We claim that momentum is conserved, yet most moving objects eventually slo *dagq.)hw-rvw down and wvh)g-.rdqa* stop. Explain.

When a person jumps from a tree:b:za gd:tg7s ,qbvd 2 to the ground, what happens to the momentum of tdgv:zaq ,:ts7 bdb :g2he person upon striking the ground?

When you release an inflated but unti-n5 dnsn 95q 5piak3(tqybb6ied balloon, why does it fly across the roomnadn5s 5p9-k3 5(bbqy t in6qi?

It is said that in ancient times a rich /f 1mshg9h yw43)bznm g8+wsmman with a bag of gold coins froze to death while stranded on a frozen lake. Because the ice was frictionless, he could not push himself to shore. What could9 s8mfmg zb+sh1h3gmyw/) wn4 he have done to save himself had he not been so miserly?

How can a rocket change direction when it is far out ic0fi 1*2o; xpi .eyzbmn space and is essentially in a v fx;. o02ypczem1 b*iiacuum?

According to Eq. 7–5, the longer the impc;tb 0 /ugc)x+jckk6zact time of an impulse, the smaller the force can be for the same momentum change, and hence the smaller the deformation of the object on which the force acts. On this basxc ; jzctk6bgcku)0+/is, explain the value of air bags, which are intended to inflate during an automobile collision and reduce the possibility of fracture or death.

Cars used to be built as rigid aj(ul, fzq*h 1vs possible to withstand collisions. Today, though, cars are designed to have “crumple zones” that cufql1h*v,j z( ollapse upon impact. What is the advantage of this new design?

Why can a batter hit a pitched baseball further than a ball tossed in the m.6q5s(ts*p -nyigi h air by the batq*i( pin6.gsths y m5-ter?

Is it possible for an object .d c-2c)p m w0rz4b9b o/ggfttto receive a larger impulse from a small force than from a large force? Expr/cdpb 9c2m. g0-otf w)g4zbtlain.

A light object and a heavy oord2 j3v2)an )o4)r-c vefxuubject have the same kinetic energy. Which has the greater momentvacn22ruo)x-4djrv 3uoe )f )um? Explain.

Describe a collision in9joq*e qz+-ntm mm+vm+h 1iq8 which all kinetic energy is lost.

At a hydroelectric power plant, water is dire9kpk4tc 3vg; bcted at high speed against turbine blades on an axle that turns an electric generator. For maximum power generation, should the turbine blades be designed so that the water is brought to a dead stop, or so that th4cgkp; t39kvb e water rebounds?

A squash ball hits a wall at a 4rlu,6+ b-x5 zun vgx/i5 $^{\circ} $ angle as shown in Fig. below. What is the direction (a) of the change in momentum of the ball, (b) of the force on the wall?

A Superball is dropped from a height h on byi(c4 c9nk,bto a hard steel plate (fixed to the Earth), from which it rebounds at very nearly its original speed. (a) Is the momentum of the ball conserved during any part of this process? (b) If we consider the ball and Earth as our system, during what parts of the process is momentum conserved? (c) Answer part (b) for a piece of puttb9n kbci c(4y,y that falls and sticks to the steel plate.

Why do you tend to lean back/dx1jwx kw o4clue 2v4c07if0ward when carrying a heavy load in your arms?

Why is the CM of a 1-m length of pipe5 iim9 m(-dv)jv ;vowf at its mid-point, whereas this is not true 9 ;vvwv5idm)i(fojm- for your arm or leg?

Show on a diagram how your CMhjkc*hq 4t;h rpee2 0; shifts when you change from a lying position to a sittirtje2;h4kcq*h ph0 ;eng position.

If only an external force can change tj cek+zgg(;f8 he momentum of the center of mass of an object, how can the internal force of an engine accelerate a car;g(fe8zgck +j?

A rocket following a parabolic path through the air suddenly explodes inteb2zrc;/t 3xk*aohapv u3 .n8o many pieces. Whx. h8c n/2* ka;bzuopvre a3t3at can you say about the motion of this system of pieces?

  What is the magnitude of the momentum of a 28-g sparrow flying with a spe63:u bhj6hvyied of $8.4 \; m/s$    $kg \; m/s$

  A constant friction force of 25 N acts on a 65-kg skier; mhl jeqn51*f for 20 s. What is the skier’s change in *e;h5j1m nfqlvelocity?    m/s

  A 0.145-kg baseball pitched at 39 m/s is hit on a horizontal, am 7mnjrk:q2 6hqpl* line drive straight back toward the pirhk2l 6:pqmn*qjam, 7tcher at 52m/s If the contact time between bat and ball is $3\times10^{-3}$s calculate the average force between the ball and bat during contact.    N

  A child in a boat throws a 6.40-kg package out :zq7qd8yzxte 7xb*u t7k1n2t horizontally with a speed of 10 m/s Fig. below Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resiq72b7e 1ztn yx xkzuq*td7: 8tstance. The magnitude of the velocity of the boat is    m/s

