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7 mm caliber | |
---|---|
«6 mm Firearm cartridges |
This article lists firearmcartridges which have a bullet in the 7.0 millimetres (0.2756 in) to 7.99 millimetres (0.3146 in) caliber range.
- Length refers to the cartridge case length.
- OAL refers to the overall length of the cartridge.
All measurements are in mm (in), and all charts are sortable by clicking on the icon beside the title of the column you wish to sort.
Pistol cartridges[edit]
Name | Bullet | Case type | Case length | Rim | Base | Shoulder | Neck | OAL |
---|---|---|---|---|---|---|---|---|
7×20mm Nambu[1] | 7.112 (.280) | rimless bottleneck | 19.81 (0.78) | 9.12 (.359) | 8.91 (.351) | 8.56 (.337) | 7.52 (.296) | 26.92 (1.06) |
7.5 FK[2] | 7.5 | rimless bottleneck | 27.0 | - | 10.8 | - | - | 35.0 |
7.62×42mm | 7.62 | - | 42.0 | - | - | - | - | - |
7.65mm Roth–Sauer[1] | 7.645 (.301) | rimless straight | 12.95 (0.51) | 8.51 (.335) | 8.51 (.335) | - | 8.43 (.332) | 21.34 (0.84) |
7.62×25mm Tokarev | 7.798 (.307) | rimless bottleneck | 24.99 (.984) | 9.96 (.392) | 9.83 (.387) | 9.47 (.373) | 8.48 (.334) | 34.29 (1.35) |
7.65×25mm Borchardt | 7.798 (.307) | rimless bottleneck | 25.15 (.990) | 9.91 (.390) | 9.78 (.385) | 9.4 (.370) | 8.41 (.331) | 34.54 (1.36) |
7.65mm Mannlicher[1] | 7.823 (.308) | rimless straight | 21.34 (0.84) | 8.48 (.334) | 8.43 (.332) | - | 8.41 (.331) | 28.45 (1.12) |
7.63×25mm Mauser | 7.823 (.308) | rimless bottleneck | 25.15 (.990) | 9.91 (.390) | 9.68 (.368) | 9.4 (.370) | 8.43 (.332) | 34.54 (1.36) |
7.65mm Longue[1] | 7.849 (.309) | rimless straight | 19.81 (0.78) | 8.56 (.337) | 8.56 (.337) | - | 8.53 (.336) | 30.23 (1.19) |
7.65×21mm Parabellum | 7.861 (.3095) | rimless bottleneck | 21.59 (.850) | 10.01 (.394) | 9.906 (.390) | 9.627 (.379) | 8.433 (.332) | 29.84 (1.175) |
.32 ACP (7.65×17mmSR Browning) | 7.938 (.3125) | semi-rimmed straight | 17.27 (.680) | 9.093 (.358) | 8.585 (.338) | N/A | 8.55 (.336) | 25.0 (.984) |
.32 NAA | 7.95 (.3125) | rimless bottleneck | 17.27 (.680) | 9.50 (.374) | 9.50 (.374) | 9.47 (.373) | 8.55 (.336) | 25.0 (.984) |
Revolver cartridges[edit]
Name | Bullet | Case type | Case length | Rim | Base | Neck | OAL |
---|---|---|---|---|---|---|---|
.30 Short[3] | 7.26 (.286) | rimmed straight | 13.08 (.515) | 8.79 (.346) | 7.42 (.292) | 7.42 (.292) | 20.88 (.822) |
7.62×38mmR (7.62mm Nagant {Rimmed})[1] | 7.82 (.308) | rimmed straight | 38.86 (1.53) | 9.855 (.388) | 8.51 (.335) | 7.26 (.286) | 38.86 (1.53) |
.32 Smith & Wesson[1] | 7.950 (.312) | rimmed straight | 15.49 (0.61) | 9.53 (.375) | 8.51 (.335) | 8.48 (.334) | 23.37 (0.92) |
.32 Short Colt (.320 Revolver)[1] | 7.950 (.313) | rimmed straight | 16.51 (.650) | 9.576 (.377) | 8.077 (.318) | 7.95 (.313) | 24.38 (.960) |
