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Chapters 6 and 8: Some Additional Forces. Key Terms Newton’s Law of Gravity Orbit Hooke’s Law Equilibrium position. Orbital Motion. If a launch speed is great enough, there comes a point at which the curve of the trajectory and the curve of the earth are parallel.
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Chapters 6 and 8: Some Additional Forces • Key Terms • Newton’s Law of Gravity • Orbit • Hooke’s Law • Equilibrium position
Orbital Motion • If a launch speed is great enough, there comes a point at which the curve of the trajectory and the curve of the earth are parallel. • In this case, the projectile “falls” but it never gets any closer to the ground! • Such a trajectory around a planet or star is called an “orbit”.
Weightlessness in Orbit • Weightlessness does not occur from an absence of weight or gravity. • Instead, astronauts in orbit are “weightless” (apparent weight of 0) because they are falling freely, along with the spacecraft and everything in it. • Space stations rotate to create “artificial gravity” for safety.
Newton’s Law of Gravity • The force that attracts the moon to the earth (and the planets to the sun) is identical to the force that attracts an apple to the earth.
Sample Problem #1 (Ex. 6.14, page 186) • The gravitational force between two giant lead spheres is 0.010 N when the centers of the spheres are 20 m apart. What is the distance between their centers when the gravitational force is 0.160 N?
Sample Problem #2 (Ex. 6.15, page 187) • You are seated in your physics class next to another student 0.60 m away. Determine the magnitude of the gravitational force between you assuming that you both have a mass of 65 kg.
Sample Problem #3 (Ex. 6.16, page 187) • What is the magnitude of the gravitational force of the earth on a 60 kg person? The earth has a mass of 5.98 x 1024 kg and radius 6.37 x 106 m.
Sample Problem #4 (Ex. 6.17, page 189) • Saturn, at 5.68 x 1026 kg, has nearly 100 times the mass of the earth. It is also much larger, with a radius of 5.85 x 107 m. What is the value of g on the surface of Saturn?
Sample Problem #5 (Ex. 6.18, page 189) • Mars has two moons, each much smaller than the earth’s moon. The smaller of these two bodies, Deimos, has an average radius of 6.3 kmand a mass of 1.8 x 1015 kg. At what speed would a projectile movie in a very low orbit around Deimos? • How much time would it take to complete this orbit?
Elastic Systems • A system that exhibits a restoring force is called elastic. • Examples: rubber bands, springs • When no forces act on a spring to compress or extend it, it will relax to its equilibrium position.
Hooke’s Law • The negative sign reflects the fact that the force due to a spring always opposes to direction of stretching/compression.
Sample Problem #6 (Ex. 8.6, page 240) • A scale used to weight a fish consists of a spring connected to the ceiling. The spring’s equilibrium length is 30 cm. When a 4.0 kg fish is suspended from the end of the spring, it stretches to a length of 42 cm. • A) What is the spring constant for this spring? • B) If an 8.0 kg fish is suspended from the spring, what will be the length of the spring?
Sample Problem #7 (Ex. 8.7, page 241) • The figure below shows a spring attached to a 2.0 kg block. The other end of the spring is pulled by a motorized toy train that moves forward at 5.0 cm/s. The spring constant is 50 N/m, and the coefficient of static friction between the block and the surface is 0.60. The spring is at its equilibrium length at t = 0 s, when the train starts to move. When does the block slip?
