Edits to “Statement”, “Answer”
en/2.1.55.md
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| @@ -1,11 +1,5 @@ | |||
| ### Statement | |||
| − | $2.1.55.$ [Insert the problem statement] | ||
| − | |||
| − | ### Solution | ||
| − | |||
| − | ### Statement | ||
| − | |||
| $2.1.55.$ Two small spheres, each of mass $m$, connected by a thread of length $l$, are moving with a velocity $v$ on a horizontal table in a direction perpendicular to the connecting thread (the thread is taut). The middle of the thread hits a nail. What is the tension force of the thread immediately after this? | |||
| ### Solution | |||
|  | |||
| Since the thread is taut: | |||
| $$ | |||
| T_1 = T_2 = T | |||
| $$ | |||
| As soon as the thread hits the nail, both bodies continue to move with velocity $v$ along a new trajectory with radius $r=\\frac{l}{2}$: | |||
| $$ | |||
| T=ma_n | |||
| $$ | |||
| $$ | |||
| T=m\\frac{v^2}{\\frac{l}{2}} | |||
| $$ | |||
| We obtain the tension force of the thread immediately after this: | |||
| $$ | |||
| \\boxed{T = \\frac{2m v^2}{l}} | |||
| $$ | |||
| #### Answer | |||
| @@ -39,7 +33,3 @@Answer | |||
| $$ | |||
| T = \\frac{2m v^2}{l} | |||
| $$ | |||
| − | |||
| − | #### Answer | ||
| − | |||
| − | [Insert a concise answer or boxed result] | ||
| @@ -1,11 +1,5 @@ | |||
| ### Statement | ### Statement | ||
| $2.1.55.$ [Insert the problem statement] | |||
| ### Solution | |||
| ### Statement | |||
| $2.1.55.$ Two small spheres, each of mass $m$, connected by a thread of length $l$, are moving with a velocity $v$ on a horizontal table in a direction perpendicular to the connecting thread (the thread is taut). The middle of the thread hits a nail. What is the tension force of the thread immediately after this? | $2.1.55.$ Two small spheres, each of mass $m$, connected by a thread of length $l$, are moving with a velocity $v$ on a horizontal table in a direction perpendicular to the connecting thread (the thread is taut). The middle of the thread hits a nail. What is the tension force of the thread immediately after this? | ||
| ### Solution | ### Solution | ||
|  |  | ||
| Since the thread is taut: | Since the thread is taut: | ||
| $$ | $$ | ||
| T_1 = T_2 = T | T_1 = T_2 = T | ||
| $$ | $$ | ||
| As soon as the thread hits the nail, both bodies continue to move with velocity $v$ along a new trajectory with radius $r=\\frac{l}{2}$: | As soon as the thread hits the nail, both bodies continue to move with velocity $v$ along a new trajectory with radius $r=\\frac{l}{2}$: | ||
| $$ | $$ | ||
| T=ma_n | T=ma_n | ||
| $$ | $$ | ||
| $$ | $$ | ||
| T=m\\frac{v^2}{\\frac{l}{2}} | T=m\\frac{v^2}{\\frac{l}{2}} | ||
| $$ | $$ | ||
| We obtain the tension force of the thread immediately after this: | We obtain the tension force of the thread immediately after this: | ||
| $$ | $$ | ||
| \\boxed{T = \\frac{2m v^2}{l}} | \\boxed{T = \\frac{2m v^2}{l}} | ||
| $$ | $$ | ||
| #### Answer | #### Answer | ||
| @@ -39,7 +33,3 @@Answer | |||
| $$ | $$ | ||
| T = \\frac{2m v^2}{l} | T = \\frac{2m v^2}{l} | ||
| $$ | $$ | ||
| #### Answer | |||
| [Insert a concise answer or boxed result] | |||