最美情侣中文字幕电影,在线麻豆精品传媒,在线网站高清黄,久久黄色视频

歡迎光臨散文網(wǎng) 會員登陸 & 注冊

[Relativity] Relativistic Energy-Momentum Relation

2021-09-11 15:37 作者:AoiSTZ23  | 我要投稿

By: Tao Steven Zheng (鄭濤)


【Problem】

Begin with the relativistic momentum and energy:

p%3D%20%5Cfrac%7Bmv%7D%7B%5Csqrt%7B1-%5Cfrac%7Bv%5E2%7D%7Bc%5E2%7D%7D%7D

E%3D%5Cfrac%7Bmc%5E2%7D%7B%5Csqrt%7B1-%5Cfrac%7Bv%5E2%7D%7Bc%5E2%7D%7D%7D

Derive the relativistic energy-momentum relation:

E%5E2%3D(pc)%5E2%2B(mc%5E2)%5E2


【Solution】


With a little algebra we discover that

%5Cfrac%7Bp%7D%7BE%7D%3D%5Cfrac%7Bv%7D%7Bc%5E2%7D

Square the equation for relativistic energy

E%5E2%3D%5Cfrac%7B(mc%5E2)%5E2%7D%7B1-%5Cfrac%7Bv%5E2%7D%7Bc%5E2%7D%7D

And rearrange to arrive at

E%5E2-%5Cfrac%7BE%5E2%20v%5E2%7D%7Bc%5E2%7D%20%3D(mc%5E2)%5E2

E%5E2%3D%5Cfrac%7BE%5E2%20v%5E2%7D%7Bc%5E2%7D%20%2B(mc%5E2%20)%5E2%20

From the relation

%5Cfrac%7Bp%7D%7BE%7D%3D%5Cfrac%7Bv%7D%7Bc%5E2%7D

we find

%5Cfrac%7Bp%7D%7BE%7D%3D%5Cfrac%7Bv%7D%7Bc%5E2%7D

and

(pc)%5E2%3D%5Cfrac%7BE%5E2%20v%5E2%7D%7Bc%5E2%7D

Substitute this result into

E%5E2%3D%5Cfrac%7BE%5E2%20v%5E2%7D%7Bc%5E2%7D%20%2B(mc%5E2)%5E2

to get

E%5E2%3D(pc)%5E2%2B(mc%5E2)%5E2


Note: When the momentum of an object is zero, the expression reduces to Einstien's famous mass-energy equivalence principle E%3Dmc%5E2.



[Relativity] Relativistic Energy-Momentum Relation的評論 (共 條)

分享到微博請遵守國家法律
和硕县| 西和县| 凤山市| 水城县| 晋江市| 会东县| 平昌县| 沅江市| 获嘉县| 淅川县| 台州市| 乌拉特后旗| 丹巴县| 丰顺县| 高青县| 达拉特旗| 长葛市| 赣榆县| 灵丘县| 云林县| 天全县| 高雄县| 青浦区| 隆德县| 张家界市| 新沂市| 华安县| 个旧市| 怀仁县| 常州市| 吴川市| 全州县| 红河县| 正宁县| 丹江口市| 阿尔山市| 张掖市| 额济纳旗| 诸暨市| 清新县| 尉氏县|