kinetic energy, spring exten, pressure of water, rotational inertia?

Question

1. 2 kg mass whirled in vertical cirle of radius 3 m at constant speed of 4 m/s. What is its kinetic energy?

2. A mercury barometer reads 780 mmHg. The pressure in Pa= 104,000 what will it read if the working fluid is changed to water?

3. 20 g mass is hung from spring length 16 cm. Adding 10 g increases length to 19 ccm. What is unstretched length of spring?

4. formula for rotational inertia?


PLEASE HELP FINAL THIS WEEK!

Answer 1

1. Trick question; If the speed is constant, the KE is also constant and = ½mv² = ½*2*4² = 16 J
2. Let R = ρ(Hg)/ρ(H2O). Then the water barometer reading will be 780*R mmH2O
3. k = (30-20)/(19-16) = 10/3........∆y = ∆m/k→∆y = 20/(10/3) = 6cm when you remove the 20 g weight. L = 16 - ∆y = 10 cm.
4. Rotational inertia = I*ω where I is the moment of inertia about the axis of rotation in kg.m² and ω is the angular velocity in radians per sec.

Answer 2

Good marks for Steve except for item 4. His formula is that of angular momentum. Rotational inertia is another name for moment of inertia, symbolized by I. For a point mass m at distance r from the measurement point, the moment of inertia I = m*r^2. If it's not a point mass but a body with its own moment of inertia I2, I = I2 + m*r^2. 3-D bodies have moments of inertia described by a 3x3 matrix. Along their "principal axes", only moments of inertia exist, so the matrix has diagonal elements only. In any other set of axes there are also "products of inertia" which are nondiagonal elements. See the ref. if you are interested in the derivation of this matrix, and for simple formulas for finding the moments of inertia for basic geometric forms.