  Calculate the force exerted on a rocket, given that the propellingvqz-c23q axo7 gases are expelled at -7q zcav23oq xa rate of $1500 \; kg/s$ with a speed of $ 4\times10^{4 } \; m/s$ (at the moment of takeoff). F =    $\times 10^7 \; N$

  A 95-kg halfback moving adnz *3f: a;ue 2x)vc:r lk/tbqt $4.1 \; m/s$ on an apparent breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at $5.5 \; m/s$ in the same direction, what was their mutual speed immediately after the tackle?    $m/s$

  A 12,600-kg railroad car travels alone on alevel frictionl .0xh* gktx+eless track with a constant speed of 18m/s A 53 l+exh*k0.gxt50-kg load,initially at rest, is dropped onto the car. What will be the car’s new speed?    m/s

  A 9300-kg boxcar travelin.ed;0bl3 dce c k(w*sf:g3zccg at $15 \; m/s$ strikes a second boxcar at rest. The two stick together and move off with a speed of $6 \; m/s$ What is the mass of the second car?    $m/s$

  During a Chicago storm 0d ,xkyhx; lcu5kzga 7j81u1n, winds can whip horizontally at speeds of 100km/h If the air strikes a perso ,unzkl81j cd5xhg 1 k;7xuay0n at the rate of 40kg/s per square meter and is brought to rest, estimate the force of the wind on a person. Assume the person is 1.50 m high and 0.50 m wide. Compare to the typical maximum force of friction $\mu\approx1.0$ between the person and the ground, if the person has a mass of 70 kg.    N
$F_{on person}$  ----待选择----<> $F_{fr}$

  A 3800-kg open railroad car coasts along witrsdwk1u1;va+*m9 poi8 h +r ceh a constant speed of 8.6m/s on a level track. Snow begins to fall vertically and fills the car at a rate of 3.5kg/min Ignoring friction withrv+w*ch 8+eo9imsp;rda11 ku the tracks, what is the speed of the car after 90.0 min?$\approx$    m/s

  An atomic nucleus initially moving at 420m/s emits an aty5:3(xl tx2t inh. 9ayjy7fk lpha particle in the direction of its velocity, and the remaining nucleus slows to 350m/s If the alpha particle has a mass of 4.0 u and the original nucleus has ttly9 ika5j yxfxh .y(t23n7:a mass of 222 u, what speed does the alpha particle have when it is emitted?    m/s

  A 23-g bullet traveling 230m/s penetrates a 2.0-kg block eva b2fw6dz7b7irm5w4 1 hrfhz9fh(( of wood and emerges cleanly at 170m/s If the block is stationary on a fricr(vh 1hir z476ef7fw zf2ad(m 9wbhb5tionless surface when hit, how fast does it move after the bullet emerges?    m/s

  A 975-kg two-stage rocket is traveling at a ..li-mq eh-tu wz9hy n8:8tizspeed of $5.80\times10^3\mathrm{~m/s}$ with respect to Earth when a pre-designed explosion separates the rocket into two sections of equal mass that then move at a speed of $2.20\times10^3\mathrm{~m/s}$ relative to each other along the original line of motion. Let “A” represent the upper stage (that moves away faster) and “B” represent the lower stage.
(a) What are the speed and direction of each section (relative to Earth) after the explosion? $v'_A$   m/s  ----待选择----away from the Earthtowards the Earth  $v'_B$   m/s  ----待选择----away from the Earthtowards the Earth 
(b) How much energy was supplied by the explosion? [Hint: What is the change in KE as a result of the explosion? $a\times10^8$ a =    J

  A rocket of total mass 3c pi8*ol yxt/1up;m+p 180 kg is traveling in outer space with a velocity of 115m/s To alter its coursci p;pp+*8x lou1/tym e by 35.0 $^{\circ} $, its rockets can be fired briefly in a direction perpendicular to its original motion. If the rocket gases are expelled at a speed of 1750m/s how much mass must be expelled?    kg

  A golf ball of mass 0.045 kg is hit off the tee at a speed of 45m/s The golf 91f x6 ujwz znk74gr/vw*r.ji club was in contactnw6 z1*4rr wuvxf 97k/zji.gj with the ball for $3.5\times10^{-3}$s Find (a) the impulse imparted to the golf ball,    kg*m/s
(b) the average force exerted on the ball by the golf club.    N

  A 12-kg hammer strikes a nail at a velocity of 8.5m/s and comes to repwcs , :m yr)ek*8ks9ny*mh4wst in a time interval of 8.0 ms. (a) What,p*94wye8yn sck mk:)s* r whm is the impulse given to the nail?    kg*m/s
(b) What is the average force acting on the nail?    N

