# Energy and Gravity

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A particle P of mass m is fastened to the end of a string with length L. The particle starts from rest, in a position where the string is taut, and the direction of the string forms an angle of 60 degrees with the vertical. In the lowest point of the circular arc, the particle P hits the body A.

Before the collision the body A is at rest on a frictionless horizontal table. The body A has a mass nm where n is some positive number.

The central collision between P and A is completely elastic. The acceleration of gravity is g, and we neglect air resistance. The known quantities are thus n, m, L, and g.

1) Just before the collision the particle P has a kinetic energy T_0. Find T_0.

2) Determine the velocity of the body A and the particle P just after the collision. Furthermore, determine that fraction q of the kinetic energy T_0 of the particle that is transferred to the body A.

3) Examine the limiting value of q as n -> infinity.

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#### Solution Summary

The solution discusses a problem regarding energy and gravity.

Density of Energy in a Point and Specific Gravity of Material

Please show all the work.

1. Determine the density of energy in a point if v=15m/s and P=30N/cm2 for a liquid with ѳx=1.4(specific gravity).

2. A hollow sphere with R (exterior) = 10cm and r (interior) = 8.5cm, floats in water with 30% of its volume submerged. Determine the specific gravity of the material of the sphere.

3. Determine the discharge (Q) in an area of .08m2 if the pressure of 12N/cm2 correspond to the velocity of fluid in this area.

4. A particle oscillates in a spring with a K = 800N/m and f = 2.5 Hz. Determine m.

5. A particle in simple harmonic motion has an xm = .03m and f = 8 Hz. Determine v(t) in t = .03T.

6. If x = .3 xm for a particle in simple harmonic motion, what fraction of the total energy is the kinetic energy in x?