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Gravitation: Potential energy, field, force

A. Height of a Projectile
A projectile is fired straight up from the south pole of earth with an initial speed of 8.0km/s. Find the maximum height it reaches, neglecting effects due to air resistance.

b. Speed of a Projectile.
A projectile is fired straight up from the south pole of earth with an initial speed of 15.0km/s. Find speed of the projectile when it is very far from the Earth neglecting effect due air height it reaches, neglecting effects due to air resistance.

c. Gravitational field of two point particles
Two point particles, each of mass M, are fixed in the position on y axis at y = +a and y =-a. Find the gravitational field must include at all on the axis as a function of x.

d. A small block with mass 0.300kg is attached to a string passing through a hole in a frictionless, horizontal surface. The block is originally revolving in a circle with a radius of 0.790m about the hole with a tangential speed of 4.50m/s . The string is then pulled slowly from below, shortening the radius of the circle in which the block revolves. The breaking strength of the string is 33.0N.

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Projectiles and Circular motion
a. Height of a Projectile
A projectile is fired straight up from the south pole of earth with an initial speed of 8.0km/s. Find the maximum height it reaches, neglecting effects due to air resistance.
As the projectile is fired along the axis of rotation of earth, no effect of rotation of earth is to be considered.
As the velocity of the projectile is too large, the height reached will be too large and thus the potential energy of the projectile is given by

Where m is the mass of the projectile, M is the mass of the earth and r is the distance of the projectile from the center of earth,
As there is no non-conservative force to be considered, according to law of conservation of mechanical energy we get
Gain in potential energy = loss in kinetic ...

Solution Summary

Four good problems of gravitation and circular motion. The speed of projectiles are determined.

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