.32 Long Colt (.32 Colt) | 7.950 (.313)[1] | rimmed straight | 23.37 (0.92) | 9.500 (.374) | 8.077 (.318) | 7.95 (.313) | 32.00 (1.26) |
.32 S&W Long (.32 Colt New Police)[1] | 7.950 (.312) | rimmed straight | 23.62 (0.93) | 9.53 (.375) | 8.51 (.335) | 8.48 (.334) | 32.26 (1.27) |
.32 H&R Magnum | 7.950 (.312) | rimmed straight | 27.3 (1.075) | 9.5 (.375) | 8.6 (.337) | 8.6 (.337) | 34.30 (1.35) |
.327 Federal Magnum | 7.950 (.312) | rimmed straight | 30.00 (1.20) | 9.5 (.375) | 8.6 (.337) | 8.6 (.337) | 37.00 (1.47) |
Rifle cartridges[edit]
6.8 mm (.277 in) rifle cartridges (commonly known as .270 or 6.8 mm)[edit]
Name | Bullet | Case length | Rim | Base | Shoulder | Neck | OAL |
---|---|---|---|---|---|---|---|
.277 FURY | 7.036 (.277) | 51.18 (2.015) | TBA | ||||
.270 British | 7.04 (.277) | 46 (1.8) | 11.3 (.44) | 11.3 (.44) | - | - | 62.3 (2.45) |
.270 Weatherby Magnum[4] | 7.043 (.2773) | 64.52 (2.540) | 13.50 (.5315) | 12.997 (.5117) | 12.49 (.492) | 7.747 (.305) | 83.69 (3.295) |
.27 Nosler[4] | 7.061 (.2780) | 65.79 (2.590) | 13.56 (.534) | 13.970 (.5500) | 13.416 (.5282) | 7.976 (.3140) | 84.84 (3.340) |
.270 Winchester[4] | 7.061 (.2780) | 64.52 (2.540) | 12.01 (.473) | 11.933 (.4698) | 11.201 (.4410) | 7.82 (.308) | 84.84 (3.340) |
.270 Winchester Short Magnum[4] | 7.061 (.2780) | 53.34 (2.100) | 13.59 (.535) | 14.097 (.55 50) | 13.665 (.538) | 7.976 (.3140) | 72.64 (2.860) |
6.8mm Remington SPC[4] | 7.061 (.2780) | 42.835 (1.6864) | 10.72 (.422) | 10.686 (.4207) | 10.196 (.4014) | 7.772 (.306) | 57.40 (2.260) |
7.0 mm (.284 in) rifle cartridges (commonly known as 7mm)[edit]
Name | Bullet | Case length | Rim | Base | Shoulder | Neck | OAL |
---|---|---|---|---|---|---|---|
.276 Enfield | 7.163 (.282) | 59.69 (2.35) | 13.13 (.517) | 13.41 (.528) | 11.7 (.460) | 8.20 (.323) | 82.04 (3.23) |
.284 Winchester | 7.214 (.284) | 55.12 (2.170) | 12.01 (.473) | 12.72 (.501) | 12.06 (.475) | 8.13 (.320) | 71.12 (2.80) |
7mm BR (Bench Rest) | 7.214 (.284) | 38.61 (1.520) | 12.01 (.473) | 11.94 (.470) | 11.68 (.460) | 7.82 (.308) | - |
.280 British | 7.214 (.284) | 43.434 (1.71) | 11.633(.458) | 11.94 (.470) | 11.38 (.448) | 7.95 (.313) | 64.516 (2.54) |
.280/30 British | 7.214 (.284) | 43.434 (1.71) | 12.01 (.473) | 11.94 (.470) | 11.38 (.448) | 7.95 (.313) | 64.516 (2.54) |
7mm-08 Remington | 7.214 (.284) | 51.689 (2.035) | 12.01 (.473) | 11.94 (.470) | 11.53 (.454) | 8.00 (.315) | 71.12 (2.80) |
7mm Raptor | 7.214 (.284) | 40.0 (1.575) | 9.6 (.378) | 9.548 (.3759) | 9.103 (.3573) | - | 57.4 (2.26) |
7mm Remington SAUM (Short Action Ultra Magnum) | 7.214 (.284) | 51.69 (2.035) | 13.564 (.534) | 13.97 (.550) | 13.564 (.534) | 8.128 (.320) | 71.76 (2.825) |
7-30 Waters | 7.214 (.284) | 52 (2.04) | 12.9 (.506) | 10.7 (.422) | 10.137 (.3991)[4] | 7.8 (.306) | 64 (2.52) |
