A rat trap is made using a basket on the end of a pole of length L = 85 cm. The

Question

A rat trap is made using a basket on the end of a pole of length L = 85 cm. The trap is propped up at an angle theta = 15 degrees using a short stick of negligible mass. The static friction force of the ground on the stick is maximal, i.e. mu_s, = tan theta. The other end of the trap is fixed to the ground by a hinge. A heavy disk-shaped weight of mass M = 15 kg and radius R = 6.0 cm is affixed to the pole so that the center of the weight lies a distance d = 13 cm from the hinge. The moment of inertia of the trap (pole + basket + weight) about the hinge is 0.55 kg m^2. The normal force between the stick and the trap points along the axis of the stick (normal to the pole) and gives a torque of magnitude 24 N m on the trap about the hinge. Which of the following is the best extended free body diagram of the trap? Notation: E = Earth, h = hinge, s = stick, t = trap. What is the moment of inertia of just the pole + basket about the hinge? What torque does the (vertically pointing) normal force between the ground and the stick apply on the stick about the point where the stick and the trap are touching? When the rat knocks the stick, the trap begins to fall. What is the initial acceleration of a point on the front edge of the basket (a distance L from the hinge)?

Explanation / Answer

9)
Reaction from the ground will make an angle with the vertical. There are two force vectors here, One is along the axis of the rod and the other is pointing down and the resultant will make an angle with the vertical.
Earth's gravity will always act at the center of mass. Here is the center of mass will not coincide with the center of the sphere since the masses of the basket and pole are need to be considered. It will always point down.

10)
Total moment of inertia = 0.55 kg.m2.
Moment of inertia of the disc at length disc = Md2 + 1/2Mr2 [ Using parallel axis theorem]
= 15 x 0.132 + 0.5 x 15 x (0.06)2 = 0.2535 + 0.027
Moment of inertia of the pole + basket = 0.55 - 0.2805 = 0.2695 kg m2.

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