Choose an isotope and describe its radioactive decay process and how it is used. Write a minimum of 150 words.

The velocity of a particle moving in the xy plane is given by ,v=(5t-4.5t^2)i+8.3j with in meters per second and t (> 0) in seconds. At t = 2.4 s and in unit-vector notation, what are (a) the x component and (b) the y component of the acceleration? (c) When (if ever) is the acceleration zero? (d) At what positive time does the speed equal 10 m/s?

A camera lens has a focal length of 100 mm (thick lens). The photographer first adjusts the location of the lens to look at an object very far away (infinite distance). Then he tries to take a picture of a person 2 meters away from the lens. How is he going to adjust (move) the lens relative to its original position? What is the distance of the adjustment?

Steam locomotives have an efficiency of 18.0% and operate with a hot steam temperature of 425°C.

(a) What would the cold reservoir temperature (in °C) be if this were a Carnot engine? °C

(b) What would the maximum efficiency of this steam engine be if its cold reservoir temperature were 150°C? %

A car is going at 11.2 m/s on a horizontal straight road. When the traffic light is 30 m away, it turns red.
The reaction time of the driver is 0.3 s.
The car stops just before the traffic light with constant deceleration when the break is applied.

1. Find the time it takes for the car to stop, from the moment the light becomes red.

2. Plot speed of the car on y-axis and the time on the x-axis, taking t=0 at the

   moment when the traffic light turns red.

3. In the table provided below fill-up the blanks. It will help you to plot the graphs.

4. Plot the acceleration as a function of time.

5. Plot the distance covered as a function of time, using the v vs. t graph, taking zero

   at t=0.

The intensity pattern formed by a diffraction grating of N slits is

where θ is the angle of diffraction. The radiation reaches the grating at normal incidence.

Using the formula above and m = 0, ±1, ±2 ... and p = an integer ≠ mN

1. show that
   • the interference maxima occur for β = mπ
   • and minima occur for  β = pπ/N .
2. show that the orders m=pd/a (of interference) are missing if d/a is an integer .

Q2.

a) Explain what is meant by diffraction of waves, and give two examples of when diffraction is useful.

b) A loudspeaker has a diameter of 0.15 m. Using the principle of circular hole diffraction, calculate the angle at which the first minimum occurs when a. Sound of frequency 3400 Hz ( = 0.10 m) is emitted. b. Sound of frequency 10 kHz ( = 0.034 m) is emitted.

c) Use these answers to give one reason why woofers (speakers with a larger diameter used for lower frequencies) and tweeters (speakers with smaller diameters used for higher frequencies) are used in speaker cabinets to improve sound quality.

d) Give another reason why different diameter speakers are used for different frequencies.

Two projectiles with 50kg mass each are launched in opposite directions towards each other, both at an angle of 30 degrees off the horizontal. They both have the same initial velocity of 75m/s and they are separated by a distance of 200m.

a.) What is their combined initial kinetic energy?

b.) Right before they collide, how high off the ground are they?

c.) What is their total momentum here? (both directions)

d.) When they collide they stick together and lost kinetic energy. What is it now?

e.) How high does this combined projectile get?

f.) When the thing finally lands, what's the impact velocity?

1) Does the fact that the speed of light is a definite, predictable quantity conflict with the uncertainty relations?

2) How could you tell if electrons in very distant galaxies obey the Pauli exclusion principle?

Can you answer these question,please?

1. A mass weighing 10 lbs. is attached to a spring suspended from the ceiling. The mass will stretch the spring 6 inches. If the mass is pulled 5 inches below its equilibrium point and given an initial upward velocity of 0.3 ft./sec. and if damping forces are neglected, then what is the equation of motion of the mass? What is the amplitude of the motion?

2. A 980-newton force stretches a spring 0.4 meters. If a 200 kg mass is attached to the spring and pulled 0.5 meters below its equilibrium point and released, neglecting damping forces, what is the equation of motion of the mass?

3. A mass weighing 8.2 pounds will stretch this spring 1.36 feet. The spring/mass system is damped by a force that is 1.5 times the instantaneous velocity of the mass. Determine the equation of motion of the mass, if the mass is stretched 1 foot below its equilibrium point and released.

4. A 1 newton force will stretch a spring 1 meter. The spring/mass system is damped by a force that is 8 times the instantaneous velocity. A 12 kg mass is attached to the spring. The spring is compressed 0.8 meters above the equilibrium position and given an initial downward velocity of 3 m/s. Determine the equation of motion of the mass

5. A mass weighing 3(1/5) pounds stretches a spring by 1 foot. If the spring/mass system is damped by a force that is twice the instantaneous velocity and this same mass is given an initial upward velocity of 1.3 ft/sec from the equilibrium position, then what is the equation of motion of the mass?

The speed of light 3 × 10⁸ m / s, can be expressed in terms of other fundamental constants relating to electricity and magnetism. Give this algebraic expression and briefly explain where it comes from.

The 1.0 kg block in the figure is tied to the wall with a rope. It sits on top of the 2.0 kg block. The lower block is pulled to the right with a tension force of 20 N. The coefficient of kinetic friction at both the lower and upper surfaces of the 2.0 kg block is μk = 0.43.

What is the tension in the rope holding the 1.0 kg block to the wall?

What is the acceleration of the 2.0 kg block?

The figure shows an 8.5 kg stone at rest on a spring. The spring is compressed 11 cm by the stone. (a) What is the spring constant? (b) The stone is pushed down an additional 32 cm and released.What is the elastic potential energy of the compressed spring just before that release? (c) What is the change in the gravitational potential energy of the stone–Earth system when the stone moves from the release point to its maximum height? (d) What is that maximum height, measured from the release point?

Describe the different ways that radioactivity is used to measure the ages of different objects. Give as much detail as you can. Include such things as what is meant by the “age” of an object. Your write-up should be about 200-300 words for this part of the exercise.

Physics Hang Glider

You are flying a hang glider at 14 mph in the northeast direction (45°). The wind is blowing at 4 mph from due north.

a) What is your airspeed?

b) What angle (direction) are you flying?

c) The wind increases to 14 mph from the north. Now what is your airspeed and what direction are you flying? If your destination is to the northeast, how would you change your speed or direction so you might make it there? Test your answer using the sim.