Consider a dripping faucet, where the faucet. gqnltq e+3f0 is $10\,\mathrm{cm}$ above the sink. The time between drops is such that when one drop hits the sink, one is in the air and another is about to drop. At what height above the sink will the drop in the air be right as a drop hits the sink?

  A cannonball is launched with initial velocity of magnitis9nh t+ryunn()wk7 .ude $v_{0}$ over a horizontal surface. At what minimum angle $\theta_{min}$ above the horizontal should the cannonball be launched so that it rises to a height $H$ which is larger than the horizontal distance $R$ that it will travel when it returns to the ground?

  An equilateral triangle is sitting on an inclined pla 8q40jxa 1n.oa)rr bczne. Friction is too high for it to slide under any cir8. 0rxaaq b)1jnzo4crcumstance, but if the plane is sloped enough it can "topple" down the hill. What angle incline is necessary for it to start toppling?

  A particle at rest explodes if1rr:ktg*nh00: a 1ahvd tu,knto three particles of equal mass in the absence of external forces. Two particles emerge:g*khavr1h1d t0 f a:rnut0k, at a right angle to each other with equal speed $v$. What is the speed of the third particle?

  A $12\,\mathrm{kg}$ block moving east at $4\,\mathrm{m/s}$ collides head on with a $6\,\mathrm{kg}$ block that is moving west at $2\,\mathrm{m/s}$. The two blocks move together after the collision. What is the loss in kinetic energy in this collision?

  Two cannons are arranged vertically, with the lower cannon pointing upwardyt3o 0x/oj g y4d6p8;6zrrlab (towards the upper cannon) and the upper cannon pointing yt o;dzojrby/ 0r843gpla66xdownward (towards the lower cannon), $200\,\mathrm{m}$ above the lower cannon. Simultaneously, they both fire. The muzzle velocity of the lower cannon is $25\,\mathrm{m/s}$ and the muzzle velocity of the upper cannon is $55\,\mathrm{m/s}$.

How long after the cannons fire do the projectiles collide?

  Two cannons are arranged vertically, with the lower9 53czv lrt3oh cannon pointing upward (towards the upper cannon) and the upper cannon poi 3lvzo9r tc35hnting downward (towards the lower cannon), $200\,\mathrm{m}$ above the lower cannon. Simultaneously, they both fire. The muzzle velocity of the lower cannon is $25\,\mathrm{m/s}$ and the muzzle velocity of the upper cannon is $55\,\mathrm{m/s}$.

How far beneath the top cannon do the projectiles collide?

  A block of mass $m=3.0\,\mathrm{kg}$ is moving on a horizontal surface towards a massless spring with spring constant $k=80.0\,\mathrm{N/m}$. The coefficient of kinetic friction between the block and the surface is $\mu_{k}=0.50$. The block has a speed of $2.0\,\mathrm{m/s}$ when it first comes in contact with the spring. How far will the spring be compressed?

  A uniform spherical planet has radiu6ec8en)8x5jzbyzz4 7 vse8ihs $R$ and the acceleration due to gravity at its surface is $g$. What is the escape velocity of a particle from the planet's surface?

  Four objects are placed at rest at the top of an, gx o0(gwepg+e;0n+iviipi7 inclined plane and allowed to roll without slipping to the bottom in the absence of rolling resistance a gepi oi+xg,0wp0;egni+i 7v( nd air resistance.
* Object A is a solid brass ball of diameter $d$.
* Object B is a solid brass ball of diameter $2d$.
* Object C is a hollow brass sphere of diameter $d$.
* Object D is a solid aluminum ball of diameter $d$. (Aluminum is less dense than brass.)
The balls are placed so that their centers of mass all travel the same distance. In each case, the time of motion $T$ is measured. Which of the following statements is correct?

  As shown below, Lily is using th5z bmfo )8pjy9e rope through a fixed pulley to move a box withzy9o5 b)fjmp 8 constant speed $v$. The kinetic friction coefficient between the box and the ground is $\mu < 1$; assume that the fixed pulley is massless and there is no friction between the rope and the fixed pulley.

Then, while the box is moving, which of the following statements is correct?

  A rigid hoop can rotate about the center. Two(b *g7k2s( yp 0yzs:x0wzhtqz massless strings are attached to the hoop, one at A, the other at B. These strings are tied together at the center of the hoop at O, and a weight G is s 0027ps hw((xtz b:g*yyzzksquspended from that point. The strings have a fixed length, regardless of the tension, and the weight G is only supported by the strings. Originally OA is horizontal.

