Ex. 3: Projectile motion. A particle of mass (m) is launched up at an angle of elevation (0) with some initial speed (v). (a) Derive the equations of motion for projectile motion for a particle subject to constant downward gravitational force. (b) Determine the velocity as a function of position of the particle. (c) Determine the potential energy, kinetic energy, and total mechanical energy of the particle. Find the turning points of motion. (d) Consider the same problem (parts a, b, c), but considering a downward gravitational force which varies with position given by: GMm F(r) (Take into account the initial height of the mass being at the surface of the Earth) For what circumstances can we assume that this force is constant? == -11, where: G = 6.67 x 10 ¹¹Nm²/kg and M = 5.97 x 10²4 kg.
Ex. 3: Projectile motion. A particle of mass (m) is launched up at an angle of elevation (0) with some initial speed (v). (a) Derive the equations of motion for projectile motion for a particle subject to constant downward gravitational force. (b) Determine the velocity as a function of position of the particle. (c) Determine the potential energy, kinetic energy, and total mechanical energy of the particle. Find the turning points of motion. (d) Consider the same problem (parts a, b, c), but considering a downward gravitational force which varies with position given by: GMm F(r) (Take into account the initial height of the mass being at the surface of the Earth) For what circumstances can we assume that this force is constant? == -11, where: G = 6.67 x 10 ¹¹Nm²/kg and M = 5.97 x 10²4 kg.
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Transcribed Image Text:Ex. 3: Projectile motion. A particle of mass (m) is launched up at an angle of elevation (0)
with some initial speed (v).
(a) Derive the equations of motion for projectile motion for a particle subject to constant
downward gravitational force.
(b) Determine the velocity as a function of position of the particle.
(c) Determine the potential energy, kinetic energy, and total mechanical energy of the
particle. Find the turning points of motion.
(d) Consider the same problem (parts a, b, c), but considering a downward gravitational
force which varies with position given by:
GMm
F(r)
24
where: G = 6.67 × 10-¹¹ Nm²/kg² and M = 5.97 × 10²4 kg.
r
(Take into account the initial height of the mass being at the surface of the Earth)
For what circumstances can we assume that this force is constant?
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