7mm WSM | 7.214 (.284) | 53.34 (2.100) | 13.59 (.535) | 14.10 (.555) | 13.67 (.538) | 8.15 (.321) | 72.64 (2.860)[4] |
7mm Remington Magnum | 7.214 (.284) | 63.50 (2.50) | 13.51 (.532) | 13.00 (.512) | 12.47 (.491) | 8.00 (.315) | 83.56 (3.290) |
7mm Dakota | 7.214 (.284) | 63.50 (2.500) | 13.84 (.545) | 13.84 (.545) | 13.49 (.531) | 8.00 (.315) | - |
.280 Remington 7mm-06 Remington 7 mm Remington Express | 7.214 (.284) | 64.52 (2.54) | 12.01 (.473) | 11.94 (.470) | 11.20 (.441) | 8.00 (.315) | 84.58 (3.33) |
7mm Weatherby Magnum | 7.214 (.284) | 65.0 (2.55) | 13.5 (.530) | 13.0 (.511) | 12.4 (.490) | 7.9 (.312) | 83.0 (3.25) |
7mm STW[5] (Shooting Times Westerner) | 7.214 (.284) | 72.39 (2.850) | 13.02 (.5126) | 13.51 (.532) | 12.36 (.4868) | 8.00 (.315) | 91.44 (3.60) |
7mm RUM (Remington Ultra Magnum) | 7.214 (.284) | 72.39 (2.85) | 13.564 (.534) | 13.97 (.550) | 13.335 (.525) | 8.179 (.322) | 92.71 (3.650) |
7x61mm Sharpe & Hart | 7.214 (.284) | 60.8 (2.394) | 13.5 (.532) | 13.08 (.515) | 12.14 (.478) | 8.12 (.320) | 83.06 (3.27) |
.276 Pedersen | 7.218 (.284) | 51.38 (2.023) | 11.43 (.450) | 11.43 (.450) | 9.78 (.385) | 7.95 (.313) | 72.39 (2.85) |
.28 Nosler[4] | 7.226 (.2845) | 65.79 (2.590) | 13.56 (.534) | 13.970 (.5500) | 13.399 (.5275) | 8.128 (.3200) | 84.84 (3.340) |
.280 Ackley Improved[4] | 7.226 (.2845) | 64.14 (2.525) | 11.99 (.472) | 11.900 (.4685) | 11.534 (.4541) | 8.001 (.3150) | 84.58 (3.330) |
7×57mm Mauser 7 mm Mauser Spanish Mauser .275 Rigby | 7.24 (.285) | 57.00 (2.244) | 12.01 (.473) | 11.99 (.472) | 10.92 (.430) | 8.23 (.324) | 77.72 (3.06) |
7×64mm[6] | 7.24 (.285) | 64.00 (2.520) | 11.95 (.470) | 11.85 (.467) | 10.80 (.425) | 7.95 (.313) | 84.00 (3.307) |
7 × 33 Sako[7] | 7.26 (.286) | 33.33 (1.312) | 10.00 (.394) | 9.93 (.391) | 9.52 (.375) | 7.95 (.313) tapering to 7.90 (.311) | 44.44 (1.750) |
.280 Ross[8] .280 Rimless .280 Nitro | 7.29 (.287) | 65.79 (2.59) | 14.12 (.556) | 13.56 (.534) | 10.26 (.404) | 8.05 (.317) | 88.9 (3.50) |
7.8 mm (.308 in) rifle cartridges (commonly known as .308, 30 caliber, 7.62 mm)[edit]
Name | Bullet | Case length | Rim | Base | Shoulder | Neck | OAL |
---|---|---|---|---|---|---|---|
7.35×51mm Carcano | 7.57 (.298) | 51.50 (2.028) | 11.40 (0.449) | 11.40 (0.449) | 10.85 (0.427) | 8.32 (0.328) | 73.70 (2.902) |
7.5×55mm Swiss | 7.77 (.306) | 55.499 (2.185) | 12.598 (.496) | 12.548 (.494) | 11.481 (.452) | 8.484 (.334) | 77.47 (3.05) |
.30 Carbine | 7.798 (.307) | 32.77 (1.290) | 9.14 (.360) | 8.99 (.354) | N/A | 8.41 (.331) | 41.91 (1.65) |
.30 Pedersen | 7.82 (.308) | 19.76 (.778) | 8.48 (.334) | 8.48 (.334) | N/A | 8.43 (.332) | 30.38 (1.196) |
7.62×40mm Wilson Tactical | 7.82 (.308) | 39.8 (1.565) | 9.6 (.378) | 9.6 (.377) | - | - | 57.15 (2.25) |
7.62×51mm NATO | 7.82 (.308) | 51.05 (2.01) | 11.94 (.470) | 11.84 (.466) | 11.35 (.447) | 8.58 (.338) | 69.85 (2.75) |
