Topics to be discussed: circular motion, ch



Topics to be discussed: Newton’s law of universal gravitation. I find that, amazingly, the biggest trouble that students have when solving universal gravitation problems is plugging correctly into their calculators. To be sure you don’t screw up, follow this advice:

• Solve in variables as far as possible in each problem. Only plug in values at the end.

• Do an order of magnitude estimate of your answer without the calculator, to be sure you’re not way, way off.

• Check the reasonability of the answer. When you’re asked to make a comparison, do this right – don’t just say “that’s a big mass”, say “that’s twice the mass of the earth” or “that’s close to the mass of the sun”. Astronomical data is easily available online, and there are astronomical tables in all physics texts.

• I will be looking at comparisons VERY CAREFULLY on gravitation problems. Do these right.

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Due Wednesday, March 12 – quiz will cover some issues from the lecture and HW

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1. A 0.50-kg ball that is tied to the end of a 1.5-m light cord is revolved in a horizontal plane, with the cord making a 30° angle with the vertical. (See the figure above.)

a) Determine the ball's speed.

b) Justify the reasonability of the speed determined in part (a).

2. After the Sun exhausts its nuclear fuel, its ultimate fate may be to collapse into a white dwarf state. In this state, it would have approximately the same mass as it has now, but its radius would be equal to the radius of earth.

a) Calculate the average density of the white dwarf.

b) Calculate the acceleration of a mass in free fall near the surface of this white dwarf.

c) Compare density of the white dwarf to the density of anything else you may be familiar with.

3. In a popular amusement park ride, a rotating cylinder of radius 3.0 m is set in rotation at an angular speed of 0.80 revolutions per second. The floor then drops away, leaving the riders suspended against the wall in a vertical position.

a) What minimum coefficient of friction between a rider’s clothing and the wall is needed to keep the rider from slipping?

b) Be sure the coefficient of friction makes sense… compare the coefficient of friction you derive to one that might be typical for amusement park riders against a wall.

Due Thursday, March 13

4. A geosynchronous satellite, which always remains above the same point on a planet’s equator, is put in orbit around Jupiter to study that planet’s red spot. Jupiter rotates once every 9.84 h. Use astronomical data in the chart above to find the altitude of the satellite. Compare your answer to the radius of Jupiter.

5. A satellite is in circular orbit around an unknown planet. The satellite has a speed of 6.36 x 104 m/s, and the radius of its orbit (measured from the center of the planet) is 2.11 x 106 m. A second satellite also has a circular orbit around this same planet. The orbit of this second satellite has a radius of 8.44 x 106 m.

a) What is the orbital speed of the second satellite?

b) Check the order of magnitude of your answer to be sure it is reasonable compared to the order of magnitude of the original speed.

6. Two equal-mass stars maintain a constant distance apart of 8.0 X 1010 m and rotate about a point midway between them at a rate of one revolution every 12.6 yr.

a) Why don’t the two stars crash into one another due to the gravitational force between them?

b) What must be the mass of each star?

c) Convince me briefly that the mass you calculated in (b) is reasonable.

Due Friday Oct. 15 – Fundamentals quiz today

7.

a) At what distance from the Earth will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and opposite forces?

b) Check the reasonability of your answer… is the spaceship closer to the earth or moon? Does this make sense?

c) Are the gravitational forces on the spaceship (one force caused by the moon, one caused by the earth) a Newton’s third law force pair? Why or why not?

8. A block of mass 2.5 kg is pushed 2.2 m along a frictionless horizontal table by a 16 N pushing force directed 25o below the horizontal.

a) Calculate the work done by the pushing force.

b) Calculate the work done by the normal force exerted by the table.

c) Calculate the work done by gravity.

d) Calculate the net work done on the block.

e) Assuming the block started from rest, calculate the speed of the block after 2.2 m.

9. Two identical arrows, one with twice the speed of the other, are fired into a bale of hay. Assuming the hay exerts a constant friction force on the arrows, the faster arrow will penetrate how much farther than the slower arrow? Explain. [Do this any way you want, but I’ll give you bonus points if you use the work-energy theorem.]

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