a) Calculate the x- and y-components of the following two force vectors:

F1 = 200 Newtons @ 30°, F2 = 100 Newtons @ 135°

b) What is the magnitude & direction of the resultant vector:

R = F1 + F2

3. A football is kicked on a horizontal field at an angle of 40° and a speed of 27 m/sec.

a) What are the horizontal & vertical components of the initial velocity?

b) Using just your answer for part a, what are the horizontal & vertical components of the final velocity (no calculation necessary although you can calculate the values if that turns you on)?

c) How long was the football in the air? (Hint: use the two values for y-velocities above - don’t forget about minus signs.)

d) How far horizontally did the ball travel?

4. A car has a maximum acceleration of 5.4 m/s2 when it carries only the driver and has a total mass of 1100 kg. What is its maximum acceleration after picking up four passengers, adding an additional 300 kg of mass?

(Hint: the maximum acceleration in both cases is when the car’s engine is putting out the most power it can, which is the same in both cases.)

5. Calculate the average force (just magnitude) a bumper would have to exert to bring a 1200-kg car to rest in 15 cm when the car had an initial speed of 2.0 m/s (about 4.5 mph).

A group is considering installing a solar power station and has asked you for your recommendation for a photovoltaic system or a solar thermal system. At this stage you are asked not to include cost factors. The single point design condition they have given you is for an incident solar radiation on the collector of 550 W/m2, a surrounding temperature of 18 C. The dead state for this problem should be taken as To = 291 K, Po = 1 bar. You can perform your analysis at steady state conditions. In addition to determining the power output and first law efficiency of the options, you have been requested to determine the exergy destroyed for each of them. The photovoltaic system has an efficiency of 0.15 defined as the power output/incident solar radiation. The basic photovoltaic collector is 1.1 m2 and losses heat from both the front and back surface. The edge area can be neglected. The convective heat transfer coefficient is 10 W/m2 K. The inverter and signal conditioning device used to connect the photovoltaic collector to the grid and household has an efficiency of 0.87. The inverter operates isothermally. The solar thermal collector will heat the working fluid from a temperature of 32 C and has a concentration factor of 10,000. The concentration factor is the ratio of the incident solar radiation on the heat transfer surface to the incident solar radiation area. It is a concentrating collector with an opening of 1.1 m2 and a heat transfer area of 0.05 m2. The mass flow rate of the working fluid through the system is 0.009 Kg/s. The heat transfer area is not equal to the area of absorption. The convective heat transfer coefficient is 1.0 W/m2 K. The heat transfer from the collector can be considered to be at the average temperature of the working fluid, (Tin + Tout)/2. The specific heat of the working fluid is 678 J/(Kg K). The useful energy from this collector system is the change in the enthalpy of the flow through the system. The working fluid enters a heat engine with an efficiency of 0.30 that is connected to a generator with an efficiency of 0.90. The generator operates isothermally.

Answer the following:

a) Determine the power output for each type of system for a basic collector area.

b) Determine the exergy destroyed for each type of system.

c) Which system would you recommend on this analysis? This question neglects the costs.

A solenoid having an inductance of 3.3 ? is connected in series with a 4.7 Ω resistor. If a
10.0 ? battery is connected across the pair
Please Answer these 3 following questions.

(a) Find the equilibrium current in the circuit.
(b) How long will it take for the current to reach 80% of its final value?
(c) How much energy is dissipated by the resistor during the first 3 seconds?

A projectile is launched with an initial velocity vo at an angle theta above the horizontal.
In terms of vo, theta and acceleration due to gravity g, determine for the projectile
i) the time to reach its maximum height and
ii) its maximum height.

Suppose that you live in a flat-land, i,e a 2d flat universe, produce a derivation for the form of the translation partition function, and comment on the equations with clear explanation?

The wave function for a harmonic wave on a string is y(x, t) = (0.0010 m) sin((69.8 m^-1)x + (309 s^-1)t).

(a) In what direction does this wave travel?

