Three identical stars of mass M form an equilateral triangle that rotates around the triangle’s center as the stars move in a common circle about that center. The triangle has edge length L. What is the speed of the stars? b.) What is the period of revolution? c.) What is the total potential energy of the 3 star system? Express your answers in terms of the star mass M and triangle edge length L. Hint: Draw a diagram showing the gravitational forces on each star. d.) Find the gravitational force on a single star due to the gravitational attraction of the other two stars, (magnitude and direction). Hints: the 2nd law for a single particle orbiting a planet i.e. Fg = M v 2 /R. You will need to express R in terms of the triangle edge length L. Use v T = 2πR to find the period. it is a symbols-only problem. All work must be done in symbols. There are no numbers.

10. Water at a pressure of 3.60 atm at street level flows into an office building at a speed of 0.60 m/s through a pipe 4.40 cm in diameter. The pipes taper down to 1.50 cm in diameter by the top floor, 23.0 m above. Calculate the water pressure in such a pipe on the top floor.

A 0.478 kg puck, initially at rest on a horizontal, frictionless surface, is struck by a 0.129 kg puck moving initially along the x axis with a speed of 2.19 m/s. After the collision, the 0.129 kg puck has a speed of 1.19 m/s at an angle of 29◦ to the positive x axis. Determine the magnitude of the velocity of the 0.478 kg puck after the collision. Answer in units of m/s.

The mass of a hot-air balloon and its cargo (not including the air inside) is 220 kg. The air outside is at 10.0°C and 101 kPa. The volume of the balloon is 490 m³. To what temperature must the air in the balloon be warmed before the balloon will lift off? (Air density at 10.0°C is 1.244 kg/m³.)
K

You found the two main angular velocities of the Earth: one due to the Earth's motion around the sun, and one due to its rotation about its own axis. Now let's figure out the energy and momentum associated with that motion. For the purposes of this problem, treat the Earth as a solid, uniform sphere with mass 5.97×10²⁴ kg and radius 6.37×10⁶ m , and assume that the Earth's orbit around the sun is circular with a radius of 1.5×10¹¹ m .

Part A) What is the angular kinetic energy of the Earth due to its orbit around the sun?

Part B) What is the magnitude of the Earth's angular momentum due to its orbit around the sun?

Part C) What is Earth's angular kinetic energy due to its rotation around its axis?

Part D) What is the magnitude of the Earth's angular momentum due to its rotation around its axis?

Part E) Which of the following best explains where the Earth's angular kinetic energy and momentum came from?

Remember that energy and momentum are always conserved (though energy can change forms). In other words, if you start with a certain amount of energy and momentum, you must end with the same amount of energy and momentum. By conservation of energy and momentum, the values you've calculated in this problem must have come from somewhere.

Which of the following best explains where the Earth's angular kinetic energy and momentum came from?

a. The solar system formed from a massive cloud of gas and dust, which was slowly rotating. As the cloud collapsed under its own gravitational pull, the cloud started to spin faster, just as an ice skater pulling his arms in will spin faster. Because all of the material that accreted to form the planet was rotating, the planet was rotating as well.

b. As the Earth formed, it experienced a series of collisions with asteroids and comets. These asteroids and comets hit the ball of rock that was forming into the planet off-center. Over time, the off-center collisions gradually caused the planet to rotate faster.

c. As the Moon orbits around the Earth, it creates tides on the Earth. Over time the tides have caused the Earth to rotate faster and faster.

d. Sheer force of will.

A horizontal spring with a spring constant of 190 N/cm is compressed 6.3 cm. A wooden block with a mass of 1.5 kg is placed in front of and in contact with the spring. When the spring is released it pushes the block, which slides on a frictionless horizontal surface for some distance. The block then slides up a frictionless incline of 27 degrees above the horizontal and comes to a momentary stop before sliding back down. The system is the spring, the block, the incline, and the Earth. Ignore air resistance.

A) What is the potential energy of the spring before it is released?

B) What is the kinetic energy and the speed of the block as it slides on the horizontal surface after the spring has pushed it?