.308 Winchester | 7.82 (.308) | 51.18 (2.015) | 11.94 (.470) | 11.94 (.470) | 11.53 (.454) | 8.74 (.344) | 69.85 (2.75) |
.300 RSAUM | 7.82 (.308) | 51.181 (2.015) | 13.564 (.534) | 13.97 (.550) | 13.564 (.534) | 8.74 (.344) | 71.8 (2.825) |
7.5×54mm French[9] | 7.82 (.308) | 53.59 (2.11) | 12.24 (.482) | 12.19 (.480) | 11.2 (.441) | 8.64 (.340) | 75.95 (2.99) |
.30-40 Krag | 7.82 (.308) | 58.674 (2.31) | 13.84 (.545) | 11.608 (.457) | 10.541 (.415) | 8.585 (.338) | 78.74 (3.10) |
.300 Winchester Magnum | 7.82 (.308) | 66.55 (2.62) | 13.51 (.532) | 13.03 (.513) | 12.42 (.489) | 8.61 (.339) | 84.84 (3.34) |
.300 Weatherby Magnum[10] | 7.82 (.308) | 71.75 (2.825) | 13.49 (.531) | 13 (.512) | 12.5 (.492) | 8.53 (.336) | 90.47 (3.562) |
.300 H&H Magnum | 7.82 (.308) | 72.4 (2.850) | 13.5 (.532) | 13.0 (.513) | 11.4 (.450) | 8.6 (.338) | 91.40 (3.600) |
.300 RUM | 7.82 (.308) | 72.39 (2.850) | 13.564 (.534) | 13.97 (.550) | 13.335 (.525) | 8.74 (.344) | 90.30 (3.555) |
.30-378 Weatherby Magnum[11] | 7.82 (.308) | 73.99 (2.913) | 14.71 (.579) | 14.78 (.582) | 14.25 (.561) | 8.56 (.337) | 93.73 (3.690) |
.300 Savage | 7.82 (.308) | 47.5 (1.871) | 12.01 (.473) | 11.96 (.471) | 11.3 (.446) | 8.6 (.339) | 66.04 (2.60) |
.303 Savage | 7.82 (.308) | 51.2 (2.015) | 12.8 (.505) | 11.2 (.442) | 10.5 (.413) | 8.5 (.333) | 64.01 (2.520) |
.30 Remington | 7.82 (.308) | 52.3 (2.06) | 10.7 (.422) | 10.7 (.421) | 64.14 (2.525) | ||
.308 Norma Magnum | 7.82 (.308) | 65.0 (2.56) | 13.5 (.531) | 13.0 (.513) | 12.4 (.489) | 8.6 (.340) | 83.82 (3.30) |
.300 Lapua Magnum | 7.82 (.308) | 69.73 (2.745) | 14.93 (.588) | 14.91 (.587) | 13.82 (.544) | 8.73 (.344) | 94.50 (3.72) |
30 BR[12] | 7.82 (.308) | 38.41 (1.512) | 12.01 (.473) | 11.94 (.470) | 11.66 (.459) | 8.33 (.328) | 58.00 (2.283) |
.300 WSM (Winchester Short Magnum) | 7.823 (.308) | 53.34 (2.100) | 13.59 (.535) | 14.10 (.555) | 13.665 (.538) | 8.74 (.344) | 72.64 (2.860) |
.30 Newton | 7.823 (.308) | 64 (2.52) | 13.3 (.525) | 13.3 (.523) | 12.5 (.491) | 8.6 (.340) | 85 (3.35) |
300 Precision Rifle Cartridge[13] | 7.833 (.3084) | 65.53 (2.580) | 13.51 (.532) | 13.513 (.5320) | 13.080 (.5150) | 8.66 (.341) | 93.98 (3.700) |
.30-06 Springfield | 7.835 (.3085) | 63.35 (2.494) | 12.01 (.473) | 11.94 (.470) | 11.07 (.436) | 8.628 (.3397) | 84.84 (3.340) |
.30-03 | 7.835 (.3085) | 64.52 (2.54) | 12.01 (.473) | 11.94 (.470) | 11.2 (.441) | 8.64 (.340) | 84.84 (3.340) |
300 AAC Blackout[4] | 7.849 (.3090) | 34.75 (1.368) | 9.60 (.378) | 9.548 (.3759) | 9.161 (.3607) | 8.484 (.3340) | 57.40 (2.260) |
300 Ruger Compact Magnum[4] | 7.849 (.3090) | 53.34 (2.100) | 13.51 (.532) | 13.513 (.5320) | 13.081 (.5150) | 8.636 (.3400) | 72.14 (2.840) |
.30-30 Winchester | 7.849 (.309) | 51.79 (2.039) | 12.85 (.506) | 10.72 (.422) | 10.18 (.401) | 8.46 (.333) | 64.77 (2.550) |
