Three resistors have values R1= 47Ω, R2 = 100Ω, and R3 = 10 Ω. There is a 1.5V battery. The battery and three resistors are all connected in various circuits described below. Calculate the equivalent (or total) resistance, and any currents for each of the following configurations:

A) Series circuit

B) Parallel circuit

C) Series-parallel combination where R1 and R2 are in parallel and that combination is in series with R3.

Explain how an experiment of a baseball rolling down a hill would be related to Angular Momentum Principle.

Part 1.
When a vehicle is passing through the atmosphere, at some point it may decelerate at a rate of 49.2 m/s² (away from the centre of Earth) while Earth's gravitational pull remains at -9.80 m/s².
a) In such a situation, what is the apparent weight in g's of an astronaut inside the vehicle?
b) In this situation, is the astronaut in a micro-gravity situation.

Part 2.
A space vehicle is in orbit around a planet and moving in a clockwise fashion. If the vehicle wants to move to a lower orbit, should the first rocket firing aim to decelerate or accelerate the vehicle, and similarly, what should the second firing of the rockets aim to do?

Part 3.
If a space vehicle re-enters Earth's atmosphere at too shallow an angle, what will happen to the vehicle and why?

Part 4.
In using the gravitational field of a planet to propel a vehicle farther into space, what two important quantities are conserved?

Part 5.

What is it about the position of the three antennas in NASA's Deep Space Network (DSN) that allows Earth-based observers to keep in contact with vehicles deep in space?

You are in charge of designing a catapult that must launch a rock of mass m using a single spring that can only be compressed a distance x. The catapult’s target is located a distance L away from the catapult, but there is a wall of height L/3 located halfway between the catapult and the target. Determine the smallest spring constant (and the corresponding launch angle) that will allow you to hit the target. (You can make the simplifying assumption that x is very small compared to L.)

1.

what is the angular separation (between a grating and screen) of the second order maximums produced by 420nm and 300 nm wavelengths incident upon a 450 lines/mm diffraction grating

2.

Boron nitride (a lubricant) with an index of refraction of 2.0 is heated within a microwave oven. If the speed of the microwaves is 3.0X10⁸m/s, what is the speed of the microwaves in the boron nitride

The depth of the water body is 2 meters.
(a) There shall be a light source at the bottom of the body of water, a disc of opaque material floating on the
the center is exactly above the light source. Calculate the minimum radius of the disk so that none
the light beam from the light source would not escape from the water. Make an explanatory drawing with it applied
the path of the light rays and the angles used in the formulas.
b) Calculate the apparent depth of the body of water for an observer looking at the water surface at an angle of 30 degrees
with respect to the vertical. Make an explanatory drawing showing the course of the light rays and the formulas
angles used.

(a) Suppose a meter stick made of steel and one made of invar are the same length at 0°C. What is their difference in length at 45.0°C? The coefficient of thermal expansion is

12 ✕ 10⁻⁶/°C for steel and 0.9 ✕ 10⁻⁶/°C for invar.

(b) Repeat the calculation for two 38.5-m-long surveyor's tapes.

Boxes A 7.00 kg and B 15.00 kg , to the right of A move on a frictionless, horizontal surface. Box B is traveling to the left at 0.500 m/s, and box A is traveling to the right at 2.00 m/s initially. The boxes are attached with ideal spring bumpers. Eventually, they have head-on collision. consider that all motion before and after it is along a horizontal axis. Assume that +x is the direction of the initial motion of A.
a) Find the maximum energy stored in the spring bumpers.
b) Calculate the velocity of block A when the energy stored in the spring bumpers is maximum.
c) Calculate the velocity of block B when the energy stored in the spring bumpers is maximum.
d)Calculate the velocity of block A after the blocks have moved apart.
e) Calculate the velocity of block B after the blocks have moved apart.

Boxes  A ( 5.00 kg ) and B( 14.00 kg , to the right of A) move on a frictionless, horizontal surface. Box BBis traveling to the left at 0.500 m/s, and box A is traveling to the right at 2.00 m/s initially. The boxes are attached with ideal spring bumpers. Eventually, they have head-on collision. consider that all motion before and after it is along a horizontal axis. Assume that  +x is the direction of the initial motion of A.

A-)Find the maximum energy stored in the spring bumpers.

B-)Calculate the velocity of block A when the energy stored in the spring bumpers is maximum.

C-)Calculate the velocity of block B when the energy stored in the spring bumpers is maximum.

D-)Calculate the velocity of block A after the blocks have moved apart.

E-)Calculate the velocity of block B after the blocks have moved apart.

If you had two solenoids of identical wire and number of turn per unit length, but different radial size, what would you expect to find if you measured the magnetic field inside at the center?

You are designing a slide for a water park. In a sitting position, park guests slide a vertical distance h down the water-slide, which has negligible friction. When they reach the bottom of the slide, they grab a handle at the bottom end of a 6.00-m-long uniform pole. The pole hangs vertically, initially at rest. The upper end of the pole is pivoted about a stationary, frictionless axle. The pole with a person hanging on the end swings up through an angle of 72.0∘, and then the person lets go of the pole and drops into a pool of water. Treat the person as a point mass. The pole’s moment of inertia is given by I=1/3ML^2 where L = 6.00 m is the length of the pole and M = 31.0 kg is its mass. For a person of mass 70.0 kg, what must be the height h in order for the pole to have a maximum angle of swing of 72.0∘ after the collision?

What is the gain material and its phase, typical pumping method, typical output power, and efficiency for laser of your choice producing tunable visible light?

Daniel with mass 65.0 kg and Rebecca with mass 45.0 kg are skating. While Daniel stands at rest, He is struck by Rebecca. She is moving at 13.0 m/s before she collides with him. Rebecca has a velocity of magnitude 6.00 m/s at an angle of 55.1 ∘ from her initial direction after the collision. Both skaters move on the frictionless and horizontal surface .
a)Find the magnitude of Daniel's velocity after the collision?
b)Find the direction of Daniel's velocity after the collision? ∘ from the Rebecca's original direction
c)Find the change in total kinetic energy of the two skaters as a result of the collision?

A box with mass 0.0325 kg moves in a vertical circle that has a radius of 0.600 m on the inside of a circular track. When the box is at the bottom of its path, point A, the magnitude of the normal force exerted on the box by the track has magnitude 3.75 N. When the box reaches the top of its path, point B, the magnitude of the normal force exerted on the box has magnitude 0.665 N.

How much work was done on the box by friction during the motion of the box from point A to point B?

Two long parallel wires 20 cm apart carry currents of 5.0 A and 8.0 A in opposite directions. At what point is the net magnetic field due to the two of them zero?