2) Two charged spheres separated by 2m are suspended vertically from a horizontal beam by insulating strings. The spheres have the same mass 4kg. The charges on the spheres are 2 ?C and -3 ?C.

(a) Calculate the electric force between the charges. Give both magnitude and direction.

(b) Determine the electric potential (Volts) at a point midway between the charges.

(c) What direction are the electric field lines for each charge?

In a calorimetry experiment to determine the specific heat capacity of a metal block, the following data was recorded: Quantity Mass of the metal block 0.50 kg Mass of empty calorimeter + Stirrer 0.06 kg Mass of calorimeter + stirrer + water 0.20 kg Mass of water 0.14 kg Initial Temperature of metal block 55.5 ⁰C Initial Temperature of water and calorimeter 22 ⁰C Final Temperature of block- water system 27.4 ⁰C Take the specific heat capacity of water to be 4186 J/Kg °C. The calorimeter and stirrer are made of Copper. Specific heat capacity of Copper is 387 J/Kg °C. Ignore the mass of the stirrer. Use the data and the information given to: a) Calculate the specific heat capacity of the metal block. (Please show ALL work for full credit) b) From your result above, what is the metal block probably made up of? c) Calculate the final temperature of the block – water system if the mass of the water in the calorimeter is increased to 0.50 kg (the same as the mass of the metal block).

A) a roller coaster it's traveling with a velocity of 20 m/s at the top of an incline. If the incline has a height of 10m, determine the coasters velocity at the middle of the incline. Neglect friction and use 10 m/s^2 for gravity

B) a vehicle weighing 15000 nt is traveling at 50 m/s in the i direction. It collides with a wall and stops in 1/10 second. If the collision was inelastic, determine the average force of the vehicle on the wall.

1-Explain a physical system has block attached to the end of string?

2-A rope of length and mass has a string of force constant at distance d. Calculate the frequency?

You are analysing data collected by a rover on the moon. You may assume that the rover starts at the origin (0,0,0), and that each coordinate it transmits contains an East-West component, a North-South component and an altitude component, relative to the origin. Let positive movement in the i direction be East, positive movement in the j direction be North, and positive movement in the k direction be increasing altitude. All values are in meters. Assume the moon is flat (neglect its curvature). The rover relays the following four coordinates in order, as it descends into a crater. Coordinates are issued each time the rover changes direction. As such, you may assume that each trajectory between these points is a straight line:
O : (0, 0, 0).
P₁: (2000, 5000, -500).
P₂: (3000, 8000, -600).
P₃: (6000, 9000, z).

Unfortunately, the transmission of the fourth coordinate is corrupted, and does not have an altitude component. For now, you label this component as z.

(a) Determine the displacement vectors describing the rover's straight-line trajectory between each of their transmissions. You may keep z as an unknown.

(b) Upon reaching P₂, the rover's battery has drained and requires recharging. Assuming the battery was initially at full charge, calculate the approximate range of the rover from one battery charge (i.e. what distance can it travel before requiring a recharge).

(c) For communication with the rover, mission control needs to point their antenna (located at O) towards the rover. Ignoring the altitude component (i.e. treat the problem as two-dimensional), calculate the angle that the antenna must be rotated to point towards P₂ if it is currently pointing at P₁.

(d) Based on the time taken to send and receive communications, you calculate that at P₃ the rover must be 10,850 meters from O. Determine z, the altitude component of the co-ordinate P₃. You may assume that P₃ is the lowest point in the crater.

1. The diffusion rate of a gas is directly proportional to what variables and inversely proportional to what variables?

A) The medium-power objective lens in a laboratory microscope has a focal length fobjective = 4.00 mm . If this lens produces a lateral magnification of -37.0, what is its "working distance"; that is, what is the distance from the object to the objective lens B) What is the focal length of an eyepiece lens that will provide an overall magnification of -115? Assume student's near-point distance is N = 25 cm.