+x-x    

What is its speed?
m/s

(b) Find the wavelength of this wave.
m
Find its frequency.
Hz
Find its period.
s

(c) What is the maximum speed of any string segment?
m/s

As shown below, a 840 kg car traveling east collides with a 1730 kg pickup truck that is traveling north. The two vehicles stick together as a result of the collision. After the collision, the wreckage is sliding at v_f = 19 m/s in the direction θ = 25° east of north. Calculate the speed of each vehicle before the collision. The collision occurs during a heavy rainstorm so you can ignore friction forces between the vehicles and the wet road. Express your answers using apropriate mks units.

A.) v_car,i =

B.) v_truck,i =

C.) Determine what fraction of the total initial KE is turned into thermal energy as a result of the collision.

=

A mystery planet and its moon are found revolving around a nearby star. The star is a K3 Main Sequence star with a mass of approximately 0.8 M☉ and a radius of 0.78 R☉. The planet is believed to be terrestrial (Earth-like, and therefore of a similar density) and has an observed orbital period of 243 days. The moon orbits the planet every 13.2 hours with an average orbital radius of 19,600 km. Using this information, find:

(a)the orbital radius of the planet,

(b)the distance at which another planet in the system would have an orbital speed of 24,000 m/s,

(c)the point between the star and the planets at which the net force on a spacecraft would be zero, and

(d)the period of a 80-cm long simple pendulum with a mass of 30 grams that is swinging on the planet’s surface

Consider an ideal gas turbine cycle with two stages of compression and two stages of expansion.  The pressure ratio across each compressor stage and each turbine stage is 5 to 1. The pressure at the entrance to the first compresor is 100 kPa, the temperature entering each compressor is 25°C (298 K), and the temperature entering each turbine is 1100°C (1373 K). An ideal regenerator is also incorporated into the cycle.  For the air involved, it may be assumed that Cp = 1.005 kJ/kg.K and the specific heat ratio, k = 1.4.

(a) The compressor work is __ kJ/kg. (b) The turbine work is __ kJ/kg. (c) The cycle efficiency is __ %.

A plane mirror rotates about a vertical axis in its plane at 35 revs s^-1 and reflects a narrow beam of light to a stationary mirror 200 m away. This mirror reflects the light normally so that it is again reflected from the rotating mirror. The light now makes an angle of 2.0 minutes with the path it would travel if both mirrors were stationary. Calculate the velocity of light.

Please can you explain the solution to this question step by step with a clear diagram! I am really confused on what to picture when about a vertical axis in its plane at 35 revs s^-1 and when it says , light now makes an angle of 2.0 minutes with the path? how can an angle be in seconds?

I worked out the fields radiated by an electric dipole in class, and they are also in 11.1.2 of the text. These fields carry energy away and we know the radiated power. From the point of view of the source of the time dependent current (and charge) in the dipole, the antenna could just as well be a resistance with resistance R. Find the value of this resistance, known as the “radiation resistance.”

Griffiths Intro to Electrodynamics

What is the qualitative mouvement for an electric dipole sitting in situation a) horizontally below a charge q and b) vertically below a charge q? Explain whether one has a translation, which one has a faster translation, or why there is no translation at all.

In Chapter 10, we are working on simple harmonic motion. What similarities do you see in the motion of the skater in the simulation to the simple harmonic motion described in Chapter 10? Use the pendulum as an example and discuss changes in velocity, potential energy, kinetic energy and damped motion.

Light of wavelength 650 nm is incident on a long, narrow slit. Find the angle of the first diffraction minimum for each of the following widths of the slit

(a) 1 mm

............rad

(b) 0.1 mm

...........rad

(c) 0.01 mm

..........rad

A solid, homogeneous sphere with a mass of m₀, a radius of r₀ and a density of ρ₀ is placed in a container of water. Initially the sphere floats and the water level is marked on the side of the container. What happens to the water level, when the original sphere is replaced with a new sphere which has different physical parameters? Notation: r means the water level rises in the container, f means falls, s means stays the same. Combination answers like 'f or s' are possible answers in some of the cases.

The new sphere has a mass of m = m₀ and a radius of r < r₀. (choose from r, f, s, r or s, f or s )
The new sphere has a radius of r = r₀ and a density of ρ > ρ₀. (choose from r, f, s, r or s, f or s )
The new sphere has a radius of r = r₀ and a mass of m < m₀. (choose from r, f, s, r or s, f or s )