As the temperature of a metal rod varies, so does the resistance and the dimensions of the rod. If a copper rod has a resistance of 4.78 Ω at 20.0°C, determine the resistance of the rod (in Ω) at 120°C by accounting for the changes in both the resistivity and the dimensions of the rod. The coefficient of linear expansion for copper is 1.67 ✕ 10−5 (°C)−1 and the temperature coefficient of resistivity is 4.04 ✕ 10−3 (°C)−1.

Snell's Law and the Law of Reflection explain how light is redirected when it encounters a surface between two media. In the extreme, light may only reflect at a boundary, and go back into the medium it was in. More often, some of it reflects and some goes through. If the boundary is plane and flat, then these laws are easy to interpret. When the boundary is curved, they describe happens at every point on the surface. One of the classic types of glass is called "crown" glass, which has an index of refraction for visible light of 1.52 and is usually free of significant impurities. It was one of the first glasses discovered, and windows are made from it. Another glass is called "flint" glass, and it has lead oxide added, which makes it heavier, more "dispersive", and increases its index of refraction to 1.62. 1. A ray of light enters a flat surface of crown glass at a 25 degree angle to the surface. At what angles do the reflected and refracted rays leave the surface? 2. As in the first part, but for flint glass, what are the angles? 3. For the flint glass, the refracted ray goes through the glass to the other side. If the glass is a parallel slab, what happens when the ray reaches the opposite side from the inside? At what angle to the surface does it exit the glass back into air? 4. What is the smallest angle to the surface that light can have and still be transmitted from the inside to the outside in the case of flint glass? What angle is the light going at as it leaves in that case? Hint: The laws of reflection and refraction are usually stated in terms of the angles to the perpendicular or "normal" to the surface. These questions are rephrased in terms of the angles to the surface so take care in interpreting the laws and your answers.

1. You have a massless, ideal spring with an unknown spring constant ?. You hang the spring from the ceiling. You then attach a mass (? = 21.0 kg) to the spring, which causes it to fall a distance of 2.75 m before stopping immediately before hitting the floor.

   (a) What is ??
   (b) Graph gravitational potential energy versus the position of the mass above the floor. (c) Graph elastic potential energy versus the position of the mass above the floor.
   (d) Graph the kinetic energy of the mass versus the position of the mass above the floor.

Suppose you’re eating in yet another restaurant where the dishes are shared at the table and all placed uniformly on a rotating disk-like surface. Model this surface as a thin disk of radius 45.3 cm. Someone else has spun the surface, such that it is initially at an angular speed of 0.4 rev/s. The surface and food has a combined mass of 3.3 kg. The waiter, to show off, throws a new dish of dumplings (mass 0.8 kg) onto the surface at a speed of 0.5 m/s, such that the dish lands on and sticks to the very edge of the surface moving in the same direction as the rotating food. While this is happening, you quickly calculate the final angular speed of the food so that you can predict its location at any time before others have a chance to eat the dumplings. What is this speed, in rad/s?

A container has a flat bottom made of aluminum that is 1.18 -cm thick. The walls are insulated with thick styrofoam. The exterior bottom of the container is in continual contact with boiling water. Inside the container, ethanol (ethyl alcohol) is boiling. How long until the alcohol completely boils away if initially it has a depth of 5 cm? Assume that the thermal conductivity of aluminum is 220 W/m· ◦C, the latent heat of vaporization of ethanol is 854 kJ/kg, the boiling point of ethanol is 78.2 ◦C, and the density of ethanol is 785 kg/m3 . [50, 80 s]

A proton is fired from far away toward the nucleus of a mercury atom. Mercury is element number 80, and the diameter of the nucleus is 14.0 fm.

If the proton is fired at a speed of 4.4

A bicycle racer sprints at the end of a race to clinch a victory. The racer has an initial velocity of 13.0 m/s and accelerates at the rate of 0.450 m/s^2 for 7.00 s.

(a) What is his final velocity (in m/s)? 16.15 m/s

(b) The racer continues at this velocity to the finish line. If he was 300 m from the finish line when he started to accelerate, how much time (in s) did he save?

(c) One other racer was 5.00 m ahead when the winner started to accelerate, but he was unable to accelerate and traveled at 13.2 m/s until the finish line. How far ahead of him (in meters and in seconds) did the winner finish?

distance m?

time s?

A spacecraft starts from rest, and makes a journey to a destination 134000 km from its starting point. It does so by accelerating at a constant rate of 8.91 m/s^2 up to the midpoint of the journey, and then decelerates at the same constant rate of 8.91 m/s^2 for the second half of the journey, ending at rest. How long did the entire journey take?

A car drives around a circular track of diameter 75 m at a constant speed of 36.0 m/s. During the time it takes the car to travel 232 degrees around, what is the magnitude of the car s average acceleration?

An electron is at the origin. (a) Calculate the electric potential V_Aat point A, x= 0.250 cm. (b) Calculate the electric potential V_Bat point B, x= 0.750 cm. What is the potential difference V_B- V_A? (c) Would a negatively charged particle placed at point Anecessarily go through this same potential difference upon reaching point B? Explain.

A sphere of radius 2.09 cm and a spherical shell of radius 6.97 cm are rolling without slipping along the same floor. The two objects have the same mass. If they are to have the same total kinetic energy, what should the ratio of the sphere\'s angular speed to the spherical shell\'s angular speed be? Please provide a clear explanation. I have tried to look this problem u, but I was unable to understand exactly how the solution was found.

A person pushes a 10.5-kg shopping cart at a constant velocity for a distance of 37.6 m on a flat horizontal surface. She pushes in a direction 20.2 ° below the horizontal. A 53.1-N frictional force opposes the motion of the cart. (a) What is the magnitude of the force that the shopper exerts? Determine the work done by (b) the pushing force, (c) the frictional force, and (d) the gravitational force.

Is there a material which can allow light (or any other EM radiation) to pass through from one side as if it is transparent but its other side reflects light like a mirror?

a glass tube both ends are open is dipped inside mercury so that one half is above the mercury level. then the one half of open end is closed and taken out there with a

10 cm long mercury left. if atmospheric pressure is 76cnHG calculate the length of the tube

answer is 16 cm pls explain the answer