Physics 50 Test 2

Name:

Feb 25, 2016

Calculators are allowed. Notes and books are not allowed.

Answer all the questions in any order you like. For full credit you must show your workand/or explain your logic.

Scale symbols

Scale Prefix Symbol103 kilo- k100 — —

10−1 deci- d10−2 centi- c10−3 milli- m

g = 9.81 m/s2

Trigonometric Identities

sin2 θ + cos2 θ = 1

sin(2θ) = 2 sin(θ) cos(θ)

cos(2θ) = cos2 θ − sin2 θ

sin(α± β) = sinα cos β ± cosα sin β

cos(α± β) = cosα cos β ∓ sinα sin β

cosα cos β = 12[cos(α− β) + cos(α + β)]

sinα sin β = 12[cos(α− β) − cos(α + β)]

sinα cos β = 12[sin(α + β) + sin(α− β)]

sin(θ + π

2

)= cos θ

cos(θ + π

2

)= − sin θ

sec θ := 1cos θ

csc θ := 1sin θ

cot θ := 1tan θ

1. On a hot summer day, a young girl swings on a rope above the local swimming hole.When she lets go of the rope her initial velocity is 2.50 m/s at an angle of 35.0◦ abovethe horizontal. If she is in flight for 0.650 s, how high above the water was she whenshe let go of the rope?

PROBLEMS 103

35.0°

v0

▲ FIGURE 4–21 Problem 37

28. •• Repeat the previous problem for a bounce pass in which theball is thrown 15° above the horizontal.

29. •• IP Snowballs are thrown with a speed of 13 m/s from aroof 7.0 m above the ground. Snowball A is thrown straightdownward; snowball B is thrown in a direction 25° above thehorizontal. (a) Is the landing speed of snowball A greater than,less than, or the same as the landing speed of snowball B? Ex-plain. (b) Verify your answer to part (a) by calculating the land-ing speed of both snowballs.

30. •• In the previous problem, find the direction of motion of thetwo snowballs just before they land.

31. •• A golfer gives a ball a maximum initial speed of 30.0 m/s.(a) What is the longest possible hole-in-one for this golfer?Neglect any distance the ball might roll on the green andassume that the tee and the green are at the same level. (b) Whatis the minimum speed of the ball during this hole-in-one shot?

32. •• What is the highest tree the ball in the previous problemcould clear on its way to the longest possible hole-in-one?

33. •• The “hang time” of a punt is measured to be 4.50 s. If theball was kicked at an angle of 63.0° above the horizontal andwas caught at the same level from which it was kicked, whatwas its initial speed?

34. •• In a friendly game of handball, you hit the ball essentiallyat ground level and send it toward the wall with a speed of14 m/s at an angle of 34° above the horizontal. (a) How longdoes it take for the ball to reach the wall if it is 3.8 m away?(b) How high is the ball when it hits the wall?

35. •• IP In the previous problem, (a) what are the magnitudeand direction of the ball’s velocity when it strikes the wall?(b) Has the ball reached the highest point of its trajectory atthis time? Explain.

36. •• A passenger on the Ferris wheel described in Problem 18drops his keys when he is on the way up and at the 10 o’clockposition. Where do the keys land relative to the base of theride?

37. •• On a hot summer day, a young girl swings on a rope abovethe local swimming hole (Figure 4–21). When she lets go ofthe rope her initial velocity is 2.25 m/s at an angle of 35.0°above the horizontal. If she is in flight for 0.616 s, how highabove the water was she when she let go of the rope?

38. ••• A certain projectile is launched with an initial speed Atits highest point its speed is What was the launch angle?v0>4.

v0.

Section 4–5 Projectile Motion: Key Characteristics39. • Punkin Chunkin In Sussex County, Delaware, a post-

Halloween tradition is “Punkin Chunkin,” in which contestantsbuild cannons, catapults, trebuchets, and other devices tolaunch pumpkins and compete for the greatest distance.Though hard to believe, pumpkins have been projected a dis-tance of 4086 feet in this contest. What is the minimum initialspeed needed for such a shot?

40. • A dolphin jumps with an initial velocity of 12.0 m/s at anangle of 40.0° above the horizontal. The dolphin passes throughthe center of a hoop before returning to the water. If the dolphinis moving horizontally when it goes through the hoop, howhigh above the water is the center of the hoop?

41. • A player passes a basketball to another player who catches itat the same level from which it was thrown. The initial speed ofthe ball is 7.1 m/s, and it travels a distance of 4.6 m. What was(a) the initial direction of the ball and (b) its time of flight?

42. • A golf ball is struck with a five iron on level ground. It lands92.2 m away 4.30 s later. What was (a) the direction and (b) themagnitude of the initial velocity?

43. • A Record Toss Babe Didrikson holds the world record forthe longest baseball throw (296 ft) by a woman. For the follow-ing questions, assume that the ball was thrown at an angle of45.0° above the horizontal, that it traveled a horizontal distanceof 296 ft, and was caught at the same level from which it wasthrown. (a) What was the ball’s initial speed? (b) How long wasthe ball in the air?

