College Physics for AP® Courses

# Chapter 6

1.

723 km

3.

$5×107rotations5×107rotations size 12{9 "." "79" times "10" rSup { size 8{8} } "rotations"} {}$

5.

7.

728 rpm

8.

(b) 500 N

(c) 40.8 m

10.

12.9 rev/min

12.

$4×1021m4×1021m size 12{ {underline {4 times "10" rSup { size 8{"21"} } " m"}} } {}$

14.

a) $3.47×104m/s23.47×104m/s2 size 12{3 cdot "47" times "10" rSup { size 8{"4"} } m/s rSup { size 8{2} } } {}$, $3.55×103g3.55×103g size 12{3 cdot "55" times "10" rSup { size 8{"3"} } g} {}$

b) $51.1m/s51.1m/s size 12{3 cdot "75" m/s} {}$

16.

a) $31.4 rad/s 31.4 rad/s$

b) $118 m/s 118 m/s$

c) $384 m/s 384 m/s$

d)The centripetal acceleration felt by Olympic skaters is 12 times larger than the acceleration due to gravity. That's quite a lot of acceleration in itself. The centripetal acceleration felt by Button's nose was 39.2 times larger than the acceleration due to gravity. It is no wonder that he ruptured small blood vessels in his spins.

18.

a) 0.524 km/s

b) 29.7 km/s

20.

(a) $1.35 × 10 3 rpm 1.35 × 10 3 rpm$

(b) $8.47 × 10 3 m/s 2 8.47 × 10 3 m/s 2$

(c) $8.47 × 10 –12 N 8.47 × 10 –12 N$

(d) $865 865$

21.

(a) $23.4 m/s 23.4 m/s$

(b) 39.2 m / s 2 39.2 m / s 2 alignl { stack { size 12{a \) " 16" cdot "6 " {m} slash {s} } {} # size 12{b \) " 19" cdot "6 " {m} slash {s rSup { size 8{2} } } } {} } } {}

(c)

(d) $2 . 9399 × 10 3 N or 5 . 00 w 2 . 9399 × 10 3 N or 5 . 00 w size 12{" 1" cdot "76" times "10" rSup { size 8{3} } " N or 3" cdot "00 "w} {}$ , that is, the normal force (upward) is five times her weight.

(e) This answer seems reasonable, since she feels like she's being forced into the chair MUCH stronger than just by gravity.

22.

a) $40 . 5 m / s 2 40 . 5 m / s 2$

b) 905 N

c) The force in part (b) is very large. The acceleration in part (a) is too much, about 4 g.

d) The speed of the swing is too large. At the given velocity at the bottom of the swing, there is enough kinetic energy to send the child all the way over the top, ignoring friction.

23.

a) 483 N

b) 17.4 N

c) 2.24 times her weight, 0.0807 times her weight

25.

$4.14º4.14º size 12{4 "." "14"°} {}$

27.

a) 24.6 m

b) $36.6 m/s236.6 m/s2 size 12{"36" "." 6m/s rSup { size 8{2} } } {}$

c) $ac=3.73g.ac=3.73g.$ This does not seem too large, but it is clear that bobsledders feel a lot of force on them going through sharply banked turns.

29.

b) $5.71º5.71º size 12{5 cdot "71" rSup { size 8{0} } } {}$

30.

a) 16.2 m/s

b) 0.234

32.

a) 1.84

b) A coefficient of friction this much greater than 1 is unreasonable .

c) The assumed speed is too great for the tight curve.

33.

a) $5.979×1024 kg5.979×1024 kg size 12{ {underline {5 cdot "979" times "10" rSup { size 8{"24"} } " kg"}} } {}$

b) This is identical to the best value to three significant figures.

35.

a) $1.62 m/s21.62 m/s2 size 12{1 cdot "62"" m"/s rSup { size 8{2} } } {}$

b) $3.75 m/s23.75 m/s2 size 12{1 cdot "62"" m"/s rSup { size 8{2} } } {}$

37.

a) $3.42×10–5m/s23.42×10–5m/s2 size 12{3 cdot "42" times "10" rSup { size 8{"-5"} } m/s rSup { size 8{2} } } {}$

b) $3.34×10–5m/s23.34×10–5m/s2 size 12{3 cdot "34" times "10" rSup { size 8{"-5"} } m/s rSup { size 8{2} } } {}$

The values are nearly identical. One would expect the gravitational force to be the same as the centripetal force at the core of the system.

39.

a) $7.01×10–7N7.01×10–7N size 12{7 cdot "01" times "10" rSup { size 8{"-7"} } N} {}$

b) $1.35×10–6N1.35×10–6N size 12{1 cdot "35" times "10" rSup { size 8{"-6"} } N} {}$, $0.5210.521 size 12{0 cdot "521"} {}$

41.

a) $1.66×10–10m/s21.66×10–10m/s2 size 12{1 cdot "66" times "10" rSup { size 8{"-10"} } m/s rSup { size 8{2} } } {}$

b) $2.17×105m/s2.17×105m/s size 12{2 cdot "17" times "10" rSup { size 8{"5"} } m/s} {}$

42.

a) $2.94×1017kg2.94×1017kg size 12{2 cdot "94" times "10" rSup { size 8{"17"} } kg} {}$

b) $4.92×10–84.92×10–8 size 12{4 cdot "92" times "10" rSup { size 8{"-8"} } } {}$

of the Earth's mass.

c) The mass of the mountain and its fraction of the Earth's mass are too great.

d) The gravitational force assumed to be exerted by the mountain is too great.

44.

$1.98 × 10 30 kg 1.98 × 10 30 kg size 12{1 "." "98" times "10" rSup { size 8{"30"} } "kg"} {}$

46.

$M J M E = 316 M J M E = 316 size 12{ { {M rSub { size 8{J} } } over {M rSub { size 8{E} } } } ="316"} {}$

48.

a) $7.4×103m/s7.4×103m/s size 12{2 "." "11" times "10" rSup { size 8{4} } "m/s"} {}$

b) $1.05×103m/s1.05×103m/s size 12{2 "." "98" times "10" rSup { size 8{4} } "m/s"} {}$

c) $2.86×10−7s2.86×10−7s size 12{1 "." "01" times "10" rSup { size 8{ - 7} } s} {}$

d) $1.84×107N1.84×107N size 12{1 "." "48" times "10" rSup { size 8{3} } s} {}$

e) $2.76×104J2.76×104J size 12{2 "." "22" times "10" rSup { size 8{5} } J} {}$

49.

a) $5.08×103km5.08×103km size 12{5 "." "08" times "10" rSup { size 8{3} } "km"} {}$

b) This radius is unreasonable because it is less than the radius of earth.

c) The premise of a one-hour orbit is inconsistent with the known radius of the earth.

1.

(a)

3.

(b)

5.

(b)