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?