If the density of the universe great than a critical value, then

A 16.4-kg block rests on a horizontal table and is attached to one end of a massless, horizontal spring. By pulling horizontally on the other end of the spring, someone causes the block to accelerate uniformly and reach a speed of 4.50 m/s in 1.55 s. In the process, the spring is stretched by 0.236 m. The block is then pulled at a constant speed of 4.50 m/s, during which time the spring is stretched by only 0.0565 m. Find (a) the spring constant of the spring and (b) the coefficient of kinetic friction between the block and the table.

A charge of -2.75 nC is placed at the origin of an xy-coordinate system, and a charge of 2.05 nC is placed on the y axis at y = 3.60 cm .

A. If a third charge, of 5.00 nC , is now placed at the point x = 2.65 cm , y = 3.60 cm find the x and y components of the total force exerted on this charge by the other two charges.

B. Find the magnitude of this force.

C. Find the direction of this force.

1) Two vectors, r  and s lie in the x y plane. Their magnitudes are 4.84 and 6.09 units respectively, and their directions are 341^o and 65.0^o respectively, as measured counterclockwise from the positive x axis. What are the values of vectors (a) r . s and (b) | r × s |?

2) For the following three vectors A B C, what is 3⋅C . (3A × B) ?
A =3.00î + 2.00ĵ - 3.00k̂
B =-4.00î + 3.00ĵ + 3.00k̂
C =6.00î - 7.00ĵ

a) How much heat is required to change a 31.3 g ice cube from ice at -10.6°C to water at 47°C? (if necessary, use cice=2090 J/kg°C and csteam= 2010 J/kg°C) b)How much heat is required to change a 31.3 g ice cube from ice at -10.6°C to steam at 110°C?

Two hockey pucks are moving to the right with puck 1 behind puck 2. Puck 1 is moving twice as fast as puck 2, but its mass is half that of puck 2. If puck 2's Vi is 8 m/s, then what is the velocity of each puck after they collide?

A man stands on the roof of a building of height 16.8m and throws a rock with a velocity of magnitude 30.6m/s at an angle of 29.3? above the horizontal. You can ignore air resistance.

      Calculate the magnitude of the velocity of the rock just before it strikes the ground.

      Calculate the horizontal distance from the base of the building to the point where the rock strikes the ground.

A car accelerates uniformly from rest to 26.5 m/s in 8.60 s along a level stretch of road. Ignoring friction, determine the average power required to accelerate the car if (a) the weight of the car is 7.76 x 10^3 N, and (b) the weight of the car is 1.83 x 10^4 N.

You are in a boat traveling perpendicular to waves in water. The wave speed is 8.40 m/s, your speed is 6.50 m/s, and you are heading into the waves. If the wavelength of the waves is 6.70 m, how much time passes between hitting the top of one wave and the next? [This Doppler effect in water is just like that in sound; you can also calculate it from velocities and length.]

_____________ s

Two carts (100 g and 150 g) on an air track are separated by a compression spring. The spring is released. Represent the process with a momentum bar chart (a) with one cart as the system and (b) with both carts as the system. (c) Write expressions for all the physical quantities you can from this information. Identify your object of reference.

Draw and explain the P-V graph for both adiabatic and isothermal processes and explain the difference.

A box with an inertia of 2kg is held on a 1m high table against a spring with k = 75N which is initially compressed 0.5m. The coefficient of friction between the box and the table is 0.2. The spring is released, and it pushes the box until it reaches its equilibrium length. At this point, the spring is stopped by a stopper and the box continues to slide across the table with only the force of friction acting on it. After losing contact with the spring, the box travels the distance of the rest of the table, another 0.5m, where it then flies off the end of the table and lands on the floor. Assuming no air resistance,

1. (a) What was the net work done on the box while it was being pushed by the spring?

2. (b) What was the net work done on the box from the time it left the spring until it reached the edge of the table?

3. (c) How fast was the box moving when it flew off the table?

4. (d) How far from the table did the box land?

Question about wave propagation

1. Explain what is: line of sight propagation, tropospheric propagation and ionospheric propagation.
2. What is fading? Why is diversity needed?
3. State the cause of ionospheric propagation.

an ideal gas has C_v=(7/2)R. A 2.00 mole sample of gas starts at P=1*10^5 Pa and T=300K. determine the total P, V&T for each of the following cases, as well as ΔE_int, W and Q

a) gas is heated at constant P to 400K

b) gas is heated at constant V to 400K

c) isothermal conpression to P=1.2*10^5 Pa

d) adiabatic to compression P= 1.2*10^5

Which of the following types of energy can be considered "mechanical" energy? (Select all that apply.)