  A tennis ball of mass m=0.06kg and)a w86zdtv2sz v0 m*bc speed v=25m/s strikes a wall at a 45 $^{\circ} $ angle and rebounds with the same speed at 45 $^{\circ} $ (Fig. 7–32). What is the impulse (magnitude and direction) given to the ball?   kg*m/s to the  ----待选择----leftright 

  You are the design engineer in cw:vh)-q, 7(lymz ns xqharge of the crashworthiness of new automobile models. Cars are tested by smashing them into fixed, massive barriers at 50km/h (30 mph). A new model of mass 1500 kg takes 0.15 s from the time of impact until it is brought to rest. (a) Calculate the average force exerted on the car b,:y 7(ls-v x)hmnqqzwy the barrier. $\approx$$a\times10^5$N a =   
(b) Calculate the average deceleration of the car.    m/$s^2$

  A 95-kg fullback is running at 4m/s to the east and5s*9 rq es8rf(ytze1t i:4ckj is stopped in 0.75 s by a head-on tackle by:sjz8i *yte5q(t9esf4 k1r cr a tackler running due west. Calculate
(a) the original momentum of the fullback    kg*m/s
(b) the impulse exerted on the fullback    kg*m/s
(c) the impulse exerted on the tackler,    kg*m/s
(d) the average force exerted on the tackler.    N

  Suppose the force acting on a tennis ball (mass 0.060 kg) points in the +x direc4 gpuz6yj x6.jtion a6y 64gp.xu zjjnd is given by the graph of Fig. 7–33 as a function of time. Use graphical methods to estimate
(a) the total impulse given the ball    N*s
(b) the velocity of the ball after being struck, assuming the ball is being served so it is nearly at rest initially.    m/s

  From what maximum height can a 75-kg person jump without break3z:zxqy a +fx yvr:w)1ing the lower leg bone of either leg? Ignore air resistance and assume the CM of the person moves a distance of 0.60 m from the standing to the seated position (that is, in breaking the fall). Assume the br+::a 1zf z)vw y3ryxqxeaking strength (force per unit area) of bone is $170\times10^6\mathrm{~N/m^2}$ and its smallest cross-sectional area is $2.5\times10^{-4}m^2$ [Hint: Do not try this experimentally.]    m

  A ball of mass 0.440 kg moving east (+x direction) wit geb5 p x)b4d:nuip(8wh a speed of collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the collision?Let A represent the 0.440-kg ball, and B represent the 0.220-kg ball. gw4( ub 8ppeid)bn:x5 $v'_A$    m/s  ----待选择----eastwest  $v'_B$    m/s  ----待选择----eastwest 

  A 0.450-kg ice puck, moving east with a srkmkx 4k0t-zd):g+vr6tavj(peed of 3m/s has a head-on collision with a 0.900-kg puck initially at rest. Assuming a perfectly elastic collision, what w vtkrx:-mj( k) 0adk+ vzrgt46ill be the speed and direction of each object after the collision?Let A represent the 0.450-kg puck, and let B represent the 0.900-kg puck. v'$_A$ =    m/s ----待选择----eastwest  v'$_B$ =    m/s ----待选择----eastwest 

  Two billiard balls of equab5l.x *jjm/zsl mass undergo a perfectly elastic head-on collision. If one ball’s initial speed was 2m/s and the other’s was 3m/s in the opposite direction, what will be their speeds after the collision?(Let A represent the ball moving at 2.00 m/s, and call that direction the positive direction.Let B represent the ball moving at 3.00 m/s 5m.jb*sx /z jlin the opposite direction. ) v'$_A$ =    m/s v'$_B$ =    m/s

  A 0.060-kg tennis ball, moving with a speed of 2.5m/s collides head-onsebc 1 3/ wok4lhh.rb( with a 0.090-kg ball initially moving away from it at a speed of 1.15m/s Assuming a perfectly elastic collision, what are the speed and direction of each ball after the collision?(Let A represent the 0.060-kg tennis ball, and.1r( /4kwhblsoec h3b let B represent the 0.090-kg ball.)v'$_A$ =    m/s v'$_B$ =    m/s

  A softball of mass 0.220 kg that is moving with a speed ouj e3g)n76s26okq e) l 5fpj6s9s cqfxf 8.5m/s collides head-on and elastically with another ball initially at rest. Afterward the incoming softball bounces backward with a speed of 3.7m/s6cjpq63f2 q og)juf ekesls9n5s6x7) Calculate
(a) the velocity of the target ball after the collision    m/s
(b) the mass of the target ball.    kg
(Let A represent the moving softball, and let B represent the ball initially at rest.)