30 Remington AR[4] | 7.849 (.3090) | 38.86 (1.530) | 12.50 (.492) | 12.700 (.5000) | 12.407 (.4885) | 8.687 (.3420) tapering to 8.661 (.3410) | 57.40 (2.260) |
.307 Winchester[4] | 7.849 (.3090) | 51.18 (2.015) | 12.85 (.506) | 11.946 (.4703) | 11.532 (.4540) | 8.725 (.3435) | 56.02 (2.550) |
300 HAM'R[14] | 7.849 (.309) | 40.72 (1.603) | 9.60 (.378) | 9.548 (.3759) | 9.261 (.3646) | 8.43 (.332) | 57.40 (2.260) |
7.62×45mm | 7.85 (.309) | 44.9 (1.768) | 11.18 (.440) | 11.20 (.441) | 10.46 (.412) | 8.48 (.334) | 60.00 (2.560) |
7,62 × 53 R[15] | 7.85 (.309) | 53.50 (2.106) | 14.40 (.567) | 12.42 (.489) | 11.61 (.457) | 8.55 (.337) tapering to 8.50 (.335) | 77.00 (3.031) |
7.87 mm (.310 in) and greater rifle cartridges[edit]
Name | Bullet | Case length | Rim | Base | Shoulder | Neck | OAL |
---|---|---|---|---|---|---|---|
7.62×39mm M43 | 7.899 (.311) | 38.65 (1.522) | 11.30 (.445) | 11.25 (.443) | 10.01 (.394) | 8.636 (.340) | 55.80 (2.197) |
7,62 × 54 R[16] | 7.92 (.31) | 53.72 (2.115) | 14.48 (.570) | 12.37 (0.487) | 11.61 (.452) | 8.53 (.335) | 77.16 (3.038) |
.303 British | 7.925 (.312) | 55.88 (2.2) | 13.46 (.530) | 11.61 (.457) | 10.19 (.401) | 8.53 (.336) | 76.48 (3.011) |
.32-20 Winchester .32-20 WCF | 7.937 (.3125) | 33.401 (1.315) | 10.287 (.405) | 8.966 (.353) | 8.687 (.342) | 8.280 (.326) | 40.386 (1.59) |
7.65×53mm Argentine | 7.95 (.313) | 53.188 (2.094) | 11.938 (.470) | 11.887 (.468) | 10.897 (.429) | 8.585 (.338) | 75.387 (2.968) |
7.7×58mm Arisaka | 7.95 (.313) | 57.15 (2.25) | 11.94 (.470) | 11.89 (.468) | 10.9 (.429) | 8.59 (.338) | 74.93 (2.95) |
See also[edit]
References[edit]
- ^ abcdefghiBarnes, Frank C., ed. Amber, John T., Cartridges Of The World (3rd Edition), (DBI, 1978), ISBN0-695-80326-3
- ^'The Cartridge'. fkbrno.com. Archived from the original on February 20, 2020. Retrieved February 13, 2019.
- ^Barnes, Frank C. (1993). Bussard, Mike (ed.). Cartridges of the world (7th rev. and expanded ed.). Northbrook, IL: DBI Books. p. 382. ISBN0-87349-145-9. OCLC29683953.
- ^ abcdefghijklmSAAMI: Voluntary Industry Performance Standards for Pressure and Velocity of Centerfire Rifle Ammunition for the Use of Commercial Manufacturers
- ^'7mm Shooting Times Westerner' data from Accurate Powder
- ^Barnes, Frank C. (1997) [1965]. McPherson, M.L. (ed.). Cartridges of the World (8th ed.). DBI Books. pp. 355, 374. ISBN0-87349-178-5.
- ^'7 × 33 Sako'(PDF). C.I.P. May 15, 2002. Retrieved October 8, 2020.
- ^Barnes, Frank C. (2006) [1965]. Skinner, Stan (ed.). Cartridges of the World (11th ed.). Iola, WI, USA: Gun Digest Books. pp. 384, 408. ISBN0-89689-297-2.
- ^Barnes, Frank C. (2006) [1965]. Skinner, Stan (ed.). Cartridges of the World (11th ed.). Iola, WI, USA: Gun Digest Books. pp. 353, 375. ISBN0-89689-297-2.
