The volume of a cylinder is V space equals space pi space r squared space h, where r is the radius of the circular faces and h is the height of the cylinder. Your measurements show that the mean value of r is 21 cm and its statistical and instrumental uncertainties turned out to be 0.10 cm and 0.20 cm, respectively. Likewise, that of h are 13 cm for the mean, 0.2 cm (statistical) and 0.3 cm (instrumental) for its uncertainties. What can you say about which source of uncertainty has the largest contribution to the overall uncertainty of V ? What would you need to do to improve (reduce) the uncertainty on your calculation of V?

A moving ball (ball #1) makes a perfectly elastic collision with a stationary ball (ball #2). After the collision it is observed that the speed of ball #2 is five times that of ball #1. Determine the angles θ1 and θ2 that the two balls scatter as measured from the initial direction of ball #1. You may assume that the two balls have identical masses, and you may need the identity

sin2(x) + cos2(x) = 1.

Please explain any concepts and how you got your answer.

2)

A bullet having a mass of m = 0.005 kg is fired toward a wooden block that is initially at rest on a wooden floor. The mass of the wooden block is M = 4.0 kg.

1. a.) Determine the minimum speed that the bullet must strike the block if it is to cause the block to start sliding along the floor. You may assume that it takes about T = 0.05 seconds for the bullet to come to rest while embedding into the block.

2. b.) Assuming the bullet hits the block at the speed computed in part (a), determine how far the wooden block (with the bullet embedded in it) will slide along the wooden floor before coming to rest.

A solid disk with a mass of 0.85 kg starts at the top of a 0.79 m tall hill and rolls down without slipping. What is the translational speed of the disk at the bottom of the hill? What fraction of the disk's kinetic energy is rotational at the bottom of the hill?

You are standing 2.50m directly in front of one of the two loudspeakers shown in the figure. They are 3.00m apart and both are playing a 686Hz tone in phase.

As you begin to walk directly away from the speaker, at what distances from the speaker do you hear a minimum sound intensity? The room temperature is 20?C.

Enter your answers numerically in increasing order separated by commas.

A block is placed on a plane inclined at 35 degrees relative to the horizontal. If the bloc k slides down the plane with an acceleration of magnitude g/3, determine the coefficient of the kinetic friction between the block and plane.

To a rough approximation, the Earth can be treated as a greybody sphere with uniform temperature, absorptance ? = 0.70 and emissivity ? = 0.61. The low absorptance is largely due to reflection of the incoming sunlight by clouds and ice, while the low emissivity is largely due to greenhouse gases in the atmosphere.

Q1) Over timescales of decades, the total solar irradiance at the Earth varies between about 1360.3 W/m² and 1362.0 W/m² . Using the greybody Earth approximation, how large of a temperature change can be expected due to these natural changes in solar irradiance? [Answer in K as a positive number.]

Q2) Over the last century, the amount of CO2 in the atmosphere has increased dramatically, which has resulted in a change in ? from 0.62 to 0.61. Using the greybody Earth approximation, how large of a temperature change can be expected due to this change in emissivity? [Answer in K as a positive number.]

Q3) The average temperature of the Earth is about 15 ^oC. Assuming a greybody surface, at what wavelength does the Earth emit most intensely? [Answer in µm].

A 283 g air track glider moving at 0.69 m/s on a 2.4 m long air track collides elastically with a 467 g glider at rest in the middle of the horizontal track. The end of the track over which the struck glider moves is not frictionless, and the glider moves with a coefficient of kinetic friciton = 0.02 with respect to the track. Will the glider reach the end of the track? Neglect the length of the gliders.

What are Newton’s 3 laws of motion? With each response, provide a common example/application for each from everyday life (15 points)

Analysis of waves in shallow water (depth much less than wavelength) yields te following wave equation:

where h is the water depth and gthe gravitational acceleration. Give an expression for the wave speed.

A cylindrical metal can, 0.1 m high and 0.05 m in diameter, contains liquid helium at its normal boiling point of -452.074 degrees Fahrenheit. At this temperature Helium's heat of vaporization is 20.4 kJ/kg. The walls of the helium container are 1.2 cm thick and have a thermal conductivity of 13.889 W/(m K). The helium container is surrounded by liquid nitrogen at a temperature of -327.64 degrees Fahrenheit.

A. What is the conductive surface area of the metal cylinder?

B. What is the temperature of the liquid helium in Kelvin?

C. What is the temperature of the walls in Kelvin?

D. What is the rate of heat flow into the Helium due to the conduction?

E. How much Helium is lost per hour due to conduction?

Obtain the equations that describe the motion of a body thrown vertically at a speed greater than the escape velocity. Discount air resistance.

On a dark desert highway, a car leaves a gas station and heads straight for 10 km, heading exactly northeast.

(i.e., directed 45 degrees northward of due east). The car then turns onto a dirt road and drives completely

straight until it reaches a hotel located exactly 12 km north and 9.0 km east of the gas station. How far did the

car drive along the straight dirt road?

A distant galaxy emits light that has a wavelength of 596.8 nm. On earth, the wavelength of this light is measured to be 601.9 nm. (a) Decide whether this galaxy is approaching or receding from the earth. (b) Find the speed of the galaxy relative to the earth. (Give your answer to 4 significant digits. Use 2.998 × 108 m/s as the speed of light.)