Consider a dripping fw v4./pks:h+61uj ib yj*oddh qi-a(q aucet, where the faucet 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 magnizwk( xtsgxqd/x 67l8-tude $v_{0}$ 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 plane.l4+ch.dsh,i0lap jg jau14g: Friction is too high for it to slide under any circumstance, but if the plane is sloped enough it can "topple" down the hill. What angle incline is necessary for it cjg:.apl 1 ,+h aj044shlig udto start toppling?

  A particle at rest explode2b w uc5) s (ql)s(f+hsrxd7wos into three particles of equal mass in the absence of external forces. Two particles emerge at a right angle to each other withws()hs)f 7b+q s5lxduwrc(o 2 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 cann(1* jbj.1 uaghvso9r ron pointing upward (towards the upper cannon) and the upper (hago*1sbrj1v.jur 9 cannon pointing 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 long after the cannons fire do the projectiles collide?

  Two cannons are arrangn4bsp a:ncyf2. zz:3xed vertically, with the lower cannon pointing upward (towa:yp s:nf zn3 2x.z4cabrds the upper cannon) and the upper cannon pointing 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 rad*e1bz .rp6oaq8 cw +tfius $R$ 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 inclined plane and allh: n9fw8hp (a8jzyy 0dowed to roll without slipping to the z:n8ph0 d 8j y(wyfh9abottom in the absence of rolling resistance and 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 isjjm rh3(j+6hm using the rope through a fixed pulley to move a box with constm m(hj h6+rjj3ant 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 massless strings/9/rdiaodopynn t5).vjk 7(2ewj y* f 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 suspended from that point. The strings have a fixed length, regardless of oney ydna(wp2o .*t5) jk/7f v9/rd jithe 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 component of force v rb(wnmzox uh+t7u+2 4z/kr-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;xye5v ercht 26e9k- b .ctrw, 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 acceleration)aheybjggi(3k0. d w3ie/ra lte 6 (/m $\vec{a}$, 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 ideal spring. With the box ncje c0yr/ 0:t)lg g)o8e 3mkfheld 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 eo8c0 mfy0:cgenr g tk))j3/land allowed to fall. To 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 sittinglz nk2up(gerqp o6 0gne62/n( 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 foll iw1hzjav,w 4f 4/duc:ows: a platform 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 ha- j:w.9q.row qu 234qdmbisrxs an intensity 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 of equipment cannot 9be ;n b50v2sb (g lyze/mbrg1be used to measure the local value of the acceleration due to gravg21bzl;bv ngy0 bm/sb95 ee(rity ($g$)?

  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 the sun shown below. Orbit P is i5 ;)skdgm bfiu./f7w circular with radiui5m/bdk). wf gsf iu;7s $R$, 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?