- ^.300 Weatherby Magnum at Accurate PowderArchived August 27, 2010, at the Wayback Machine
- ^Cartridge Dimensions at Steve's Pages
- ^'30 BR'(PDF). C.I.P. May 25, 2011. Retrieved October 8, 2020.
- ^'300 Precision Rifle Cartridge [300 PRC]'(PDF). SAAMI. June 13, 2018. Retrieved October 13, 2020.
- ^'300 HAM'R [300 HAMR]'(PDF). SAAMI. January 20, 2020. Retrieved October 13, 2020.
- ^C.I.P.: 7,62 × 53 R
- ^C.I.P.: 7,62 × 54 R
External links[edit]
- 7mm Cartridge Guide from AccurateShooter.com
Retrieved from 'https://en.wikipedia.org/w/index.php?title=7_mm_caliber&oldid=983347288'
Homework
Ch 3, Vectors
Ch 3; 2, 20, 37, 44, 50, 51, 57, 61
Questions 3, 5, 6, 7, 8
Additional problems from Serway's fourth edition
(4 ed) 3.1 A point is located in a polar coordinate systemby the coordinates r = 2.50 m and = 35.0o .
Find the cartesian coordinates of this point, assuming the twocoordinate systems have the same origin.
Conceptual Questions
Q3.3 The magnitudes of two vectors A and B are A = 5units and B = 2 units. Find the largest and smallest valuespossible for the resultant vector R = A + B.
If vectors A and B point in the samedirection, the magnitude of R is 7 units.
If vectors A and B point in the oppositedirection, the magnitude of R is 3 units.
Q3.5 If the component of vector A along the direction of vectorB is zero, what can you conclude about these two vectors.
The two vectors areperpendicular (it can also besaid they are orthogonal).
Q3.6 Can the magnitude of a vector have a negativevalue?
No, a magnitude is always positive or zero.
Q3.7 Which of the following are vectors and which arenot:
force --> vector
temperature -->scalar
volume -->scalar
rating of a television show -->scalar
height --> vector(a well would have a negative height)
velocity -->vector
age --> scalar
Q3.8 Under what circumstances would a nonzero vector lying inthe xy plane ever have components that are equal inmagnitude?
If the vector lies along the 45o line in the first orthird quadrants the two components will be exactly equal. If thevector lies along the 45o line in the second or fourthquadrants the two components will be equal in magnitude.
Problems from the current (5th) edition of Serway and Beichner.
3.2 Two points in the xy plane have cartesian coordinates(2.00, - 4.00) m and ( - 3.00, 3.00) m.
Determine
(a) the distance between these points and
We can find the distance between the two points from the Pythagorean Theorem, distance = d = SQRT [ (x)2 + (y)2 ] d = SQRT [ ( - 3.00 - 2.00 )2 + ( 3.00 - ( - 4.00) )2 ] m
d = SQRT [ ( - 5 ) 2 + ( 7.00) 2 ] m
d = SQRT [ 25.00 + 49.00 ] m
d = SQRT [ 74.00 ] m
d = 8.60 m
(b) their polar coordinates
P1 = (2.00, - 4.00) m
P1's distance from the origin, or its radius r1, is
r1 = SQRT [ (2.00)2 + ( - 4.00 )2 ] m = SQRT [ 4 + 16 ] m = SQRT [ 20 ] m r1 = 4.47 m
tan [1 ] = opp/adj = y1 / x1 = ( - 4) / 2 = - 2
1 = - 63.4o
The cartesian coordinates (r, ) for point P1, are
P1 = (4.47 m, - 63.4o)
Now, the same thing for point P2,
P2 = (- 3.00, 3.00) m
P2's distance from the origin, or its radius r2, is
r2 = SQRT [ ( - 3.00)2 + ( 3.00 )2 ] m = SQRT [ 9 + 9 ] m = SQRT [ 18 ] m r2 = 4.24 m
tan [2 ] = opp/adj = y2 / x2 = 3 / ( - 3) = - 1
2 = 135o
The cartesian coordinates (r, ) for point P2, are
P2 = (4.24 m, 135o)
NOTE! Always use caution with the inverse tangent function (and all other inverse trig functions). When you tell your calculator that you want the inverse tangent of ( - 1) it will probably tell you the angle is - 45o. An angle of - 45o does, indeed, have a tangent of - 1. A point located at ( + 3, - 3) is located at an angle of - 45o (measured from the + x-axis). But our point, P2, is located at ( - 3, + 3). So, from a diagram, we conclude that it is located at an angle of 135o.
