey can be treated as a sphere of radius 30 cm. Find the moment of inertia of the monkey about its centre.

Please enter in a numeric value in m.

Part 5#

The parallel axis theorem states that moment of inertia of an object of mass $$m$$ about an axis, a distance $$d$$ from its centre of mass is given by $$I$$ = $$I\_{cm}$$ + $$m$$$$d^{2}$$ . Find the moment of inertia of the spherical monkey about the branch.

Please enter in a numeric value in m.

Part 6#

Find the angular acceleration of the monkey.

Please enter in a numeric value in m.

Part 7#

Find the tangential acceleration of the centre of mass of the monkey about the branch.

Please enter in a numeric value in m.

Part 8#

Your result from part 7 is not the same as you would get from solving for the acceleration from the free body diagram in part 1. Explain why this is, referring to the particle model.