Now, the outer hoop will start to slowly rotate $90^{\circ}$ clockwise until OA will become vertical, while keeping the angle between the strings constant and keeping the object static. Which of the following statements about the tensions $T_{1}$ and $T_{2}$ in the two strings is correct?

  Shown below is a graph of the compusjx8l.r 1xm/onent of force versus position for a $4.0\,\mathrm{kg}$ cart constrained to move in one dimension on the $x$ axis. At $x=0$ the cart has a velocity of $-3.0\,\mathrm{m/s}$ (in the negative direction).

Which of the following is closest to the maximum speed of the cart?

  A uniform cylinder of b4r) bz1x 2krz33gqje radius $a$ originally has a weight of $80\,\mathrm{N}$. After an off-axis cylinder hole at $2a/5$ was drilled through it, it weighs $65\,\mathrm{N}$. The axes of the two cylinders are parallel and their centers are at the same height.

A force $T$ is applied to the top of the cylinder horizontally. In order to keep the cylinder is at rest, the magnitude of the force is closest to:

  A car of mass $m$ has an engine that provides a constant power output $P$. Assuming no friction, what is the maximum constant speed $v_{max}$ that this car can drive up a long incline that makes an angle $\theta$ with the horizontal?

  Inside a cart that is accelerating horizontally at acceleratiog el 9lly;13xrn $\vec{a}$, there is a block of mass $M$ connected to two light springs of force constants $k_{1}$ and $k_{2}$. The block can move without friction horizontally. Find the vibration frequency of the block.

  Shown below is a $log/log$ plot for the data collected of amplitude and period of oscillation for certain non-linear oscillator.

According to the data, the relationship between period $T$ and amplitude $A$ is best given by

  A mass hangs from the ceiling of a box by an ideamev81pj+p: upe c6ny3ic - h,vl spring. With the box held fixed, the mass is given an initial velocity and oscillates with purely vertical motion. When the mass reaches the lowest point of its motion, the box is released and allowed to fall. To hepcp8 v,mnu+1e cjy6p3-iv:an observer inside the box, which of the following quantities does not change when the box is released? Ignore air resistance.

  A $1,500\,\mathrm{Watt}$ motor is used to pump water a vertical height of $2.0\,\mathrm{meters}$ out of a flooded basement through a cylindrical pipe. The water is ejected though the end of the pipe at a speed of $2.5\,\mathrm{m/s}$. Ignoring friction and assuming that all of the energy of the motor goes to the water, which of the following is the closest to the radius of the pipe? The density of water is $\rho = 1000\,\mathrm{kg/m^{3}}$.

  A container of water is sittin ;s*12)10q ko:pj3jwzcn bjn9 shzd itg on a scale. Originally, the scale reads $M_{1}=45\,\mathrm{kg}$. A block of wood is suspended from a second scale; originally the scale read $M_{2}=12\,\mathrm{kg}$. The density of wood is $0.60\,\mathrm{g/cm^{3}}$; the density of the water is $1.00\,\mathrm{g/cm^{3}}$. The block of wood is lowered into the water until half of the block is beneath the surface.

What is the resulting reading on the scales?

  A spring system is set up as follows: a pizh ljdf9h.jp8 4k;j) latform with a weight of $10 N$ is on top of two springs, each with spring constant $75 N/m$. On top of the platform is a third spring with spring constant $75 N/m$. If a ball with a weight of $5.0 N$ is then fastened to the top of the third spring and then slowly lowered, by how much does the height of the spring system change?

  The softest audible sound has an intensikteod4 *g)1aety of $I_{0}=10^{-12} W/m^{2}$. In terms of the fundamental units of kilograms, meters, and seconds, this is equivalent to

  Which of the following sets ow0x ylkc u d*43mrvu-p)pq5 d.f equipment cannot be used to measure the local value of the acceleration due 3*r.v -0l)dqpyu5 uxpk m4dwc to gravity ($g$)?

  Three point masses $m$ are attached together by identical springs. When placed at rest on a horizontal surface the masses form a triangle with side length $l$. When the assembly is rotated about its center at angular velocity $\omega$, the masses form a triangle with side length $2l$. What is the spring constant $k$ of the springs?

  Consider the two orbits around theg-,ssphwamp6w9h 6 *t sun shown below. Orbit P is circular with radiwm * 96,hat-p6gsphsw us $R$, orbit Q is elliptical such that the farthest point $b$ is between $2R$ and $3R$, and the nearest point $a$ is between $R/3$ and $R/2$. Consider the magnitudes of the velocity of the circular orbit $v_{c}$, the velocity of the comet in the elliptical orbit at the farthest point $v_{b}$, and the velocity of the comet in the elliptical orbit at the nearest point $v_{a}$. Which of the following rankings is correct?