3.20 Find the horizontal and vertical components of the 100-mdisplacement of a superhero who flies from the top of a tall buildingfollowing the path shown in Figure P3.19 .x = r cos = (100 m) cos 30o = (100 m) ( 0.866) x = 86.6 m
y = r sin = - (100 m) sin 30o = - (100 m) (0.500)
y = - 50.0 m
( x, y ) = (86.6 m, - 50.0 m)
3.37 The helicopter view in Figure P3.37 shows two peoplepulling on a stubborn mule.Find
(a) the single force that is equivalent to the two forcesshown, and
(b) the force that a third person would have to exert onthe mule to make the resultant force equal to zero.
We want the resultant R,After a good diagram most vector addition problems begin with finding the components of the vectors.
F1x = F1 cos 60o = (120 N) ( 0.50) = 60 N F1y = F1 sin 60o = (120 N) ( 0.866) = 104 N
F1 = 60 N i + 104 N j
F2x = - F2 cos 75o = - (80 N) ( 0.260) = - 20.8 N
F2y = F2 sin 75o = (80 N) ( 0.966) = 77.3 N
F2 = - 20.8 N i + 77.3 N j
R = F1 + F2
R = (60 N i + 104 N j) + (20.8 N i + 77.3 N j)
R = ( 60 - 20.8 ) N i+ ( 104 + 77.3 ) N j
R = 39.2 N i + 181.3 N j
As before, we now need to find the magnitude of the resultant and its direction,
R = SQRT [ 39.22 + 181.32 ] NR = SQRT [ Rx2 + Ry2 ]
R = 186.5 N Acon digital acoustica 7 1 8.
Notice from the diagram that we are now measuring the angle from the positive x-axis; therefore,
tan = opp/adj = Ry / Rx = 181.3 / 39.2 = 4.65
Go 75 paces at 240o,
turn to 135o and walk 125 paces,
then travel 100 paces at 160o.
Determine the resultant displacement from the starting point.
Each piece of these directions is a displacement vectorA: Go 75 paces at 240oAx = A cos = (75 paces) cos 240o = (75 paces) ( - 0.5) = - 37.5 paces Ay = A sin = (75 paces) sin 240o = (75 paces) ( - 0.866) = - 64.95 paces
That is,
A = - 37.5 i - 64.95 j
B: turn to 135o and walk 125 paces
Bx = B cos = (125 paces) cos 135o = (125 paces) ( - 0.707) = - 88.39 paces By = B sin = (125 paces) sin 135o = (125 paces) (0.707) = 88.39 paces
That is,
B = - 88.39 i + 88.39 j
C: travel 100 paces at 160o
Cx = C cos = (100 paces) cos 160o = (100 paces) ( - 0.940) = - 93.97 paces Cy = C sin = (100 paces) sin 160o = (100 paces) (0.342) = 34.20 paces
That is,
C = - 93.97 i + 34.2 j
Now we add these displacement vectors to find the resultant, R
R = A + B + C
Remember, tho', that vector notation or vector addition is really elegant shorthand for the two scalar equations
Rx = Ax + Bx + Cx
and
Ry = Ay + By + Cy
Using numerical values for these, we have
Rx = Ax + Bx + CxRx = ( - 37.50 - 88.39 - 93.97 ) paces
Rx = - 219.86 paces
and
Ry = Ay + By + CyRy = ( - 64.95 + 88.39 + 34.20 ) paces
Ry = 57.64 paces
So we expect the buried treasure to be located at
(X, Y) = (Rx, Ry) = ( - 219.86, 57.64 ) paces
Or, we can find this displacement in polar coordinates,
R = SQRT [ X2 + Y2] = SQRT [ ( - 219.86 )2 + (57.64)2 ] paces R = 227.29 paces
tan = opp / adj = Y / X = 57 / ( - 220) = - 0.26
= 165.5o
So we can state this resultant as
R = ( R, ) = (227.3 paces, 165.5o )3.50 An airplane starting from airport A flies 300 km east,then 350 km 30.0o west of north, and then 150 km north toarrive at airport B. There is no wind on this day.
(a) The next day, another plane flies directly from A to Bin a straight line. In what direction should the pilot travel in thisdirect flight?
(b) How far will the pilot travel in this directflight?
We can describe each leg of this airplane's path as a vector: The airplane flies 300 km east then 350 km 30.0o west of north
and then 150 km north
Now we can add those vectors to find the resultant R,
Install4j 7 0 11 Mod
To carry out this vector addition, we can write vectors A, B, and C in component form. Remember, this time we are given, and will find, angles measured from North (or y). Be careful as you use the trig functions.