  Two bumper cars in anj1. hfi14cyxbur.n0 l amusement park ride collide elastically as one approaches the other directly from the rear (Fig. 7–34). Car A has a mass of 450 kg and car B 550 kg, owing to differences in passenger mass. If car A approachesu xl0rhbfy14 c..j 1in at 4.5m/s and car B is moving at 3.7m/s calculate
(a) their velocities after the collision v'$_A$ =    m/s v'$_B$ =    m/s
(b) the change in momentum of each.$\Delta p_{\mathrm{A}}$$\approx$    kg*m/s $\Delta p_{\mathrm{B}}$$\approx$    kg*m/s

  A 0.280-kg croquet ball makes an elastic head-on collisio3 r+ jj5wmtj9 f2lt/qun with a second ball initially at rest. The second ball moves off with half the orjtw /j 9m+q tf2jr3lu5iginal speed of the first ball.
(a) What is the mass of the second ball?    kg
(b) What fraction of the original kinetic energy $(\Delta\mathrm{kE/KE})$ gets transferred to the second ball?   

  In a physics lab, a cube slides down a frictioz gh68i -sc*sy-c q)9 qppwlg(nless incline as shown in Fig. 7–35, and elastically strikes another cube at the bottom that is only one-half its mass. If the incline is 30 cm high and the tab c lcg6pwz8)q sygq(-*p 9s-ihle is 90 cm off the floor, where does each cube land? [Hint: Both leave the incline moving horizontally.]$\Delta x_{m}$$\approx$    m $\Delta x_{M}$$\approx$    m

ake the general case of an object of ry07iim u91uc mass m$_A$ and velocity v$_A$ elastically striking a stationary object of mass head-on. (a) Show that the final velocities v'$_A$ and v'$_B$ are given by$v_{\mathrm{A}}^{\prime}=\left(\frac{m_{\mathrm{A}}-m_{\mathrm{B}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}},v_{\mathrm{B}}^{\prime}=\left(\frac{2m_{\mathrm{A}}}{m_{\mathrm{A}}+m_{\mathrm{B}}}\right)\nu_{\mathrm{A}}.$(b) What happens in the extreme case when m$_A$ is much smaller than m$_B$ Cite a common example of this. (c) What happens in the extreme case when m$_A$ is much larger than m$_B$ Cite a common example of this. (d) What happens in the case when m$_A$=m$_B$ Cite a common example.

  In a ballistic pendulum experiment, projectile 1 results in a 9 l u)+tt o*0xt/r4btmtbsd9b maximum height h of the pendulum equal to 2.6 cm. A second projectile causes the the pendulum to swx )*tl+umrbd9bt b9/ 4 stt0oting twice as high, $h_2=5.2\mathrm{cm}$ The second projectile was how many times faster than the first? $v_1$ =    $v_2$ ([color=rgba(0, 0, 0, 0.85)]Round to three decimal places)

  A 28-g rifle bullet traveling 230m/s buries itself in a 3.dm-safoga-v)i:jy( 0g6q ;v31- mhqsg zi9 kn6-kg pendulum hanging on a 2.8-m-long string, which makes the pendulum swing upward in an arc. Determine the vertical ands i-)m-i - myqa0h6vf3gns ;ojzgv(: 9dq g1ak horizontal components of the pendulum’s displacement.vertical$\approx$    m horizontal =    m

(a) Derive a formula for the fraction of kinetic energy lostb.bkd*cz) u.qf0n tp mp5-k3l, $(\Delta\mathrm{KE/KE})$ for the ballistic pendulum collision of Example 7–10. (b) Evaluate for m=14g and M=380g

  An internal explosion brekc)8+ 2 zkbba2uu-d:p ocwq 0gaks an object, initially at rest, into two pieces, one of which has 1.5 times the mass of the other. If 7500 J were released in the explosion, c 2p:2)uk- q z8kb gouw+0dcbahow much kinetic energy did each piece acquire? (Let A represent the heavier particle, and B represent the lighter particle. ) KE'$_A$ =    J KE$_B$ =    J

  A 920-kg sports car collides into the rear end of a 2300-kg SUV stopped at a re3yu/ e9pgjb. am( k pq)lh:; ic1lck,ed light. The bumpers lock, the brakes are locked, and the two cars skid forward 2.8 m befoigu)kyec.,;1mh(je3 cq bal lpp:/ 9kre stopping. The police officer, knowing that the coefficient of kinetic friction between tires and road is 0.80, calculates the speed of the sports car at impact. What was that speed?(Let A represent the sports car, and B represent the SUV) $\approx$    m/s

  A ball is dropped from a height of 1.2occfi ji * ,q.ir9rv3:7u frralk7e(50 m and rebounds to a height of 1.20 m. Approximately how many rebounds will the ball make before losing 90% of i3rqccrfk7 vorr j:7ali2ii.(f,ue*9 ts energy?   

