Derive the moment of inertia, of triatomic linear rotors

(a) An object is subjected to the force F = 3x³ z ı ^ + 5 z^{2k ^} N, where x and z are in metres. The object can only move in the xz-plane.

          (i) The object moves from the origin by moving first along the x-axis to (a, 0) and then parallel to the z-axis to the point with coordinates (a,b). How much work does the force do?

[2 marks]

          (ii) The object moves from the origin by moving first along the z-axis to (0,b) and then parallel to the x-axis to the point with coordinates (a,b). How much work does the force do?

[2 marks]

          (iii) Is this a conservative force?

[1 mark]

          (iv) Can this force be expressed as the gradient of a potential? If so, give an expression for the potential. If not, give reasons why.

[2 marks]

(b) In the figure, we show a spring compressed by 85 cm. It is used to launch a physics student of mass 88 kg. The track is frictionless until it starts up the incline. Assume that the acceleration of gravity is 9.8 m/s². The student has a coefficient of kinetic friction of 0.23 on the 30^o incline.

Figure 3 (If the image above does not appear, click here.)

          (i) What is the student's speed just after losing contact with the spring?

[3 marks]

          (ii) Once the student has reached the lowest point on the track, they continue back up the other side, slowed down by friction and gravity. How far does the student travel up the incline before stopping?

[3 marks]

A roller coaster starts at ground level and rises up 139 m above the ground on the first hill. What is the maximum speed it can have when it rolls down to the ground level?

1.The same horizontal force, of magnitude F, is applied to two different blocks, of mass m and 3m The blocks move on a frictionless surface and both blocks begin from rest. If each block moves the same distance as the force is applied, which one of the following sentences is true?

A)The lighter block acquires 9 times as much kinetic energy as the heavier block.

B)The two blocks acquire the same kinetic energy.

C)The heavier block acquires 3 times as much kinetic energy as the lighter block.

D)The lighter block acquires 3 times as much kinetic energy as the heavier block.

E)The heavier block acquires 9 times as much kinetic energy as the lighter block.

Note: I initially came up with C as my answer, but it is supposably wrong.

1.1 Two identical objects of the same mass, initially at rest, are accelerated through the same distance by different forces such that one object gains velocity twice that of the other object. One can conclude that the force on the faster object is _________

A)10 times that of the slower object

B)Half that of the slower object

C)16 times that of the slower object

D)Twice that of the slower object

E)Four times that of the slower object.   

F)Three times that of the slower object

Please help and explain as I want to understand the question and answer. Thank you.

Consider an atom with four energy levels, where the lowest energy is -10 eV and the highest level is 0 eV. Sketch an energy-level diagram that could produce the spectrum. What are the energies of the other two energy levels. (Note: there are more than two answers.)

A -2 eV and -5 eV

B -1 eV and -4 eV

C -1 eV and -6 eV

D -6 eV and -9 eV

E -7 eV and -3 eV

A student put a red rose under blue light and the rose appears black. Student places rose under red light and it appears red. Explain this student's conclusion using the laws of physics and color.

I am playing pool and i hit a trick shot. I hit the ball at an angle 55 degrees. with a force of 10 newtons for .4seconds. The ball ihas a radius of 0.05m and a mass of .150kg. and the coeeficient of kinetic friction is 0.3.

1) determine the initial linear and angular velocity after i hit the ball? determine the distance the ball travels after it it and before it goes back? Determine the final velocity? answer all.

Provide the VHDL specification of a hybrid 32-bit adder that cascades 2 12 bit carry look ahead adders and one 10 bit carry look ahead adder.

a) Compare your adder with a full 32-bit carry-look ahead in performance and cost.

b) Compare your adder with a full combinational adder in performance and cost

c) Compare your adder with a ripple-carry adder in performance and cost.

d) Compare your adder to a bit serial (sequential) adder in performance and cost.

e) Which of the 5 designs is the best?

A sealed container of volume 7 m³ has two compartments with a barrier in between them. In one compartment, there is O2 at an initial pressure of 3 atm, initial temperature of 540 K, and volume 3 m³. In the other compartment, there is CO2 at an initial pressure of 5 atm, initial temperature of 430 K, and volume 4 m³. The barrier in the middle is punctured and the two gases mix together. What is the final pressure and temperature of the two gases and what is the change in entropy of the universe after the gases combine

Two friends, Al and Jo, have a combined mass of 166 kg. At the ice skating rink, they stand close together on skates, at rest and facing each other. Using their arms, they push on each other for 1 second and move off in opposite directions. Al moves off with a speed of 5.9 m/sec in one direction and Jo moves off with a speed of 9.7 m/sec in the other. You can assume friction is negligible.

1)What is Al's mass? kg

2)What is Jo's mass? kg

3)If you assume the force is constant during the 1 second they are pushing on each other, what is the magnitude of the force of Al on Jo? N

4)If you assume the force is constant during the 1 second they are pushing on each other, what is the magnitude of the force of Jo on Al? N

Prove the Kepler's laws with calculus.

1.- The orbit of a planet is an ellipse with the Sun at one of the two foci.

2.- A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time.

3.- The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit.

Which of the following statements are true concerning sign conventions for image formation?

Check all that apply.

a.A converging lens has a negative focal length; a diverging lens has a positive focal length.
b.For an upright image, the magnification is positive; for an inverted image, the magnification is negative.
c.A virtual image has a positive image distance; a real image has a negative image distance.
d.When the center of curvature of a spherical mirror is on the same side as the reflected light, the radius of curvature is positive; otherwise, it is negative.
e.When the object is on the same side of the reflecting or refracting surface as the incoming light, the object distance is positive; otherwise, it is negative.

he isotope 81Thallium204 has a half-life of 3.78 years and can be used as a nanotechnology MEMS (Micro Electric Mechanical System) power source device. It decays through beta emission into 82Pb204 with a branching ratio of 97.1 percent with an average decay energy of 0.764 MeV. It also decays through electron capture to 80Hg204 with a branching ratio of 2.9 percent with a decay energy of 0.347 MeV.

Calculate the energy release per decay event in [MeV/disintegration]

Calculate its total specific activity in [Becquerels / gm].

Calculate its total specific activity in [Curies / gm].

Calculate the specific power generation in [Watts(th) / gm].

For a 100 Watts of thermal power in a Radioisotope Heating Unit (RHU) power generator, how many grams of 81Thallium204 are needed?

After 3.78 years of operation, what would its power become?

Use: 1 MeV/sec=1.602x10-13 Watts, Av=0.602x1024 [nuclei/mole], 1 Curie=3.7x1010 Bq.

Two large parallel copper plates are 3.60 cm apart and have a uniform electric field of magnitude E = 7.98 N/C between them (see the figure). An electron is released from the negative plate at the same time that a proton is released from the positive plate. Neglect the force of the particles on each other and find their distance from the positive plate when they pass each other.