Europa, a satellite of Jupiter, appears to have an ocean beneath its icy surface. Proposals have been made to send a robotic submarine to Europa to see if there might be life there. There is no atmosphere on Europa, and we shall assume that the surface ice is thin enough that we can ignore its weight and that the oceans are fresh water having the same density as on the earth. The mass and diameter of Europa have been measured to be 4.78×1022 kg and 3130 km , respectively

If the submarine intends to submerge to a depth of 70.0 m , what pressure must it be designed to withstand?

If you wanted to test this submarine before sending it to Europa, how deep would it have to go in our oceans to experience the same gauge pressure on Earth as the pressure at a depth of 70.0 m on Europa?

A child pulls on a wagon of mass 47 kg at an angle 33 degrees above the horizontal with a force of F. If the wagon accelerates at 3.7 m/s2 horizontally, what is the magnitude of the force F (in unit of N)? Assume there is coefficient of friction is 0.33, and please use g = 10 m/s2 to simplify computation.

A 4.0-kg block is on an incline plane of 30 degrees angle with respect to horizontal. a)What is the minimum coefficient of static friction (μ_s)_min is need to prevent it from sliding down? b) If the surface μ_s is 0.30, less than (μ_s)_min now, how much force(F) is needed to apply to the block horizontally to prevent it from sliding down?c) If F is doubled, what’s the acceleration of the block up the incline? Assume the coefficient of kinetic friction is 0.25.

On a horizontal frictionless surface, a small block with mass 0.200 kg has a collision with a block of mass 0.400 kg. Immediately after the collision, the 0.200 kg block is moving at 12.0 m/s in the direction 30

5. The mass of the sun is 2.00 x 1030 kg. The radius of the sun is 7.00 x 108 m.
a) What is the DENSITY of the sun?
b) What are the possible errors in your calculation in a)?
c) What is the PRESSURE at the center of the sun? (HINT: think of the sun as two
gravitation masses each 1⁄2 the mass of the sun at the radius of the sun apart.)
d) What are the possible errors in your calculation in c)?
e) What is the TEMPERATURE at the center of the sun? (HINT: use the "perfect gas
law" T = P (m/k) (1/r) where T = temperature in K0, P = pressure, m = mass of each
particle that makes up the sun (what do you think that is?), k = Boltzmann constant =
1.38 x 10-23 kg m2s-2 (K0)-1, and r is density. CHECK all your UNITS first!)
f) What are the possible errors in your calculation in e)?

4.15

A small 7.40-kg rocket burns fuel that exerts a time-varying upward force on the rocket. This force obeys the equation F=A+Bt2. Measurements show that at t=0, the force is 104.0N , and at the end of the first 1.50s , it is 193.0N .

Find the constant A

Find the constants B

Find the net force on this rocket the instant after the fuel ignites.

Find the acceleration of this rocket the instant after the fuel ignites.

Find the net force on this rocket 4.90s after fuel ignition.

Find the acceleration of this rocket 4.90s after fuel ignition.

Suppose you were using this rocket in outer space, far from all gravity. What would its acceleration be 4.90s after fuel ignition?

Explain the difference between homogeneous and inhomogeneous broadening and give an example of a broadening mechanism for each of the two cases.

The wall of a house is made from a layer of wood 3cm thick and a layer of wool which is 5.3 cm thick. The layer of wood faces outside and the layer of wool faces inside. The thermal conductivity of wood is 0.08W/mK and the thermal conductivity of wool is 0.02W/mK. The temperature outside the house is 0^oC and the temperature inside the house is 19.8 ^oC. What is the temperature (in ^oC) at the contact surface between the wool and the wooden layers?

A spring constant of 250.0 N/m is suspended vertically with its upper end fixed to the ceiling and its lower end at position y=0.000 cm. A block of weight 25.0 N is attached to the lower end, held still for a moment and then released. What are the kinetic energy changes and the changes from initial values in the gravitational potential energy of the spring-block system when the block is at values of y equal to (a) -5.00 cm (b) -10.0 cm (c) -15.0 cm (d) -20.0 cm? Tabulate your results, Include units at the top of each column.

7. A single photon, from an unpolarized source, traveling in the z direction is directed through a series of three polarizers: first a polarizer with its axis in the x direction, then a polarizer at 25 degrees to the x direction, then finally a y polarizer.

a) What is the probability that the photon makes it through the first (x) polarizer and what is the photon’s polarization after it comes through the first polarizer?

b) For a photon that got through the first (x) polarizer, what is the probability that that photon goes through the next two polarizers and what is the photon’s polarization after it comes through the last polarizer?

c) If the middle (25 degree) polarizer is removed, what is the probability that the photon gets through both (remaining) polarizers?

Bob lifts a 0.9kg cup of coffee, initially at rest on the table, up to his mouth. The cup comes to rest after a vertical displacement of 0.7m. (NO IMAGE GIVEN)

a. In the process of being lifted, how much work was done on the cup by Bob?

b. Bob then hold the cup stationary for 1.8s. How much work was done on the cup by Bob during this time?

c. Realizing that the cup is empty, Bob lowers the cup 1.1m downward into the sink, where it comes to rest. How much work was done on the cup by Bob in the process of being lowered?

A. What is the moment of inertia of a solid iron sphere 20 inches in diameter about an axis passing through the sphere half way from its center to the surface (you will have to look up its density)? If the sphere rolls down an incline plane that makes an angle 20 degrees with the horizontal, what will be its acceleration?

B. Derive the formula for acceleration of a circular disk that rolls down an inclined plane that makes an angle θ with the horizontal. (draw a diagram and say in words what you are doing)

How to determine particle size using UV Visible spectroscopy

A football is kicked at ground level with a speed of 25 m/s at an angle of 45 degrees to the horizontal. How far down field does it go (assume takeoff and landing at the same height)?