A measure of inelasticity in a head-on *,bij,hvei67s e uvf 0co5t(e3b jmc, collision of two objects is the coefficient of restitu3f,5*v,oecu ehcb sjim eij0v, b6(7ttion, e, defined as$e=\frac{\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}}{\nu_\mathrm{B}-\nu_\mathrm{A}},$
where $\nu_\mathrm{A}^{\prime}-\nu_\mathrm{B}^{\prime}$ is the relative velocity of the two objects after the collision and $\nu_\mathrm{B}-\nu_\mathrm{A}$ is their relative velocity before it.
(a) Show that e=1 for a perfectly elastic collision, and e=0 for a completely inelastic collision.
(b) A simple method for measuring the coefficient of restitution for an object colliding with a very hard surface like steel is to drop the object onto a heavy steel plate, as shown in Fig. 7–36. Determine a formula for e in terms of the original height h and the maximum height h’ reached after one collision.

  A wooden block is cut into two pieces, one with thr+ 8fmzlq gv.f;;pmr 3qxjdn*8 ee times the mass of the other. A depressioxq.qpf8;3vgl md;mjf +8z n*rn is made in both faces of the cut, so that a firecracker can be placed in it with the block reassembled. The reassembled block is set on a rough-surfaced table, and the fuse is lit. When the firecracker explodes, the two blocks separate and slide apart. What is the ratio of distances each block travels? ----待选择----1/91/101/81/6 

  A 15.0-kg object moving in the +x direction at 5.5m/s collides head-onyv1wahdj /urm lpw)q7q 1+ +8u with a 10.0-kg object moving in the -x direction at 4m/s Finwhq rlj/qy+8vm +1 a wupdu17)d the final velocity of each mass if:
(a) the objects stick together;   m/s
(b) the collision is elastic; v'$_A$ =    m/s v'$_B$ =    m/s
(c) the 15.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(d) the 10.0-kg object is at rest after the collision;   m/s ----待选择----not reasonable reasonable 
(e) the 15.0-kg object has a velocity of 4m/s in the -x direction after the collision. .   m/s ----待选择----not reasonable reasonable 
Are the results in (c), (d), and (e) “reasonable”? Explain
( Let A represent the 15.0-kg object, and let B represent the 10.0-kg object.)

  A radioactive nucleus at rest decays into a second nucleus, an electro2vqx86rd) mzh n, and a neutrino. The electron and neutrino are emitted at right angles and have momenta )2xvm6hrd8q z of $9.30\times10^{-23}kg\cdot m/s$ and $5.40\times10^{-23}\mathrm{~kg}\cdot\mathrm{m/s}$ respectively. What are the magnitude and direction of the momentum of the second (recoiling) nucleus?    $ \times10^{-22}$    $^{\circ} $ from the momentum of the electron

  An eagle ($m_{\mathrm{A}}=4.3\mathrm{kg}$) moving with speed $\nu_\mathrm{A}=7.8\mathrm{~m/s}$ is on a collision course with a second eagle ($m_{\mathrm{B}}=5.6\mathrm{kg}$) moving at $\nu_{\mathrm{B}}=10.2\mathrm{m/s}$ in a direction perpendicular to the first. After they collide, they hold onto one another. In what direction, and with what speed, are they moving after the collision? v =    m/s $\theta$ =    $^{\circ} $ rel. to eagle  ----待选择----AB 

  Billiard ball A of mas*y u3gzy;xvwugf- ,6a65s hr ks $m_\mathrm{A}=0.400$kg moving with speed $\nu_\mathrm{A}=1.80$m/s strikes ball B, initially at rest, of mass $m_\mathrm{B}=0.500$kg As a result of the collision, ball A is deflected off at an angle of 30.0 $^{\circ} $ with a speed $\nu_\mathrm{A}^{\prime}=1.10$m/s (a) Taking the x axis to be the original direction of motion of ball A, write down the equations expressing the conservation of momentum for the components in the x and y directions separately. (b) Solve these equations for the speed v'$_B$ and angle $\theta_{\mathrm{B}}$ of ball B. Do not assume the collision is elastic. $\theta_{\mathrm{B}}$ =    $^{\circ} $ v'$_B$ =    m/s

  After a completely inelastic collision between two objects of equal mass, each h2 j3 4fjag8layaving initial speed the two move off together with speed v/3 What was the angle between2jlaga3j4f 8 y their initial directions?    $^{\circ} $

  Two billiard balls of equal mass move at right angles and meet at the origoxcphzqwh+j /34s+ pnnlgl (x2v 8n3*in of an xy coordinate system. Ball A is moving upward along the y axis at 2m/s and ball B is moving 3+8gwl ozc2 njx4+l vnsn/* qhx3pp(hto the right along the x axis with speed 3.7m/s After the collision, assumed elastic, ball B is moving along the positive y axis (Fig. 7–37). What is the final direction of ball A and what are their two speeds? direction of ball A is  ----待选择----x directionx direction v'$_A$ =    m/s v'$_B$ =    m/s

