A metal cylinder of mass ? = 5 kg with a coaxial hole is sliding horizontally on a metal rod. A spring with spring constant ? = 500 N/m is attached to the cylinder. The other end of the spring is attached on a table at a vertical distance of ℎ = 0.3 m below the cylinder. The spring has an equilibrium length of ?_0 = 0.5 m.

a) What is the horizontal position ?0 of the cylinder when the spring is at its natural equilibrium length of ?0 = 0.5 m? Define the attachment point of the spring on the table as position ? = 0.

b) What is the length ? of the spring when the cylinder is at any given position ??

c) Draw a free-body diagram of the cylinder.

d) Show that the horizontal force from the spring on the cylinder is: ?? = −?? (1 − ?0 √? 2 + ℎ 2 )

3. Solve for frictional force in part A and the net force in Part B . Write your final answers for parts A and B rounded to 3 significant digits.

a. A 2.14 kg block is sliding along a rough horizontal surface, and the only unbalanced force acting on the block is a constant frictional force. Suppose the block is moving at speed 88.8 m/s at t = 0, and after 38.9 seconds it comes to rest. Find the magnitude of the frictional force, in Newtons, between the block and the tabletop.

b. A box of mass 40.6 g accelerates from velocity +57.2 m/s to velocity +60.6 m/s as it moves distance 85.9 m. Find the net force F_net, in Newtons, acting on the box. The direction of the force is given by the sign of the answer.

Understanding Physics - Problem 3)

Part 1) The figure is a section of a conducting rod of radius R₁ = 1.40 mm and length L = 14.40 m inside a thin-walled coaxial conducting cylindrical shell of radius R₂ = 11.1R₁ and the (same) length L. The net charge on the rod is Q₁ = +3.72 × 10^-12 C; that on the shell is Q₂ = -2.12Q₁. What are the (a) magnitude E and (b) direction (radially inward or outward) of the electric field at radial distance r = 2.28R₂? What are (c) E and (d) the direction at r = 5.24R₁? What is the charge on the (e) interior and (f) exterior surface of the shell?

Part 2) In the figure a small, nonconducting ball of mass m = 1.1 mg and charge q = 1.5 × 10^-8 C (distributed uniformly through its volume) hangs from an insulating thread that makes an angle θ = 35° with a vertical, uniformly charged nonconducting sheet (shown in cross section). Considering the gravitational force on the ball and assuming the sheet extends far vertically and into and out of the page, calculate the surface charge density σ of the sheet.

Your neighbor is pushing a 44.0-kg bag of dirty laundry across a parking lot as shown in the figure below. The coefficient of static friction between the bag and the asphalt is 0.1, and the coefficient of kinetic friction is 0.03. Assume that up and right are the positive directions.Determine the following for case (a), where he's pushing downward at an angle of 25°. (a) Calculate the minimum force F he must exert to get the stinky bag moving. Fmin = N (b) What is its acceleration once it starts to move, if that force is maintained? a = m/s2 PopUp: Force Equations 2. Determine the following for case (b), where he's pulling upward at an angle of 25 °. (a) Calculate the minimum force F he must exert to get the stinky bag moving. Fmin = N (b) What is its acceleration once it starts to move, if that force is maintained? a = m/s2

A kid in a car is holding a helium balloon. the dad slams on the brakes. what does the kid see the helium balloon do?
a. stay where it is?
b. move forward?
c. move backward?

Two stars, A & B, have same color. This implies that
a. Both stars emit same amount of light.
b. Both stars located at equal distance from the earth.
c. Both stars has the same temperature.
d. None of the above
2. The horizontal axis of H-R diagram plots
a. mass b. Luminosity c. apparent brightness d. temperature
3. Most stars (when plotted on a H-R diagram) would fall into a region called
a. red giant b. main sequence c. blue giant d. white dwarf
4. White dwarfs compare to main sequence class O stars are
a. larger b. younger c. smaller d. same size
5. Astronomers identify the stars on the upper right hand corner of H-R diagram as
a. very hot stars b. Blue giant stars c. Red giants d. yellow giants
6. Stars that lie in different places on the main sequence of the H-R diagram different
from each other mainly having different
a. Composition b. apparent brightness c. way that they formed d. mass
7. What type of main sequence stars expects to live longest?
a) O b) M c) F d) G
10. Luminosity of a star depends on
a. distance and temperature
b. brightness and distance
c. size and distance d) size and temperature

11. Apparent brightness of a star depends on
a. temperature and distance
b. size and distance
c. distance only
d. distance and luminosity
12. If parallax of a star is 0.5 arc sec, its distance is
a. 0.5 ly b. 0.5 pc c. 2 pc d. 2 ly

13-16 Refer the H-R diagram below

13. Consider stars a, b, and c. Which star has the greatest mass?
a b c
14. Consider stars a, b, and c. Which star has the longest life time?
a b c

15. Consider stars c and e, which star is larger?
(a) c (b) e (c) both c and e has same size (d) not enough information
16. Consider stars “a” and “e” , they both have same