A![7-0 7-0](https://i.stack.imgur.com/X0tIi.png)
B = - (350 km) sin 30o i + (350 km) cos 30o j
B = - (350 km) (0.500) i + (350 km) (0.866) j Easy video converter pro 2 1 – video converter mp4.
B = - 175 km i + 303 km j
C = 0 i + 150 km j
R = A + B + C
R = (300 km i + 0 j) + ( - 175 km i + 303 km j) + (0 i + 150 km j)
R = (300 - 175 + 0 ) km i + ( 0 + 303 + 150 ) km j
R = 125 km i + 453 km j
Now we want to write this resultant in polar coordinates, finding its length and its direction.
R = SQRT [ Rx2 + Ry2 ] R = SQRT [ 1252 + 4532 ] km
R = 470 km
tan = opp/adj = Rx / Ry = 125 / 453 = 0.276
= 15o
R = ( 470 km, 15o )
3.51 Three vectors are oriented as shown in Figure P3.51,where |A| = A = 20.0 units, |B| = B = 40.0 units, and|C| = c = 30.0 units.
Find (a) the x and y components of the resultant vector (expressedin unit-vector notation) and (b) the magnitude and direction of theresultant vector (ie, in polar coordinates)
First, resolve the three vectors into their x- andy-components.
Bx = B cos 45o Bx = (40)(0.707) Bx = 28.28 Cx = C cos 45o Cx = (30)(0.707) Cx = 21.21 Rx = 0 + 28.28 + 21.21 Rx = 49.49 | By = B sin 45o By = (40)(0.707) By = 28.28 Cy = - C sin 45o Cy = - (30)(0.707) Cy = - 21.21 Ry = 20.0 + 28.28 - 21.21 Ry = 27.07 |
R = SQRT [ Rx2 +Ry2 ]
R = SQRT [ (49.49)2 + (27.07)2 ]
R = 56.4
tan =opp/adj= Ry/Rx
tan =27.07/49.49 = 0.547
=28.7o
3.57 A person going for a walk follows the path shown inFigure P3.57. The total trip consists of four straight-line paths. Atthe end of the walk, what is the person's resultant displacementmeasured from the starting point?[Remember: 'Displacement' is a vector so theanswer is a magnitude and a direction. ]
We may as well label the vectors D11,D2, D3, andD4:
D3x = - (150 m) cos 30o D3x = - (150 m) (0.866) D3x = - 130 m | D3y = - (150 m) sin 30o D3x = - (150 m) (0.500) D3x = - 75 m | |
D4x = - (200 m) cos 60o D4x = - (200 m) (0.500) D4x = - 100 m | D4y = - (200 m) sin 60o D4y = - (200 m) (0.866) D4y = - 173.2 m | |
Rx = - 130 m | Ry = - 201.8 |
R = SQRT [ Rx2 +Ry2 ]
R = SQRT [ (130)2 + (201.8)2 ] m
R = 240 m
R = 240 m
tan =Ry/Rx = - 201.8 /(- 130) = 1.55
According to my calculator, this means
Is that correct?
That depends. Be careful here! The angle (or direction) is,indeed, 57.2oas indicated in the diagram.Normally, tho', we would consider angles counterclockwise aspositive, so we would write this as
Never blindly write down an answer. Always be sureyou understand what it means. This is very important!
3.61 A rectangular parallelepiped has dimensions a, b, andc, as in Figure P3.61.
(a) Obtain a vecor expression for the face diagonalR1. What is the magnitude of this vector?
(b) Obtain a vector expression for the body diagonal vectorR2.
Note that R1, c k, andR2 make a right triangle, and prove that themagnitude of R2 is SQRT( a2 +b2 + c2 ).
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R1 is the hypotenuse of a right triangle in thexy plane -- or the diagonal of the rectangle in the xy plane. Thesides are a (along x) and b (along y). Therefore,
Adp 7-0
R2 is the hypotenuse of a right triangle in theplane containing R1 and c k (or the z-axis)-- or the diagonal of the rectangle in that plane. The sides areR1 (along R1) and c (along the z-axis).Therefore,
Solutions to the additional problems from Serway's fourth edition
(4 ed) 3.2 A point is located in a polar coordinate system bythe coordinates r = 2.50 m and = 35.0o .Find the cartesian coordinates of this point, assuming the twocoordinate systems have the same origin.
x = r cos = (2.50 m) cos 35o = (2.50 m) ( 0.819) x = 2.05 m
y = r sin = (2.50 m) sin 35o = (2.50 m) (0.574)
y = 1.43 m
( x, y ) = (2.05 m, 1.43 m)