  A neon atom (m=20u) makes a d: kjd:n.zdd3 perfectly elastic collision with another atom at rest. After the impact, the neon atom travels away zdjn:3d:kd d. at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  A neon atom (m=20u) makes a perfectly elastm- siq;v+q5w hp;a a-gic collision with another atom at rest. Af;hq a-igm5w -a vq;p+ster the impact, the neon atom travels away at a 55.6 $^{\circ} $ angle from its original direction and the unknown atom travels away at a -50 $^{\circ} $ angle. What is the mass (in u) of the unknown atom? [Hint: You can use the law of sines.](Let A represent the incoming neon atom, and B represent the target atom) $m_B$   u

  Find the center of mass of the thr) af8g uh1i1imee-mass system shown in Fig. 7–38. Specify relative to the left-hand 1.00) a8u1mhg fi1i-kg mass.    m

  The distance between a carnw ee3jvv3 zbd1.c 7f7bon atom ($m_{\mathrm{C}}=12\mathrm{u}$) and an oxygen atom ($m_{\mathrm{O}}=16\mathrm{u}$) in the CO molecule is $1.13\times10^{-10}$m How far from the carbon atom is the center of mass of the molecule?    $\times10^{-11}$m

  The CM of an empty 1050-kg car is 2.50 m behind the front of tht.nsivm0s- 5de car. How far from the f.vtnsds 5-0m iront of the car will the CM be when two people sit in the front seat 2.80 m from the front of the car, and three people sit in the back seat 3.90 m from the front? Assume that each person has a mass of 70.0 kg.    m

  A square uniform raft, 18 mzl; :pcobd)s; ai: *kv by 18 m, of mass 6800 kg, is used as a ferryboat. If three cars, each of mass 1200 kg, occupy its NE, SE, and S):bvclo k;*;pasiz:dW corners, determine the CM of the loaded ferryboat.$X_{CM}$ =    m $Y_{CM}$ =    m

  Three cubes, of side28zgnin)+7 tjdo. wb is $l_0$,$2l_0$, and $3l_0$ are placed next to one another (in contact) with their centers along a straight line and the $l=2l_{0}$ cube in the center (Fig. 7–39). What is the position, along this line, of the CM of this system? Assume the cubes are made of the same uniform material. $X_{CM}$ =    $l_0$ from the  ----待选择----leftright  edge of the smallest cube

  A (lightweight) pallet has a load of identicw 4 8.y5ebxir5v*ymf kya0k p:j00akhal cases of tomato paste (see Fig. 7–40), each of which is a cube of length l. Find thyka:p.h i m*kka48fw550 00vx yybr eje center of gravity in the horizontal plane, so that the crane operator can pick up the load without tipping it.$X_{CM}$ =    l $Y_{CM}$ =    l

  A uniform circular plate of radius 2R has a circular hole of radius R cut o0e5 buiwkh2 v:ut of it. The center of the smaller circle is a distance 0.80R from the center C of the larger circle, Fig. 7–41. What is the position of the center of mass of the plate? [Hiib 5h02k wuev:nt: Try subtraction.]   R

  Assume that your proport*i9iw*ocdz(o 4z5zuxions are the same as those in Table 7–1, and calculate the mass of one of youz oo5 dzx ui**(icwz94r legs.    kg

  Determine the CM of an outstretched arm usiw m8 g5r oipxlg6ntep *z0q023ng Table 7–1.   % of the person's height along the line from the shoulder to the hand

  Use Table 7–1 to calculate the position of the CM of anvtz3lg,.ewwd,zm 6 3+g k 8xky arm bent at a right angle. k83 wtx+ywk3vm 6.gel,zdzg,Assume that the person is 155 cm tall. $X_{CM}$ =    cm $Y_{CM}$ =    cm

When a high jumper is in a position such that his arms a+oxxhvq/s 4 c/*gl(b snd legs are hanging vertically, and his trunk and head are horizontal, calculate how far below the torso’s median line the CM will be. o(xsbhc /+*g/vlq 4xs Will this CM be outside the body? Use Table 7–1.

The masses of the Earth and Moonwnb9v8)uef 4+1zxypm 93 tfz d are $5.98\times10^{24}$kg and $7.35\times10^{22}$kg respectively, and their centers are separated by $3.84\times10^{8}$m (a) Where is the CM of this system located? (b) What can you say about the motion of the Earth–Moon system about the Sun, and of the Earth and Moon separately about the Sun?

