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{سفید بنویس} - کار نیرو انرژی
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کار نیرو انرژی
هفتم خرداد 90 ساعت 13:20 | نوشته ‌شده به دست سرباز گمنام | ( نظرات )

به نام خداوند جهان آفرین

موضوع تحقیق:

کار نیرو انرژی

تهیه کننده:

محمد زارع

درس:

علوم تئوری (تجربی سابق)

آذر89

كار و انرژی

1-كار چیست؟

كار یك كمیت نرده ای است و به صورت حاصلضرب نیرو در جابجایی تعریف میشودw = f.d cos α        

2-یكای كار چیست؟

یكای كار نیوتن.متر(N.M)     یا همان ژول است كه با نماد j  نشان داده میشود

3-اگر بر یك جسم چند نیرو اعمال شود و چند كار انجام شود كار كل انجام شده بر جسم را چگونه محاسبه میكنند؟

دو روش برای محاسبه كار برایند وجود دارد:

روش اول:  میتوان برایند تمامی نیروهای وارد بر جسم را محاسبه كرد  و سپس كار نیروی برایند را بدست اورد  wt = ft.d.cosα    

روش دوم:   چون كار یك كمیت نرده ای است كار برایند(كل ) را میتوان از حاصلجمع جبری تمامی كارهای انجام شده بر جسم محاسبه كرد

Wt = w1+w2+w3 + ….

4-ایا همواره مقدار كار مثبت است؟

خیر  - هر گاه نیروی اعمال شده در جهت جابجایی باشد یعنی 90  0 <α< باشدانگاه كسینوس الفا مثبت بوده و كار مثبت بدست می اید

  5-در چه صورتی كار منفی محاسبه میشود؟

اگر بین بردار جابجایی و نیرو زاویه ایجاد شده مابین 90 تا 180 درجه باشد انگاه كسینوس الفا منفی شده و كار نیز منفی بدست می آید.

6-در چه حالتی كار صفر است؟

در سه حالت كار صفر میشود:

اول: اگر نیرو و جابجایی بر هم عمود باشند  زاویه بین انها 90 درجه شده و مقدار كار بر اساس فرمول صفر خواهد شد

دوم:  در صورتی كه جسم تحت تاثیر نیرو جابجا نشود مقدار d=0    خواهد بود و طبق فرمول كار صفر میشود

سوم:  در صورتی كه به جسم نیرویی وارد نشود( یا جسم با سرعت ثابت حركت كند) f=0     خواهد بود و كار طبق فرمول صفر خواهد شد.

7-چه زمانی مقدار كار بیشینه(بیشترین مقدارممكنه) خواهد شد؟

اگر بردارهای نیرو و جابجایی همجهت باشند یعنی زاویه میان انها صفر شود مقدار كار بیشینه مثبت خواهد شد       w=fdcos 0 = + fd

اگر بردارهای جابجایی و نیرو دقیقا مخالف جهت یكدیگر باشند زاویه میان انها 180  درجه شده و مقدار كار بیشینه منفی  خواهد شدw=fdcos180 = -fd

8-در چه حالتی مقدار كار كمینه(كمترین مقدار ممكنه) خواهد شد؟

اگر دو بردار نیرو و جابجایی بر هم عمود باشند زاویه میان انها 90 درجه خواهد شد و چون كسینوس 90 درجه  صفر است در نتیجه مقدار كار نیز  صفر میشود

W=fdcos90 = 0

9-قضیه كار و انرژی را تعریف كنید؟

قضیه كار و انرژی رابطه بین كار و تغییرات انرژی جنبشی را بیان میكند بر طبق این قضیه كار برایند نیروی وارد بر یك جسم در یك جابجایی برابر است با تغییر انرژی جنبشی جسم در آن جابجایی    یعنی:       Δk = w              k2k1 = f.d.cosα

10-بر اساس قضیه كار و انرژی در چه حالتی انرژی جنبشی جسم تغییر نمیكند؟

اگر كار برایند نیروها صفر باشد انگاه تغییرات انرژی جنبشی نیز صفر خواهد بود و بدین معناست كه انرژی جنبشی جسم تغییر نكرده است

k2  =  k1               Δk = w =0                  k2k1 = 0

11-كار نیروی وزن را در بالا بردن جسمی به جرم m  تا ارتفاع h  محاسبه كنید ؟

W= f.d.cosα                    wmg  = mg . h. cos 180    =    -mgh   

چون f=mg  و  d=h    و  α=180    زیرا  وزن به سمت پایین است ولی جهت حركت یا همان جابجایی جسم به سمت بالا میباشد.

12-كار نیروی وزن را در سقوط جسمی به جرم m  از ارتفاع h بدست اورید؟

چون f=mg  و  d=h    و  α=0    زیرا  وزن به سمت پایین است و جهت حركت یا همان جابجایی جسم نیز به سمت پایین میباشد.:

W=f.d.cosα          wmg = mg.h.cos 0  = + mgh

13-انرژی پتانسیل گرانشی را بر اساس مفهوم كار تعریف كنید؟

انرژی پتانسیل گرانشی یك جسم در یك نقطه نسبت به زمین برابر است با كاری كه انجام میدهیم تا جسم را با سرعت ثابت از سطح زمین تا نقطه یاد شده منتقل كنیم

14-انرژی پتانسیل كشسانی فنر را بر اساس مفهوم كار تعریف كنید؟

كاری كه با سرعت ثابت برای كشیدن یا فشرده كردن فنر انجام میدهیم به صورت انرژی پتانسیل كشسانی در فنر ذخیره میشود.