Ice with a mass of 52 g originally at 0.0 deg. C is added to 450 g of water originally at 80. deg. C. Determine the final temperature once all the ice melts and all the water reaches thermal equilibrium. Assume that no heat is exchanged with the container.

How much horsepower would a Challenger SRT® Hellcat Redeye Widebody need to tow the SS Delphine up the industry standard: Davis Dam Grade Climb? Pro Tips Davis Dam assumed grade = 7% Air density is sea level conditions (.002377 slugs/f^t3) w(weight) of the SS Delphine + trailer + Redeye = 3,922,000 + 150,000 + 4451 Lbs Crr = coefficient of rolling resistance = .015 Assume Combined CDA is 1555 ft^2 SAE J2807 (Davis Dam Grande Climb) - min speed is 40mpg (59 ft/s) F(drag) = 1/2p x V^2 x C(d)A F(rolling resistance) = W x cos x Crr F(weight) = W x sin F(sum) = F(drag) + F(rr) + F(weight) P = F(sum)XV convert to horsepower = P(1hp/550ft lbf/sec)

1. State the right-hand rule for the magnetic field lines from a current-carrying wire.

2. You’ve got magnetic field lines making circles around a current-carrying wire. How do you find the magnetic field vectors?

3. How do you find the direction of the magnetic field at the center of a current-carrying loop of wire?

4. In Ampere’s law, how do you determine the sign of currents for calculating Iencl?

1.) The workdone to assemble a collection of charges is given by the formula Wensemble = (1/2)∑i(qiVi), where Vi is the scalar potential at the point occupied by the ith charge in the absence of that charge. The scalar potential is equal to the work required to move a test charge of+1 from infinity to the location of qi in the presence of all other charges in the ensemble. The constant of proportionality for Wensemble is arbitrarily taken as unity. By doing so, the value of Wensemble does not conform to standard units of energy, but we are interested only as to the value (positive or negative) of Wensemble relative to zero.

a.) The work done in moving a pair of charges from infinite separation to a finite distance r can be determined by evaluating a path integral; however, the formula for Wensemble should work for two charges as well as a dozen charges. Show that the formula for Wensemble gives the same result as the path integral, namely W=q1q2/r.

b.) Is there an equal-distant arrangement of three charges that is of lower energy that an infinite separation of those charges? In other words, can we assemble three charges at the vertices of an equilateral triangle that requires positive work to move those charges to an infinite separation? Compute Wensemble for two possibilities.

c.) The sodium ion channel is a tetramer with four-fold rotational symmetry. Each subunit provides a line of four carbonyl oxygen atoms perpendicular to the surface of the bilayer membrane. The pore selectively passes the sodium ion without the expenditure of energy, and can be represented schematically as a stack of four squares, separated by a distance of 3.8 Å, with carbonyl oxygen atoms occupying the vertices of each square. Sodium ions putatively bind at the center ofeach square, coordinating to the carbonyl oxygen atoms, but is this a stable arrangement on the basis of electrostatic interactions? For the second and third layers, the nearest neighbors to the sodium ions are given by the image below to the right. The distance between oxygen atoms and the central sodium ion is 2.5 Å. Assuming a charge of +1 for the sodium ion, what charge (sign and magnitude) must the oxygen atoms have to assemble the system on the right side with no expenditure of work? (No expenditure of work implies the sodium ion encounters no barrier in its passage through the pore). Is this a reasonable partial charge for the oxygen atom of a carbonyl group? Repeat the calculation using a distance of 3.8 Å between oxygen and sodium atoms. Can a potassium ion make it through a pore of this design?

For the highest temperature, is more of the intensity (area of the intensity vs. wavelength graph) in the visible part of the spectrum or in the infrared part of the spectrum? How could a light bulb be made more efficient so it puts out more light in the visible?

You are riding your bicycle directly away from a stationary source of sound and hear a frequency that is 0.7% lower than the emitted frequency. The speed of sound is 346 m/s. What is your speed?

Describe the process that occurs when the sound wave energy travels across the room.