True or False. Please explain answer.

a) In the absence of net external force, the center of mass of a system remains at a fixed location.

b) Total mechanical energy can be a negative quantity.

Answer True or False for each question. For the three questions indicated also provide a full explanation; this is likely to take at least two sentences.

5) It will be possible to measure all properties of a particle with perfect accuracy if our technology increases.

6) By t = 1 sec, the U contained about 25 % He nuclei and the rest H nuclei . Explain.

7) In quantum physics, Heisenberg's uncertainty principle says that matter and antimatter can appear spontaneously in empty space. Explain.

8) Our U contains mass because for every 10⁹ matter particles it created it also created 10⁹+ 1 antimatter particles. Explain.

Ernest Rutherford (the first New Zealander to be awarded the Nobel Prize in Chemistry) demonstrated that nuclei were very small and dense by scattering helium-4 nuclei (⁴He) from gold-197 nuclei (¹⁹⁷Au). The energy of the incoming helium nucleus was 7.39 ✕ 10⁻¹³ J, and the masses of the helium and gold nuclei were 6.68 ✕ 10⁻²⁷ kg and 3.29 ✕ 10⁻²⁵ kg, respectively (note that their mass ratio is 4 to 197). (Assume that the helium nucleus travels in the +x direction before the collision.)

(a)

If a helium nucleus scatters to an angle of 102° during an elastic collision with a gold nucleus, calculate the helium nucleus' final speed (in m/s) and the final velocity (magnitude in m/s and direction counterclockwise from the +x-axis) of the gold nucleus.

⁴He speed m/s?

¹⁹⁷Au velocity m/s?

¹⁹⁷Au direction ° counterclockwise from the +x-axis?

(b)

What is the final kinetic energy (in J) of the helium nucleus?

J?

3.10 Show that the minimum cation-to-anion radius ratio for a coordination number of 4 is 0.225.
3.12 On the basis of ionic charge and ionic radii, predict crystal structures for the following materials: (a) CaO (b) KBr. Justify your selections.

A wheel is rotating about an axis that is in the z-direction. The angular velocity ωz is -6.00 rad/s at t = 0, increases linearly with time, and is +4.00 rad/s at t = 19.0 s . We have taken counterclockwise rotation to be positive.

How long is the time interval during which the speed of the wheel is increasing?

A muon is created 50 km above the surface of the earth. In the earth's frame, the muon is traveling directly downward at 0.9999c.

Part A

In the earth's frame of reference, how much time elapses between the muon's creation and the time it reaches the surface?

Part B

Use time dilation to determine, in the muon's frame, how much time elapses between the muon's creation and the time it reaches the surface.

Part C

In the muon's frame of reference, length contraction reduces the distance between the point at which it is created and the surface of the earth. What is this distance?

A landing craft with mass 1.22×104 kg is in a circular orbit a distance 5.70×105 m above the surface of a planet. The period of the orbit is 5600 s . The astronauts in the lander measure the diameter of the planet to be 9.80×106 m . The lander sets down at the north pole of the planet.

A. What is the weight w of an astronaut of mass 86.0 kg as he steps out onto the planet's surface?

Agree that the derivative of entropy w/r to P at constant T is the negative of the product of volume and coefficient of thermal expansion? And that therefore deltaS is negligible for liquids and solids but can be quite substantial for gases? Please explain it!

1. A shot putter projected a shot at the angle of 28 degrees at a velocity of 47 fps. The shot was released from 7 ft from the ground.

a. Compute the velocity in the y and x direction (in fps).

b. Compute the time from release of the shot put to the highest point.

c. Compute the time from the highest point to the ground.

d. Determine the total time the shot traveled while in the air.

e. How far will the ball travel (in feet)?

Jupiter's moon Io has active volcanoes (in fact, it is the most volcanically active body in the solar system) that eject material as high as 500 km (or even higher) above the surface. Io has a mass of 8.93×1022 kg and a radius of 1821 km .

How high would this material go on earth if it were ejected with the same speed as on Io? Earth has a mass of 5.97×1024 kg and a radius of 6356 km.

The correct answer is 72.3 km. Please explain your work. Thank you~

1.) A box made of wood is sitting on a wooden floor. The box and contents has mass 40kg. The coefficient of static friction is 0.50 and kinetic friction is 0.30. A person begins to push the box horizontally by slowly increasing their force until it reaches 160N. Describe the state of motion (if any) of the box and the frictional force acting.

2.) The formula for friction is f=uN, for both static and dynamic friction. What factors that may effect the force of friction that are not listed in this equation. List three if you can and discuss them briefly.

Write brief but complete answers to the following questions

a) Write Schrodinger's time-independent,1-D equation

b) What does this equation represent?

c) What requirements must the wave equation satisfy?

d) What are the conditions for an acceptable solution to this equation?

baseball pitcher executes a pitch in 0.32 sec. (assume that his motion of the pitching arm is a circular, also assume that v₁ = 0). If his pitching arm is 90 cm long, what are the magnitudes of the tangential and radial accelerations on the ball just before ball release, when tangential ball speed is 35 m/s (in m/s²)? What is the magnitude of the total acceleration on the ball at this point (in m/s²)?