C) At what height does the block stop on the incline?

D) If the incline were rough, how would the stopping height of the block compare to the stopping height when the incline is frictionless? Explain using energy.

Harry Potter (back to his normal size) has discovered that his magic wand is exactly one meter long. After some coaxing from Hermione, Harry is persuaded to mark off his wand in centimeters. Scabbers, the rat, (of mass 0.350 kg) is clinging tightly to the 70-cm mark of Harry's wand (of mass 0.100 kg.)Model Scabbers as a sphere of radius 5 cm. (He's put on a little weight lately.) as Hermionne rotates the wand in mid air, (as if on a horizontal, frictionless table) with an angular speed of 3.00 rad/s. Harry quickly calculates the moment of inertia and angular momentum of the wand-rat system when the wand is pivoted about an axis

(a) perpendicular to the plane of rotation through the 55.0-cm mark and

I = kg·m2

L = kg·m2/s

b) perpendicular to the plane of rotation through the 0-cm mark.

I = kg·m2

L = kg·m2/s

An object of 7kg is lit and it becomes suspended at rest from the ceiling. It then explodes into 3 parts. Part 1 has a mass of 2.7kg and is traveling 3.1m/s at 22 degrees above x-axis. Part 2 has a mass of 1.75kg and moves 4.4 m/s at 53 degrees above x-axis. Determine the mass, velocity, and direction of the 3rd piece using momentum. Thank you.

1.Three identical very dense masses of 3500 kg each are placed on the x axis. One mass is at x1 = -120 cm , one is at the origin, and one is at x2 = 300 cm .

What is the magnitude of the net gravitational force Fgrav on the mass at the origin due to the other two masses?

Take the gravitational constant to be G = 6.67×10⁻¹¹ N⋅m2/kg2 .

Express your answer in newtons to three significant figures.

2.Three identical very dense masses of 5000 kg each are placed on the x axis. One mass is at x1 = -100 cm , one is at the origin, and one is at x2 = 310 cm .

What is the magnitude of the net gravitational force Fgrav on the mass at the origin due to the other two masses?

Take the gravitational constant to be G = 6.67×10⁻¹¹ N⋅m2/kg2 .

Express your answer in newtons to three significant figures.

A block of mass m = 98 kg slides along a horizontal surface. The coefficient of friction between the block and the surface is μ_k = 0.38. The block has an initial speed of v_o = 13 m/s in the positive x-direction as shown.

a) write an expression for x-component of the frictional force the block experiences, F(f), in terms of the given variables and variables available in the palette

b) what is the magnitude of the frictional force in N?

c) How far will the block travel, in meters, before coming to rest?

1. The blades of a ceiling fan have a radius of 0.380 m and are rotating about a fixed axis with an angular velocity of +1.50 rad/s. When the switch on the fan is turned to a higher speed, the blades acquire an angular acceleration of +2.00 rad/s² . After 0.500s has elapsed since the switch was reset, what is

   (a) the total acceleration (in m/s) of a point on the tip of a blade and

   (b) the angle φ between the total acceleration a and the centripetal acceleration a_c?

Quantitatively (i.e. with equations) explain fictitious force in 1) linear motion and 2) uniform circular motion.

Calculate the well potential for the fission decay channel resulting in ¹⁴⁰Ba and ⁹⁸Kr.

What is meant by the term `dynamic range' in the context of a data acquisition system? How can selection of
the wrong dynamic range affect either (a) the precision of the experimental measurements, or (b) capture of
the entire signal of interest.

A 0.300-kg ice puck, moving east with a speed of 5.84 m/s , has a head-on collision with a 0.990-kg puck initially at rest. Assume that the collision is perfectly elastic.

A) What is the speed of the 0.300-kg puck after the collision?

Express your answer to three significant figures and include the appropriate units.

B) What is the direction of the velocity of the 0.300-kg puck after the collision? East or West?

C)

What is the speed of the 0.990-kg puck after the collision?

Express your answer to three significant figures and include the appropriate units.

D) What is the direction of the velocity of the 0.990-kg puck after the collision? East or West?