  A 55-kg woman and an 80-ftjyxi2nj2-ek1mo )9 1 cwze-kg man stand 10.0 m apart on frictionless ice.
(a) How far from the woman is their CM?    m from the woman
(b) If each holds one end of a rope, and the man pulls on the rope so that he moves 2.5 m, how far from the woman will he be now?    m
(c) How far will the man have moved when he collides with the woman? He has moved    m from his original position

  A mallet consists of a uniform cylindrical head of ryyel896j1 ir tq .;ismass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindrical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will 1rie9.l s6rt8 yyjq i;follow a parabolic trajectory?    cm

  A mallet consists of a uniform cylind01l e sq74:ywr bx8b7 fyjgsv4rical head of mass 2.00 kg and a diameter 0.0800 m mounted on a uniform cylindr 7 fjs1beyg48s:x4ylrv w7 b0qical handle of mass 0.500 kg and length 0.240 m, as shown in Fig. 7–42. If this mallet is tossed, spinning, into the air, how far above the bottom of the handle is the point that will follow a parabolic trajectory?    d    d

  (a) Suppose that in Ex.nc vonm5e :ee7 8d1kiample 7–14 (Fig. 7–29), $m_{II}$=3$m_{I}$ Where then would $m_{II}$ land?    d(Round to two decimal places)
(b) What if $m_{I}$=3$m_{II}$    d

A helium balloon and its g9shg51jwx. u vondola, of mass M, are in the air and stationary with respect to the ground. A passenger, of mass m, then climbs out and slides down a rope with speed measured with respect to the balloon. With what speed and direction (relative to Earth) does the balloon then move? What happens if the passengeru5ghws.vx j 91 stops?

  An 0.145-kg baseball pitched horizontally at strikes a bat and is popped stv.6j su fnu)d;f,9h.zm vog)nz, 8krtraight up to a height of 55.6 m. If the contact time is 1.4 ms, calculate the average force on the b8 )gu kh9;n.v.t6zjod z)vf n ,u,rfmsall during the contact.    $^{\circ} $

  A rocket of mass m travelid)ki/p71gy3 uv,fj nung with speed $v_0$ along the x axis suddenly shoots out fuel, equal to one-third of its mass, parallel to the y axis (perpendicular to the rocket as seen from the ground) with speed 2$v_0$ Give the components of the final velocity of the rocket.$P_x$: v'$_x$=    $v_0$
$P_y$: v'$_y$=    $v_0$

A novice pool player is faced with the coc6:nrwwlrmjlqrf93 j3 3h, z(rner pocket shot shown in Fig. 7–43. Relative dwr93 ,rwqczf :3 r j3nm6ll(hjimensions are also shown. Should the player be worried about this being a “scratch shot,” in which the cue ball will also fall into a pocket? Give details.

  A 140-kg astronaut (including space suit) acquires a speed of 2.5m/s by pushilh dp45oja( rsw/4;fk2.qcbcng off with his leg4pao l5hd/ w;b(2cr4fcjq. sks from an 1800-kg space capsule.
(a) What is the change in speed of the space capsule?    m/s
(b) If the push lasts 0.40 s, what is the average force exerted on the astronaut by the space capsule? As the reference frame, use the position of the space capsule before the push.    N

  Two astronauts, one of mass 60 kg and the otnmfm8(;o7 i :+e hsnbpher 80 kg, are initially at rest in outer space. They then push each bmes8;o:+nnpifm7h (other apart. How far apart are they when the lighter astronaut has moved 12 m?    m

  A ball of mass m makes a head- 4- lqw.;jwacqon elastic collision with a second ball (at rest) and rebounds in the opposite direction with a speed w-.wj 4qca ;lqequal to one-fourth its original speed. What is the mass of the second ball? $m_B$ =    $m_A$(Round to two decimal places)

  You have been hired ass ttcok 81u*ep.3ry.n an expert witness in a court case involving an automobile accident. The accident involved car spttk1uyer . .o8*cn3 A of mass 1900 kg which crashed into stationary car B of mass 1100 kg. The driver of car A applied his brakes 15 m before he crashed into car B. After the collision, car A slid 18 m while car B slid 30 m. The coefficient of kinetic friction between the locked wheels and the road was measured to be 0.60. Show that the driver of car A was exceeding the 55-mph (90km/h) speed limit before applying the brakes.    mi/h

A golf ball rolls off the top of a flight of concrete steps of q6c usq d,a 0cb+g(ha+6rutw 3(wi*dvtotal vertical height 4.00 m. The ball hits four times on the way down, each time striking the horizontal part of a different step 1.0 m lower. If all collisions are perfectly elastic, what is the bounce height on the fourth bounce when the ball reaches the bottom oaw, u+6twdu6+ h icd0s( vbcagqr*(3qf the stairs?