44. • In the photograph to the left on page 84, suppose the cart thatlaunches the ball is 11 cm high. Estimate (a) the launch speed ofthe ball and (b) the time interval between successive strobo-scopic exposures.

45. •• IP Volcanoes on Io Astronomers have discovered severalvolcanoes on Io, a moon of Jupiter. One of them, named Loki,ejects lava to a maximum height of (a) What isthe initial speed of the lava? (The acceleration of gravity on Io is

) (b) If this volcano were on Earth, would the maxi-mum height of the ejected lava be greater than, less than, or thesame as on Io? Explain.

1.80 m/s2.

2.00 * 105 m.

A volcano on Io, the innermost moon of Jupiter, displays the characteristic features of projectile motion. (Problem 45)

46. •• IP A soccer ball is kicked with an initial speed of 10.2 m/sin a direction 25.0° above the horizontal. Find the magnitudeand direction of its velocity (a) 0.250 s and (b) 0.500 s afterbeing kicked. (c) Is the ball at its greatest height before or after0.500 s? Explain.

47. •• A second soccer ball is kicked with the same initial speed asin Problem 46. After 0.750 s it is at its highest point. What wasits initial direction of motion?

WALKMC04_0131536311.QXD 11/16/05 17:57 Page 103

HYPOTHESIS: [1 pts]

SOLUTION: [5 pts]

ANSWER REASONABLE / AGREES WITH HYPOTHESIS?: [1 pt]

2. Find the tension in each of the three strands of cord supporting the load, which hangsat rest.

142 Chapter 5 The Laws of Motion

diagrams of both objects. Find (b) the magnitude of the acceleration of the objects and (c) the tension in the string.

41. Figure P5.41 shows the speed of a person’s body as he does a chin-up. Assume the motion is vertical and the mass of the person’s body is 64.0 kg. Determine the force exerted by the chin-up bar on his body at (a) t 5 0, (b) t 5 0.5 s, (c) t 5 1.1 s, and (d) t 5 1.6 s.

time (s)1.0 1.50

10

20

30

0.5 2.0

spee

d (c

m/s

)

Figure P5.41

42. Two objects are connected by a light string that passes over a frictionless pulley as shown in Figure P5.42. Assume the incline is frictionless and take m1 5 2.00 kg, m2  5 6.00  kg, and u 5 55.0°. (a)  Draw free-body dia-grams of both objects. Find (b)  the magnitude of the accel-eration of the objects, (c) the ten-sion in the string, and (d) the speed of each object 2.00 s after it is released from rest.

43. Two blocks, each of mass m 5 3.50 kg, are hung from the ceiling of an elevator as in Figure P5.43. (a) If the elevator moves with an upward acceler ation aS of magni-tude 1.60 m/s2, find the tensions T1 and T2 in the upper and lower strings. (b) If the strings can withstand a maximum tension of 85.0 N, what maximum accelera-tion can the elevator have before a string breaks?

44. Two blocks, each of mass m, are hung from the ceiling of an eleva-tor as in Figure P5.43. The elevator has an upward accel-eration a. The strings have negligible mass. (a) Find the tensions T1 and T2 in the upper and lower strings in terms of m, a, and g. (b) Compare the two tensions and determine which string would break first if a is made sufficiently large. (c) What are the tensions if the cable supporting the elevator breaks?

45. In the system shown in Figure P5.45, a horizontal force FS

x acts on an object of mass m2 5 8.00 kg. The hori-

m1 m2

u

Figure P5.42

T1

T2

aS m

m

Figure P5.43 Problems 43 and 44.S

M

36. Figure P5.36 shows loads hanging from the ceiling of an elevator that is moving at constant velocity. Find the tension in each of the three strands of cord supporting each load.

50.0°40.0°

T1 T2

T3

5.00 kg

60.0°

T1

T3

10.0 kg

T2

a b

Figure P5.36

37. An object of mass m 5 1.00 kg is observed to have an accel-eration aS with a magnitude of 10.0 m/s2 in a direction 60.0° east of north. Figure P5.37 shows a view of the object from above. The force F

S2 act-

ing on the object has a magni-tude of 5.00 N and is directed north. Determine the magnitude and direction of the one other horizontal force F

S1 acting on the object.

38. A setup similar to the one shown in Figure P5.38 is often used in hospitals to support and apply a horizontal trac-tion force to an injured leg. (a) Determine the force of tension in the rope supporting the leg. (b) What is the traction force exerted to the right on the leg?

70!

8.00 kg

Figure P5.38

39. A simple accelerometer is constructed inside a car by suspending an object of mass m from a string of length L that is tied to the car’s ceiling. As the car accelerates the string–object system makes a constant angle of u with the vertical. (a) Assuming that the string mass is negligible compared with m, derive an expression for the car’s acceleration in terms of u and show that it is independent of the mass m and the length L. (b) Deter-mine the acceleration of the car when u 5 23.0°.

40. An object of mass m1 5 5.00 kg placed on a frictionless, horizon-tal table is connected to a string that passes over a pulley and then is fastened to a hanging object of mass m2  5 9.00 kg as shown in Figure P5.40. (a) Draw free-body

60.0!

m

aS F2S

F1S

Figure P5.37

BIO

m1

m2

Figure P5.40 Problems 40, 63, and 87.

