(a) (5 pts) A door of mass M, width w, height h, and thickness t hang vertically

Question

(a) (5 pts) A door of mass M, width w, height h, and thickness t hang vertically from frictionless hinges. A mass m of putty strikes the door with velocity v normal to the door at the outer edge at half height, and sticks. What is the subsequent angular velocity of the door plus putty?

(b) (5 pts) A uniform small sphere of radius R is fully immersed in a large pool of stationary uid of density . The acceleration of gravity is g and the sphere is in neutral equilibrium. If the radius is 2R with total sphere mass unchanged, and the sphere released from rest in the uid, what is the initial acceleration of the sphere? The acceleration of gravity is g.

(c) (5 pts) When a person of mass mp steps into a boat of mass mb, the water line appears a height h greater on the boat hull. What is the eective spring constant of the boat alone?

(d)(5 pts) Assuming the Earth is a spherical drop of uid with a constant density equal to the average observed density, what is the pressure in atmospheres at its center? Assume RE = 6300 km and g(RE) = 10 m/s2.

(e)(5 pts) A mass m1 has initial velocity v1 and a mass m2 has initial velocity v2 and both are subject to a uniform gravitational acceleration g. What is the velocity of the center of mass of the pair after a time t?

Explanation / Answer

(A) Applying angular momentum conservation,

( I = M w^2 / 3 )

m v w = (M w^2 / 3 + m w^2 ) w'

w' = 3 m v / w(M + 3m)

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