15-آیا نیروی كشسانی فنر در تمامی حالات یكسان است؟

خیر – نیروی كشسانی فنر متغیر است و به مقدار فشردگی یا كشیدگی فنر وابسته است هر چه فنر بیشتر كشیده یا فشرده شود (تغییرات طول فنر بیشتر باشد) نیروی فنر نیز بیشتر خواهد شد

در حالتی كه فنر در وضعیت عادی(تعادل) قرار دارد نیروی فنر صفر میباشد

16- نیروی كشسانی فنر چیست؟

نیروی كشسانی فنر یا همان نیروی بازگرداننده فنر  باعث میشود كه فنر كشیده شده یا فشرده شده به وضعیت  تعادل خود بازگردد. جهت این نیرو همواره به سمت نقطه تعادل فنر است( نقطه تعادل فنر نقطه ای است كه فنر در ان  كشیده یا فشرده نشده باشد).

17-نشان دهید كه هر چه فنر بیشتر كشیده یا فشرده شود انرژی پتانسیل آن نیز نسبت به وضعیت ازاد(تعادلی) فنر بیشتر است؟

هر چه گشیدگی یا فشردگی فنر بیشتر باشد یعنی جابجاییd انجام شده بیشتر میشودو همچنین نیروی بازگرداننده فنر نیز بیشتر میشود f=k .Δx    و در نتیجه كار انجام شده نیز افزایش میابد و چون طبق تعریف این كار همان انرژی پتانسیل ذخیره شده در فنر است پس انرژی پتانسیل فنر نیز بیشتر میشود.

18-آیا دوبار همنام كه در فاصله مشخصی از هم نگهداشته شده اند دارای انرژی پتانسیل هستند؟  چرا؟

بله- زیرا اگر رها شوند از هم دور خواهند شد پس كاری كه با سرعت ثابت برای نزدیك كردن دو بار و یا دور كردن انها انجام میشود به صورت انرژی پتانسیل الكتریكی در دو بار ذخیره خواهد شد

19- نشان دهید  هر اندازه دو بار همنام به یكدیگر نزدیكتر باشند انرژی پتانسیل الكتریكی انها بیشتر است؟

گفتیم كه كار انجام شده برای نزدیك كردن دو بار همنام به صورت انرژی پتانسیل الكتریكی در انها ذخیره میشود حال هر چه بار ها را بیشتر به هم نزدیك كنیم نیروی دافعه میان انها بیشتر شده و میزان جابجایی انجام شده نیز بیشتر میشود یعنی كار  بیشتر و انرژی پتانسیل الكتریكی نیز به همان نسبت بیشتر خواهد شد.

20-قضیه كار و انرژی را اثبات كنید؟

W= f.d.cos0 =m.a.d =m((v2-v12)/2d ).d       

w= ( mv22 /2 )    -   (mv12/2  )  = k2k1                         w=Δk

21-نشان دهید هر چه دو بار ناهمنام نسبت به هم دورتر باشندانرژی پتانسیل الكتریكی انها بیشتر است؟

انرژی پتانسیل الكتریكی همان كار انجام شده برای دور كردن دو بار ناهمنام است پس:   پس اگر این دو بار را از هم دور كنیم در حقیقت جابجایی را افزایش داده ایم و كار افزایش میابد و به همان نسبت انرژی پتانسیل الكتریكی زیاد میشود.

22-انرژی مكانیكی چیست؟

مجموع انرژی جنبشی و انرژی پتانسیل (از هر نوعی) رادر یك زمان مشخص  و برای یك جسم اانرژی مكانیكی مینامیم و انرا با نماد E      نشان میدهیم

E=K+U

نكته:  انرژی پتانسیل میتواند از نوع پتانسیل الكتریكی  یا   پتانسیل گرانشی و یا پتانسیل كشسانی  و غیره  و یا تركیبی از چند نوع باشد بسته به شرایطی كه جسم در ان قرار دارد.

23-پایستگی انرژی مكانیكی را تعریف كنید؟

در صورت نداشتن نیروهای هدر برنده(مانند اصطكاك، مقاومت هوا و غیره)  همواره انرژی مكانیكی جسم مقداری ثابت است یعنی:

E1 = E2

K1+U1 = K2 +U2

24-در چه صورتی انرژی مكانیكی پایسته  نیست؟

در صورتی كه نیروهای هدر برتده (مانند اصطكاك و مقاومت هوا و ...) داشته باشیم مقداری از  انرژی مكانیكی هدر میرود و انرژی مكانیكی دیگر پایسته نیست در این حالت باید فرمول پایستگی را به صورت زیر بنویسیم :

در صورت وجود نیروهای هدر برنده انرژی  :

E1E2

 (مقدار ا نرژی هدر رفته )+  E1E2 

25- با استفاده از پایستگی انرژی مكانیكی ثابت كنید كه تغییرات انرژی جنبشی بر خلاف تغییرات انرژی پتانسیل همان جسم میباشد.؟(در صورت نبود هدر برنده ها)

با افزایش انرژی جنبشی  انرژی پتانسیل كاهش میابد و بالعكس

E1 = E2

K1+U1 = K2 +U2                         U1U2 = K2K1                -ΔU = ΔK 

26- با رسم نمودار انرژی- ارتفاع  ،   تغییرات انرژی جنبشی و انرژی پتانسیل  و انرژی مكانیكی را  برای جسمی كه سقوط آزاد میكند را نشان دهید .                                                                                                                                                           -الف- تغییرات انرژی جنبشی K=MV2 /2                                                                                                                                                                                                                                              

ب- تغییرات انرژی پتانسیل  U = Mgh                                                                                                                

پ-تغییرات انرژی مكانیكی                                                                                                                                                                                                           E                                                                                                                                                                                       

 


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