(a) Size (b) Luminosity (c) brightness (d) temperature

17. The total amount of energy a star gives off each second is its
a. temperature b. apparent magnitude c. brightness d. luminosity
18. What is the spectral class of the Sun?
a) A b) B c) M d) G
19. The name of the star that appears brightest in the night sky is
a) Vega b) North star c) Sun d) Sirius
20. A star has apparent brightens 3 and absolute brightness 1. The distance to this star
from the earth is

a. 3 light years b. less than 10 pc c. more than 10 pc d. 100 l.y

Use the information in following table to answer questions 21-28
Name Apparent
brightness- m

Absolute
brightness M

Spectral class Distance l.y
Alderbaran 1 1.5 M 345
Arcturus 0.1 -0.6 K 182
Capella 0.4 -4 G 280
Ross 3.4 13 B 38
Cygni 18 7 M 54
Procyon 0 3.7 A 600
Eridani 5 4 K 480
21. What is the hottest star?
a. Capella b, Cygni c. Alderbaran d, Procyon
22. Which star has largest parallax angle?
a. Cygni b. Alderbaran c. Ross d. Procyon
23. Which star has the greatest luminosity?
a. Capella b, Eridini c. Alderbaran d, Ross
24. Which star appears red?
a. Arcturus b, Eridini c. Cygni d, Ross
25. Which star is not visible to naked eye?
a. Capella b, Cygni c. Sirius d, Ross
26. Compare Arcturus and Eridani, Which star is bigger
a. arcturus b. Eridani c. both stars have same size
27. Star A has apparent brightness 2 and star B has apparent brightness 8. Which star
appears brighter in the sky?
a) B b) A c) cannot tell without the distance
28. Sun is known as a normal star, but it appears very bright because
a. it has very large luminosity
b. its core temperature is very high compared to all other stars
c. It is much bigger than all other stars
d. It is very close to the earth.
29. Two stars, A & B, belong to same spectral class and same size. But A is closer to
us than B. Which star has greater “m” value?
(a) A ( b) B (c) both stars have same m value (d) cannot answer without M
30. Stars A and B have the same luminosity. Star A has apparent magnitude 1 and star
B has apparent magnitude 6 . Which star is closer?
(a) A ( b) B (c) distance is same for both stars (d) cannot answer without
knowing temperature

Please explain and give an example:

Planar Trigonometry, Right trianges, laws of sine and cosine.

Please type answer do not hand write. Thank you

1.a) What is the (average) power needed to accelerate a car of mass m=1550 kg from zero to 60 mph in 7.1 s?

b) Which simplifications did you make in that short calculation, i.e. what did you neglect?

2.The current BC hydro rates are 6.55 cents per kWh. If you have a desktop computer that uses 200 W (on average), how much does it cost you per month to run it for 6 hours per day?

3.

An elevator car has a mass of 1600 kg and is carrying passengers with a combined mass of 200 kg. A constant friction force of 4000 N is acting.

a) How much power must be delivered by the motor to lift the car with the passengers at a constant speed of 3m/s?

b) How much power must be delivered by the motor when the car with the passengers is moving with speed v = 3m/s, and it is supposed to provide an acceleration of 1.00m/s2?

How much energy is required to change a 35-g ice cube from ice at ?15°C to steam at 115°C?

An RLC series circuit has a 1.00 kΩ resistor, a 160 mH inductor, and a 25.0 nF capacitor.

(a)

Find the circuit's impedance (in Ω) at 490 Hz.

Ω

(b)

Find the circuit's impedance (in Ω) at 7.50 kHz.

Ω

(c)

If the voltage source has V_rms = 408 V, what is I_rms (in mA) at each frequency?

mA (at 490 Hz)

mA (at 7.50 kHz)

(d)

What is the resonant frequency (in kHz) of the circuit?

kHz

(e)

What is I_rms (in mA) at resonance?

mA

†

what is bigamy? what deviance theories apply to bigamy

A metal sphere hangs from a string and has 2 kg of mass. The sphere has a charge of +5.5

A spherical raindrop 2.7 mm in diameter falls through a vertical distance of 5000 m. Take the cross-sectional area of a raindrop = πr², drag coefficient = 0.45, density of water to be 1000 kg/m³,and density of air to be 1.2 kg/m³.

(a) Calculate the speed a spherical raindrop would achieve falling from 5000 m in the absence of air drag.
313.04 m/s (correct)

(b) What would its speed be at the end of 5000 m when there is air drag? (Note that the raindrop will reach terminal velocity after falling about 30 m.)
  
_______ m/s

Quantum computing / Chapter 9 - Deutsch-josza algorithm : "Suppose that f (00) = f (01) = 0, f (10)= f (11) = 1. Apply the Deutsch-Josza algorithm and show that at least one of the first two qubits ends up as a 1." I found this at Quantum Computing Explained by David McMahon Example 9.3 and i wasn't able to understand how he used Uf to get his third solution. I understand the reason behind applying the Hadamard gate. Help will be appreciated. Thanks in advance!