A measuring cylinder made of glass has a volume of 200 mL when measured at 20°C. Mercury, also at 20°C, is added to the measuring cylinder until the mercury level reads 197 mL on the measuring cylinder scale. The mercury and glass are then warmed until the mercury level reads 200 mL on the measuring cylinder scale. Taking the coefficients of volume expansion of glass to be 2.0 × 10^-5 K^-1 and for mercury to be 18 × 10^-5 K^-1, what is the final temperature?

An insulating sphere with radius R1 and density by uniform charge ρ1 is placed in the center of a thin shell spherical with radius R2 and surface charge density uniform σ2. Here are the known parameters: R1 = 0.2 m R2 = 0.6 m ρ1 = 6 µC / m3 E = 0 everywhere outside the thin shell a) Using the Gauss theorem, calculate the value of the parameter σ2 in nC / m2 . b) Using the Gauss theorem, determine the expression of the electric field in the region between the two objects, depending on the position r. c) From your answer in b), calculate the potential difference V2 - V1. Hint: there are an integral to perform. d) Using the principle of superposition of potentials (see TP solution of 4P5), calculate the potential resulting on the surface of the insulating sphere, ie V1.

A sturdy, sealed container contains 0.2 moles of helium gas. It is initially sitting in a room at 20 °C, and the pressure of the gas is observed to be 200 kPa. The container is then placed in boiling water.

(a) What will the pressure be when the temperature of the gas reaches equilibrium?

(b) What is the change in entropy of the gas during this process?

(c) Is work done on or by the gas? If so, how much?

(d) It heat transferred to or from the gas? If so, how much?

In class we showed that hot air at atmospheric pressure is less dense than cooler air at the same pressure.

Because of this difference hot-air balloons can stay aloft. Assume that you have an air-balloon that has

the volume of 500 m3 and the surrounding air is at 100C. You want to lift 250 kg object (in addition to

the mass of the hot air that is inside the balloon). What must be the temperature of the air in the balloon?

03
The density of air at 10 C and atmospheric pressure is 1.23 kg/m . The heated air inside the balloon is at

roughly the same pressure as the outside air.

Derive the Beats using trigonometric identity , and explain about the envelope and "carrier"

Draw a diagram of waves going in and out of the phase

Masses coupled through springs is a model for the behavior of atoms in a crystal. Consider a one-dimensional crystal, what if we have a crystal made of two kinds of atoms with different masses? Consider a one-dimensional lattice made up of alternating large and small masses, M and m, respectively. Assume periodic boundary conditions. (a) Calculate the normal modes of this lattice (you should find two normal modes). (b) Describe the relative motion of the two types of masses for each mode.

Neutrons are born out of fission at a high energy and must be slowed down to the low energy region, called the “thermal energy” region, to cause another fission. A material called a “moderator” is used to slow the neutrons down, or “moderate” them, by elastic scattering collisions.The average neutron energy coming out of fission of thermal neutrons is 1.98 MeV in kinetic energy. What is the number of collisions required to bring its average kinetic energy to 0.1 eV if it elastically scatters off of the following moderators:

a. Hydrogen-1

b. Hydrogen-2

c. Carbon-12

d. Uranium-238

A bullet is fired through a board 10.0cm thick in such a way that the bullet’s line of motion is perpendicular to the face of the board. If the initial speed of the bullet is 4.00 x 10^2 m/s and it emerges form the side of the board with a speed of 3.00 x 10^2 m/s, find (a) the acceleration of the bullet as it passes through the board and (b) the total time the bullet is in contact with the board.

Question 1:

(a) A gymnast jumps from a platform at vertical position s_y = 1.0m above a trampoline at s_y = 0 m. The gymnast’s vertical velocity at

the moment when she leaves the platform (time t = 0) is  v_y = 3.0 m/s. The positive vertical direction is upwards. Assume that the effects of air resistance and friction can be neglected touches the trampoline at time t= t₁

(i) Sketch a graph of the gymnast’s vertical position versus time between t=0 and t1. Label s_y =0m, t=0,and t₁ on your graph.

(ii) Sketch a graph of the gymnast’s vertical velocity versus time from the moment she leaves the platform until the moment she touches the trampoline. Label v_y = 0 ms^-1,

t = 0, and t₁ on your graph.

(iii) Calculate the vertical velocity of the gymnast at the instant she touches the trampoline.

(iv) The trampoline’s canvas is connected to its frame by a number of springs. One of these springs has a spring constant of 2000 N m^-1 Calculate the strain potential energy of the spring when it is extended by 0.15 m from its equilibrium position. Assume that this extension obeys Hooke’s Law.

(v) The gymnast now does a somersault and rotates with an average angular velocity of 6 rad s^-1.Angular momentum is a conserved quantity and the gymnast had zero angular momentum when she jumped from the platform. Explain how this is possible.

(b) A coach standing in the gym hits a drum which emits a sound with a frequency of 110 Hz. The speed of sound in air is 340 m s .

(i) An athlete is running straight towards the coach with velocity 20.0 km h^-1. What frequency will the athlete hear? (3 marks )

(ii) x defines the distance from one edge of the drum’s membrane to the opposite edge, passing through the centre of the membrane. A standing wave on the drum membrane can be described byy(x, t) = 2A cos(ωt) sin(kx)

where y is the vertical displacement of the drum’s membrane at position x and time t. Briefly explain what A,ω, and k signify in this equation.

A neutron in a nuclear reactor makes an elastic, head-on collision with the nucleus of a carbon atom initially at rest. (a) What fraction of the neutron's kinetic energy is transferred to the carbon nucleus? (The mass of the carbon nucleus is about 12.0 times the mass of the neutron.) (b) The initial kinetic energy of the neutron is 1.30 10-13 J. Find its final kinetic energy and the kinetic energy of the carbon nucleus after the collision. neutron J carbon nucleus J

A person walks into a room that has, on opposite walls, two plane mirrors producing multiple images. Find the distances from the person to the first three images seen in the left-hand mirror, when the person is 9.00 ft from the mirror on the left wall and 10.0 ft from the mirror on the right wall.

(a) What is the magnitude of the tangential acceleration of a bug on the rim of a 12.0-in.-diameter disk if the disk accelerates uniformly from rest to an angular speed of 77.0 rev/min in 3.70 s?
m/s²

(b) When the disk is at its final speed, what is the magnitude of the tangential velocity of the bug?
m/s

(c) One second after the bug starts from rest, what is the magnitude of its tangential acceleration?
m/s²

(d) One second after the bug starts from rest, what is the magnitude of its centripetal acceleration?
m/s²

(e) One second after the bug starts from rest, what is its total acceleration? (Take the positive direction to be in the direction of motion.)

Consider if you were to vary the number of washers suspended on the end of the string, how would this affect the centripetal force? How would increasing the number of washers at the end of the string affect the periodic time of moving mass? Generally, explain the effect of moving mass and radius on centripetal force.

Please give explantations