  A bullet is fired vertically into a 1.40-kg block t2r7p flsw0 1tof wood at rest directly above it. If the bullet has a mass of 29.0 g and a speed of 510m/s how high will twps1r0f2t7 tlhe block rise after the bullet becomes embedded in it?    m

  A 25-g bullet strikes and becomes ebx --kejhmdv.ms*f;(15zdls mbedded in a 1.35-kg block of wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic friction between the blh1els; mz-d 5fj(- *sxvbd. mkock and the surface is 0.25, and the impact drives the block a distance of 9.5 m before it comes to rest, what was the muzzle speed of the bullet?    m/s

  Two people, one of mass 75 kg and the other of m46,h-y.o vqms4d;wwrwf( j ikass 60 kg, sit in a rowboat of mass 80 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends of the boat 3.2 m apart6 i(rkf-4oh w4y ,;jdqsw.mwv from each other, now exchange seats. How far and in what direction will the boat move? The boat will move    towards the initial position of the 75 kg person(Round to two decimal places)

  A meteor whose mass w id-dt8l 43/2ox h lj/tblut3gas about $ 1\times10^{ 8}$kg struck the Earth ($m_E$=$6 \times10^{ 24}$kg) with a speed of about 15km/s and came to rest in the Earth.
(a) What was the Earth’s recoil speed?    $ \times10^{-13 }$m/s
(b) What fraction of the meteor’s kinetic energy was transformed to kinetic energy of the Earth?    $ \times10^{ -17}$
(c) By how much did the Earth’s kinetic energy change as a result of this collision?    J

  An object at rest is suddenly broken apart into two fragments by anz80*m,r5q 3 .xy1fzb m jvtblm explosion. One fragment acquires twice the kinetic energy of the other. What is the rat t* mz5f1m8blmvy jqxb.r3z 0,io of their masses?   

  The force on a bullet is given by62 ;dbijel8 ft the formula F = 580-( $1.8 \times10^{ 5}$t) over the time interval t=0 to t = $3.0 \times10^{-3 }$s In this formula, t is in seconds and F is in newtons.
(a) Plot a graph of F vs. t for t=0 to t=3.0ms
(b) Estimate, using graphical methods, the impulse given the bullet.    N*s
(c) If the bullet achieves a speed of 220m/s as a result of this impulse, given to it in the barrel of a gun, what must its mass be?    kg

  Two balls, of masses n,,wv, fljyq +$m_A$ = 40g and $m_B$ = 60g are suspended as shown in Fig. 7–44. The lighter ball is pulled away to a 60$^{\circ} $ angle with the vertical and released.
(a) What is the velocity of the lighter ball before impact?$\approx$    m/s
(b) What is the velocity of each ball after the elastic collision?v'$_A$ $\approx$    m/s v'$_B$ $\approx$    m/s(Round to two decimal places)
(c) What will be the maximum height of each ball after the elastic collision?    m

  An atomic nucleus at rest decays radioactively into an alpha particle and a sxu6 brk t1hdfo o;oqq6:ucd.k.n z6 55maller nucleus. What wi1.x 5z6dh5ukoo ;q:butckq . orfdn66 ll be the speed of this recoiling nucleus if the speed of the alpha particle is $ 3.8\times10^{5 }$m/s Assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle.    m/s

  A 0.25-kg skeet (clay target) qbz:q* d/i1s+;9vbr vp.u o acis fired at an angle of 30 $^{\circ} $ to the horizon with a speed of 25m/s (Fig. 7–45). When it reaches the maximum height, it is hit from below by a 15-g pellet traveling vertically upward at a speed of 200m/s The pellet is embedded in the skeet.
(a) How much higher did the skeet go up?    m
(b) How much extra distance, $\Delta{x}$ does the skeet travel because of the collision? $\approx$   

  A block of mass m=2.2kg slik 1ay6wa:kpb- des down a 30.0 $^{\circ} $ incline which is 3.60 m high. At the bottom, it strikes a block of mass M=7kg which is at rest on a horizontal surface, Fig. 7–46. (Assume a smooth transition at the bottom of the incline.) If the collision is elastic, and friction can be ignored, determine
(a) the speeds of the two blocks after the collision,v'$_A$ =    m/s v'$_B$ =    m/s
(b) how far back up the incline the smaller mass will go. $\approx$   (Round to the nearest integer) (Let A represent mass m, and B represent mass M.)

  In Problem 79 (Fig. 7–46), what is the uppvtb5v5a); abd er limit on mass m if it is to rebound from M, slide up the incline, stop, slide dow av5tb ad)b5v;n the incline, and collide with M again?    kg (Let A represent mass m, and B represent mass M.)

  The gravitational slingshot ef6r 5vfq8an f o:vfn26gfect. Figure 7–47 shows the planet Saturn moving in the negative x direction at its orbital speed (with respect to the Sun) of 9.6km/so nv6 8ff:f2vargnq65 The mass of Saturn is $5.69 \times10^{ 26}$kg A spacecraft with mass 825 kg approaches Saturn. When far from Saturn, it moves in the direction at 10.4km/s The gravitational attraction of Saturn (a conservative force) acting on the spacecraft causes it to swing around the planet (orbit shown as dashed line) and head off in the opposite direction. Estimate the final speed of the spacecraft after it is far enough away to be considered free of Saturn’s gravitational pull.    km/s