A 4 kg block is placed at the top of an inclined plane. The plane is 2.5 meters long and inclined at 34°. The coefficient of kinetic friction between the block and plane is 0.27. The block slides the 2.0 meters down the ramp. What speed does it have at the bottom?

What is the relationship between the index of refraction and the density of the transparent material? Is this relationship a rule of thumb or is it an absolute?

Water flows through the pipe in the figure below and exits to the atmosphere at the right end of section C. The diameter of the pipe is 2.12 cm at A, 4.24 cm at B, and 0.880 cm at C. The gauge pressure in the pipe at the center of section A is 1.25 atm and the flow rate is 0.856 L/s. The vertical pipes are open to the air. Find the level (above the flow midline as shown) of the liquid-air interfaces in the two vertical pipes. Assume laminar nonviscous flow.
h_A = m

h_B = m

In the series RLC circuit of problem 1 the resistor is replaced with the higher available value of 68 KOhm. The circuit is driven in forced oscillation regime up to a frequency of 200 KHz. A resonance is observed at a frequency of the order of 160 KHz. How would you explain this result? What combinations of capacitor / inductor values would produce a resonance at that frequency, and what parts of the setup are possible candidates for effective reactance elements at that frequency?

Explain the mathematical and graphical relationship between velocity and position using your own words.

A mole of atoms is 6.02 x 10^23 atoms. To the nearest order of magnitude, how many moles of atoms are in a 8 kg domestic cat? The masses of a hydrogen atom, an oxygen atom, and a carbon atom are 1.0 u, 16 u, and 12 u, respectively. (Hint: Cats are sometimes known to kill a mole.)

Acceleration of Gravity

1) Friction. Explain the role of friction in the measurement of g.

2) Time. The time resolution of the timer used in the experiment is 0.1 ms (milliseconds). Do you expect that the precision of the timer may have affected the measurement of g?

3) Distance. How do you expect that the measurement of the distance D between the photogates may have affected the measurement of g?

4) Angle. How do you expect that the measurement of the angle of incline θ may have affected the measurement of g?

5) Summary. Based on the % difference histogram, which of the possible causes listed above do you think did actually affect the measurement of g? If so, in which direction?

Most string theory compactifications analyzed so far have as backgrounds a conformal field theory corresponding to a nonlinear sigma model with a Calabi-Yau target space, or some relatively classical background, possibly with orbifolding. But as long as the central charge of the Virasoro algebra is right, and worldsheet superconformal symmetry is respected, any other superconformal field theory will do just as well. Why haven't string theorists looked at such models more often?

A parallel plate capacitor with plate separation d is connected to a battery. The capacitor is fully charged to Q Coulombs and a voltage of V. (C is the capacitance and U is the stored energy.) Answer the following questions regarding the capacitor charged by a battery.

For each statement below, select True or False. and please explain answers Thanks!

1) With the capacitor connected to the battery, decreasing d increases U

2) After being disconnected from the battery, inserting a dielectric with ? will decrease V

3) After being disconnected from the battery, decreasing d increases C

4) With the capacitor connected to the battery, inserting a dielectric with a dielectric constant "k" will decrease C

5) After being disconnected from the battery, increasing d decreases V

6) With the capacitor connected to the battery, inserting a dielectric with a dielectric constant "k" will decrease U

An energy bill on the floor of the House of Representatives is proposed by a congressperson from Nebraska that would require all cars to use fuel that contains at least 15% ethanol, derived from corn. A northeastern state representative raises the concerns that corn is best for cattle, food, and exports, and that not all cars of today are prepared to use such a fuel. Respond how you would vote on this issue and the reasoning behind your vote in a 100-word essay

A simple pendulum consists of a small object of mass m= 0.150 kg suspended from a support stand by a light string. The string has a length L= 0.750 m. The string has an initial position given by θ= 65.0° relative to the vertical. The pendulum is released from rest. Air resistance is negligible during the subsequent motion of the pendulum.

a)Calculate the work done by gravity on the pendulum as it moves from its initial position to the lowest point of its semicircular arc. b)Calculate the speed of the object as it moves through the lowest point of its semicircular arc.

c)Calculate the tension in the string right as the object is moving through the lowest point of its semicircular arc.

d)Repeat part b) using the conservation of total mechanical energy. (Is the total mechanical energy of the pendulum conserved?)

The spin cycles of a washing machine have two angular speeds, 416 rev/min and 632 rev/min . The internal diameter of the drum is 0.560 m

Part A

What is the ratio of the maximum radial force on the laundry for the higher angular speed to that for the lower speed? (F higher/F lower)=?

Part B

What is the ratio of the maximum tangential speed of the laundry for the higher angular speed to that for the lower speed? (V higher/ V lower)=?

Part C

Find the laundry's maximum tangential speed . (m/s)

Part D

Find the laundry's maximum radial acceleration, in terms of g . (a rad=? g)

A converging lens has a focal length of 21.1 cm.

(a) Locate the object if a real image is located at a distance from the lens of 63.3 cm.

(b) Locate the object if a real image is located at a distance from the lens of 105.5 cm.

(c) Locate the object if a virtual image is located at a distance from the lens of -63.3 cm.

(d) Locate the object if a virtual image is located at a distance from the lens of -105.5 cm.

A box of mass 10.2 kg with an initial velocity of 2.1 m/s slides down a plane, inclined at 28◦ with respect to the horizontal. The coefficient of kinetic friction is 0.69. The box stops after sliding a distance x.

a. How far does the box slide? The acceleration due to gravity is 9.8 m/s 2 . The positive x-direction is down the plane. Answer in units of m.

b. What is the the work done by friction? Answer in units of J.

c. What is the work done by the normal force? Answer in units of J.

d. What is the magnitude of the work done by gravity? Answer in units of J.

e. What is the magnitude of the instantaneous power generated by friction half way between the initial and final positions? Answer in units of W.

f. What is the magnitude of the average power generated by friction from start to stop? Answer in units of W.