Ball 1, with a mass of 120g and traveling at 15m/s , collides head on with ball 2, which has a mass of 310g and is initially at rest.

What are the final velocities of each ball if the collision is perfectly elastic?

A lens is made of a transparent material having an index of refraction of 1.50. One side of the lens is flat, and the other convex with a radius of curvature of 23.0 cm. (a) Find the focal length of the lens. (b) If an object is placed 110 cm in front of the lens, where will the image be located?

A 1.20 kg block slides with a speed of 0.860 m/s on a frictionless horizontal surface until it encounters a spring with a force constant of 516 N/m . The block comes to rest after compressing the spring 4.15 cm.

A. Find the spring potential energy, U, the kinetic energy of the block, K, and the total mechanical energy of the system, E, for compressions of 0 cm.

B. Find the spring potential energy, U, the kinetic energy of the block, K, and the total mechanical energy of the system, E, for compressions of 1.00 cm.

C.Find the spring potential energy, U, the kinetic energy of the block, K, and the total mechanical energy of the system, E, for compressions of 2.00 cm.\

D.Find the spring potential energy, U, the kinetic energy of the block, K, and the total mechanical energy of the system, E, for compressions of 3.00 cm.

E.Find the spring potential energy, U, the kinetic energy of the block, K, and the total mechanical energy of the system, E, for compressions of 4.00 cm.

An old grindstone, used for sharpening tools, is a solid cylindrical wheel that can rotate about its central axle with negligible friction. The radius of the wheel is 0.330 m. A constant tangential force of 200 N applied to its edge causes the wheel to have an angular acceleration of 0.804 rad/s2.

(a) What is the moment of inertia of the wheel (in kg · m2)?

_________kg · m2

(b) What is the mass (in kg) of the wheel?

__________kg

(c) The wheel starts from rest and the tangential force remains constant over a time period of 4.50 s. What is the angular speed (in rad/s) of the wheel at the end of this time period?

__________rad/s

Suppose that you have a signal source, a set of point-transducers, and a handful of moderately powerful DSPs. Is it possible to construct an arrangement of the transducers such that the original signal propagates within a given region, but is absent or significantly attenuated outside of that region?

The obvious application would be sound systems that don't leak loud sound into neighboring rooms. But this would also be useful for limiting RF propagation to a physical space. In the audio example, you can shield the room with sound-absorbing materials. You could also build a faraday cage for the RF case, but either physical solution is likely to be prohibitively expensive. Now that powerful DSPs are cheap, can this be done entirely in the signal domain?

1)A circular loop of wire lies within the horizontal plane, and you are viewing it from above. You hold a magnet above the loop, with its north pole up and south pole down, and you drop the magnet. In what rotational direction will you see the induced current in the loop flow? (clockwise-counterclockwise)

2)The current going through a capacitor is called a (conduction current/displacement current)and arises from changing (electric field/magnetic field)

3) semiconductors are (diamagnetic/ferromagnetic/paramagnetic) materials

4) A circular loop of wire lies within the xy plane. It has an area of LaTeX: 1\:m^21 m 2 and an overall resistance of 4 Ohms. A uniform magnetic field runs in the positive z direction, and its magnitude increases at a rate of 2 T/s. What is the induced current?

A hollow ball of diameter D is suspended from a string of negligible mass whose length is equal to the ball’s diameter. The string is attached to the surface of the ball.

Find an expression for the period of this physical pendulum in the small-amplitude approximation.

A cosmic ray proton streaks through the lab with velocity 0.82c at an angle of 52° with the +x direction (in the xy plane of the lab). Compute the magnitude and direction of the proton's velocity when viewed from frame S' moving with β = 0.74.

Very short pulses of high-intensity laser beams are used to repair detached portions of the retina of the eye. The brief pulses of energy absorbed by the retina weld the detached portion back into place. In one such procedure, a laser beam has a wavelength of 810 nm and delivers 255 mW of power spread over a circular spot 163 μm in diameter. The vitreous humor (the transparent fluid that fills most of the eye) has an index of refraction of 1.34.

Part A: If the laser pulses are each 1.30 ms long, how much energy is delivered to the retina with each pulse Express your answer in millijoules to three significant figures.

Part B: What average pressure does the pulse of the laser beam exert on the retina as it is fully absorbed by the circular spot? Express your answer in Pascals to three significant figures.

Part C: What is the wavelength of the laser light inside the vitreous humor of the eye? Express your answer in nanometers to three significant figures.

Part D: What is the frequency of the laser light inside the vitreous humor of the eye? Express your answer in Hertz to three significant figures.

Part E: What is the maximum value of the electric field in the laser beam? Express your answer in volts per meter to three significant figures.

Part F: What is the maximum value of the magnetic field in the laser beam? Express your answer in teslas to three significant figures.

Your job with NASA is to monitor satellite orbits. One day, during a routine survey, you find that a 400 kg satellite in a 1000-km-high circular orbit is going to collide with a smaller 100 kg satellite traveling in the same orbit but in the opposite direction. Knowing the construction of the two satellites, you expect they will become enmeshed into a single piece of space debris. When you notify your boss of this impending collision, he asks you to quickly determine whether the space debris will continue to orbit or crash into the earth. Do you think the debris will orbit or crash into the earth? Explain your reasoning.

1. Three plane mirrors intersect at right angles. A beam of laser light strikes the first of them at an angle ? with respect to the normal

a)Show that when this ray is reflected off of the other two mirrors and crosses the original ray, the angle ? between these two rays will be ?=180?? 2?.

b)For what angle ? will the two rays be perpendicular when they cross?

2.A ray of light in diamond (index of refraction 2.42) is incident on an interface with water.

a)What is the largest angle the incident ray can make with the normal in diamond and not be totally reflected back into the diamond?

Respond to the following in a minimum of 175 words:

• The world's population grows each year. Does this mean that the mass of Earth increases each year? How old are atoms? Explain your answer with an example.

PLEASE TYPE RESPONSE DO NOT HAND WRITE!!

A mass, m=1.4 kg of negligible size, is attached at the end of a uniform rod of length L= 0.99 mm which has mass M= 1.9 kg . What is the moment of inertia of this arrangement if it is to rotate at an axis located at a distance 0.39*L from the end of the rod opposite to the mass, m? (At approximately the point marked with an 'X'.)

Calculate the moment of inertia of the rod-mass system given that the moment of inertia of a rod about the center of mass is I=(1/12)* M*L^2

A rod of mass "10m" and length "L" is hanging through a pivot at one end. A lump of clay of mass "m" is thrown perpendicular to the rod hitting it at the opposite end of the pivot. The lump sticks to the rod causing the rod to swing in a vertical circle up to an angle of 90^o. Given [m, L] Determine:

a. The initial speed of the lump of clay.

b. The angular speed of the system just after the collision.