A bullet of mass m = 8.00 g is fired into a block of mass M = 210 g that is initially at rest at the edge of a table of height h = 1.00 m (see figure below). The bullet remains in the block, and after the impact the block lands d =  1.90 m from the bottom of the table. Determine the initial speed of the bullet.

________m/s

Which pair of quantities represent scalar
quantities?
(1) displacement and velocity
(2) displacement and time
(3) energy and velocity
(4) energy and time

You are on roller blades, holding a rope attached to a truck. Starting from rest, the truck pulls you. After traveling for 7.33 s, you are moving at 10.0 m/s. If the friction in your roller blades is negligible, what is the tension in the rope? Your mass is 69.0 kg. Report your answer in SI units, rounded to the nearest whole number.

Radiation from the Sun reaching Earth (just outside the atmosphere) has an intensity of 1.35 kW/m². (a) Assuming that Earth (and its atmosphere) behaves like a flat disk perpendicular to the Sun's rays and that all the incident energy is absorbed, calculate the force on Earth due to radiation pressure. (b) For comparison, calculate the force due to the Sun's gravitational attraction. Assume that the speed of light and Earth radius are 2.998 × 10⁸ m/s and 6.37 thousand km respectively.

Consider a single pane glass window that has an area of 8ft^2 and is 3/16” thick. The outside temperature is -10oC and the inside temperature is 21oC. [9]

a.How much heat flows through the window in 8 hours? Use an R-value.

b. In reality, all surfaces have a thin layer of air covering them that does not move. This air“film” is about .0005m thick. Calculate how much heat flows through the window in the 8 hour period with the addition of this film of air on both sides of the window

Most windows are double-pane glass with ½” Argon gas between the two panes. If the R-value of Argon gas is 0.54 W^-1 •m2•oC for a thickness of 1 cm, find:

i.The effective RSI-value of the window.

ii.The effective R-value of the window.

iii.The effective U -value of the window

A horizontal beam of length 4.07 m and weight 150 N is attached to a vertical wall at a right angle. There is also a support wire of length 5.01 m which attaches the far end of the beam to the wall from above. Off of the far end of the beam also hangs an object of weight 290 N.

A) What is the magnitude of the tension in the support wire?

B) What is the horizontal component of the force exerted on the beam at the wall?

C) What is the vertical component of the force exerted on the beam at the wall?

How much horsepower is needed, in a vehicle described below, to travel a distance of 1 statute mile in 35 seconds, from a standing start, with the following information:

Air density @ sea level, 59 degrees, no wind = p = .002377 slugs/ft^3

Coefficient of drag (flat plate, NASA) = C(d) = 1.28

Weight = W = 4451 lbs

Area = A = 197.5" long x 78.2" wide x (1 ft^2/ 144 in^2) ( Size of vehicle)

An object starts at the position 4.8x̂ + -9.7ŷ m, with an initial velocity of 1.5x̂ + -4.4ŷ m/s. It has an acceleration of -0.152x̂ + 0.686ŷ m/s2. After 2.31 s, what is its speed? Report your result in SI units, rounded to one decimal place.

A spherical mylar balloon filled with Hydrogen gas, with density 0.0899 kg/m³ and having radius 7 meters is immersed in a gas having density X1=1.205 for the first 10 km and X2=2.489 for the second 10 km (with the upper atmosphere density smaller than the lower atmosphere density). Determine how long it takes the balloon to reach the top of the second layer. To do this, you will have to: a) find the net force on the balloon (assume the mylar is massless) in the first layer, then assuming constant acceleration, determine the time to get to the bottom of the second layer, then b) repeat the exercise, but now calculating the buoyancy using the second layer of atmospheric gas.

Using Hamilton’s equations, show that for any solution ρ(t) of Liouville’s equation that asymptotically approaches the equilibrium solution ρ(eq), there is a time-reversed solution that diverges from it. What does this mean?

The parameters of the apparatus that are important to its function are: Solenoid winding: # turns N=1000; winding length Ls = 10 cm; radius R=2.5 cm; wire radius r=0.05 mm; wire resistivity rs= 2 x 10-8 Wm; length of the core extending above the solenoid Lc=10 cm.
a Calculate the resistance and the inductive reactance of the solenoid winding for its response when an applied e.m.f. of 110 V r.m.s, 60 Hz is applied to it.
b Calculate the impedance of the solenoid winding, and the r.m.s. current that is induced to flow in it.
c Calculate the r.m.s. magnetic flux produced inside the solenoid.
d Assume that the magnetic flux through the solenoid is channeled through the extended length of the steel rod core above the solenoid, fringes radially along the length of that extended region so that no flux leaves the top of the extended core. Calculate the radial field magnetic field in that region.
e Calculate the current that would be induced in the aluminum ring if it is located to surround the bottom of the extended region of the core. The parameters of the ring are: Length 4 cm, radial thickness 2 mm, resistivity rr= 3x10-8 Wm
f You close the switch long enough for the ring to be accelerated vertically above the top of the extended core. Estimate how high above the extended core it will travel before coming to a stop and falling.
g Identify the parameters of the entire apparatus that determine how high the ring will jump. Optimize the values for those parameters to make the ring jump to the maximum possible height. Assume the applied voltage and overall size of the apparatus cannot be changed.
h If the solenoid has 1000 turns, how many turns should the secondary have in order to apply 6 V across its terminals.
i The value of the capacitance C should be chosen so that it forms an LC circuit in series with the inductance of a 10-turn secondary winding that is resonant at the 60 Hz frequency of the AC voltage that is applied to the primary winding. What should be the value of C?

2. Answer the following questions about the motion of an object launched from the roof of a building with a height of 10 m at an initial velocity of 20 m/s and an angle of 60°. (1) Find the x and y components of the initial velocity. (2) Find the x and y components of the velocity after 2.0 seconds. (3) Find the time to reach the highest point. (4) Find the height of the highest point. (5) Find the time until it falls to the ground.