AMTW

SKETCH a Free-body Diagram: [2 pts]

HYPOTHESIS: [3 pts]

SOLUTION: [7 pts]

ANSWER REASONABLE / AGREES WITH HYPOTHESIS?: [1 pt]

3. What are Newton’s three laws of motion? (Be as complete and specific as you canbe, and include equations where you can, but say in words what each symbol in yourequation means.) [9 pts]

4. A block sits on a frictionless incline. The angle θ = 20.0◦ and the mass of the block is2.00 kg.

(a) What is the magnitude of the normal force on the block and which way is itdirected?

(b) What is the block’s acceleration and which way is it directed?

(c) If the block is given an initial velocity of 5.00 m/s up the slope, how far up theincline does the block slide before coming to rest?

Problems 143

acts on the top pin. Draw a free-body diagram of the pin. Use the condition for equilibrium of the pin to translate the free-body diagram into equations. From the equations calculate the forces exerted by struts A and B. If you obtain a positive answer, you correctly guessed the direction of the force. A negative answer means that the direction should be reversed, but the absolute value correctly gives the magnitude of the force. If a strut pulls on a pin, it is in tension. If it pushes, the strut is in compression. Identify whether each strut is in tension or in compression.

60.0°A

B

50.0°

Figure P5.48

49. Two blocks of mass 3.50 kg and 8.00 kg are connected by a massless string that passes over a frictionless pul-ley (Fig. P5.49). The inclines are frictionless. Find (a) the magnitude of the acceleration of each block and (b) the tension in the string.

3.50 kg 8.00 kg

35.0° 35.0°

Figure P5.49 Problems 49 and 71.

50. In the Atwood machine discussed in Example 5.9 and shown in Figure 5.14a, m1 5 2.00 kg and m2 5 7.00 kg. The masses of the pulley and string are negligible by comparison. The pulley turns without friction, and the string does not stretch. The lighter object is released with a sharp push that sets it into motion at vi 5 2.40 m/s downward. (a) How far will m1 descend below its initial level? (b) Find the velocity of m1 after 1.80 s.

51. In Example 5.8, we investigated the apparent weight of a fish in an elevator. Now consider a 72.0-kg man stand-ing on a spring scale in an elevator. Starting from rest, the elevator ascends, attaining its maximum speed of 1.20 m/s in 0.800 s. It travels with this constant speed for the next 5.00 s. The elevator then undergoes a uni-form acceleration in the negative y direction for 1.50 s and comes to rest. What does the spring scale register (a) before the elevator starts to move, (b) during the first 0.800 s, (c) while the elevator is traveling at con-stant speed, and (d) during the time interval it is slow-ing down?

Section 5.8 Forces of Friction 52. Consider a large truck carrying a heavy load, such as

steel beams. A significant hazard for the driver is that the load may slide forward, crushing the cab, if the truck stops suddenly in an accident or even in braking. Assume, for example, that a 10 000-kg load sits on the

AMTM

zontal surface is frictionless. Consider the acceleration of the sliding object as a function of Fx. (a) For what values of Fx does the object of mass m1 5 2.00 kg accel-erate upward? (b) For what values of Fx is the tension in the cord zero? (c) Plot the acceleration of the m2 object versus Fx. Include values of Fx from 2100 N to 1100 N.

FxS

m1

m2

Figure P5.45

46. An object of mass m1 hangs from a string that passes over a very light fixed pulley P1 as shown in Figure P5.46. The string connects to a second very light pul-ley P2. A second string passes around this pulley with one end attached to a wall and the other to an object of mass m2 on a frictionless, horizontal table. (a) If a1 and a2 are the accelerations of m1 and m2, respectively, what is the relation between these accelerations? Find expressions for (b) the tensions in the strings and (c) the accelerations a1 and a2 in terms of the masses m1 and m2, and g.

P2P1

m2

m1

Figure P5.46

47. A block is given an initial velocity of 5.00 m/s up a fric-tionless incline of angle u 5 20.0° (Fig. P5.47). How far up the incline does the block slide before coming to rest?

θ

Figure P5.47

48. A car is stuck in the mud. A tow truck pulls on the car with the arrangement shown in Fig. P5.48. The tow cable is under a tension of 2 500 N and pulls down-ward and to the left on the pin at its upper end. The light pin is held in equilibrium by forces exerted by the two bars A and B. Each bar is a strut; that is, each is a bar whose weight is small compared to the forces it exerts and which exerts forces only through hinge pins at its ends. Each strut exerts a force directed par-allel to its length. Determine the force of tension or compression in each strut. Proceed as follows. Make a guess as to which way (pushing or pulling) each force

S

SKETCH a Free-body Diagram for the block: [2 pts]

HYPOTHESIS for (a), (b), and (c): [3 pts]

SOLUTION:Part (a): [3 pts]

Part (b): [3 pts]

Part (c): [5 pts]

ANSWERS REASONABLE / AGREES WITH HYPOTHESIS?: [1 pt]