https://peda.net/id/3fda55fa15b 2019-12-03T13:01:25+02:00 https://peda.net/:static/535/peda.net.logo.bg.svg <div class="license">Tämän sivun lisenssi <a rel="license" href="https://peda.net/info">Peda.net-yleislisenssi</a></div> https://peda.net/id/fd80258415c 2019-12-03T13:49:40+02:00 13-2<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=E_p%3Dmgh" alt="E_p=mgh"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=m%3D55kg" alt="m=55kg"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=g%3D9%7B%2C%7D81%5C%20%5Cfrac%7Bm%7D%7Bs%5E2%7D" alt="g=9{,}81\ \frac{m}{s^2}"/><br/> <br/> a)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=h%3D8848m" alt="h=8848m"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=E_p%3D4%7B%2C%7D7739...%5Ccdot10%5E6J%5Capprox4%7B%2C%7D8MJ" alt="E_p=4{,}7739...\cdot10^6J\approx4{,}8MJ"/><br/> b)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=h%3D-10994m" alt="h=-10994m"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=E_p%3D-5%7B%2C%7D9318...%5Ccdot10%5E6J%5Capprox5%7B%2C%7D9MJ" alt="E_p=-5{,}9318...\cdot10^6J\approx5{,}9MJ"/><br/> <br/> 13-5<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=E%3Dmg%5CDelta%20h" alt="E=mg\Delta h"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=m%3D1%7B%2C%7D9%5Ccdot10%5E5kg%3D190000kg" alt="m=1{,}9\cdot10^5kg=190000kg"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=g%3D9%7B%2C%7D81%5C%20%5Cfrac%7Bm%7D%7Bs%5E2%7D" alt="g=9{,}81\ \frac{m}{s^2}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5CDelta%20h%3D10%7B%2C%7D70km%3D10700m" alt="\Delta h=10{,}70km=10700m"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=E%3D1%7B%2C%7D99437...%5Ccdot10%5E%7B10%7DJ%3D19%7B%2C%7D9437...GJ%5Capprox20GJ" alt="E=1{,}99437...\cdot10^{10}J=19{,}9437...GJ\approx20GJ"/> 2019-12-03T13:49:40+02:00 https://peda.net/id/384bbcac15c 2019-12-03T14:11:48+02:00 14-6<br/> <div>valitaan potentiaalitaso hyppyrin nokkaan</div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=h%3D66m" alt="h=66m"/></div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=v_a%3D0%5C%20%5Cfrac%7Bm%7D%7Bs%7D" alt="v_a=0\ \frac{m}{s}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=v_l%3D101%5Cfrac%7Bkm%7D%7Bh%7D%3D28%7B%2C%7D0555...%5Cfrac%7Bm%7D%7Bs%7D%5Capprox28%5Cfrac%7Bm%7D%7Bs%7D" alt="v_l=101\frac{km}{h}=28{,}0555...\frac{m}{s}\approx28\frac{m}{s}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=m%3D71kg" alt="m=71kg"/></div> <div> </div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=E_%7Bp%7B%2C%7Da%7D%2BE_%7Bk%7B%2C%7Da%7D%2BW%3DE_%7Bp%7B%2C%7Dl%7D%2BE_%7Bk%7B%2C%7Dl%7D" alt="E_{p{,}a}+E_{k{,}a}+W=E_{p{,}l}+E_{k{,}l}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=mgh%2B%5Cfrac%7B1%7D%7B2%7Dmv_a%5E2%2BW%3Dmgh%2B%5Cfrac%7B1%7D%7B2%7Dmv_l%5E2" alt="mgh+\frac{1}{2}mv_a^2+W=mgh+\frac{1}{2}mv_l^2"/><br/> koska liike-energia alussa ja potentiaalienergia lopussa on nolla, voidaan ne ottaa pois lausekkeesta</div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=mgh%2BW%3D%5Cfrac%7B1%7D%7B2%7Dmv_l%5E2" alt="mgh+W=\frac{1}{2}mv_l^2"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=W%3D%5Cfrac%7B1%7D%7B2%7Dmv%5E2-mgh" alt="W=\frac{1}{2}mv^2-mgh"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=W%3D%5Cfrac%7B1%7D%7B2%7D%5Ccdot71kg%5Ccdot28%5Cfrac%7Bm%7D%7Bs%7D-71kg%5Ccdot9%7B%2C%7D81%5C%20%5Cfrac%7Bm%7D%7Bs%5E2%7D%5Ccdot66m%3D-44975%7B%2C%7D66J%5Capprox-45kJ" alt="W=\frac{1}{2}\cdot71kg\cdot28\frac{m}{s}-71kg\cdot9{,}81\ \frac{m}{s^2}\cdot66m=-44975{,}66J\approx-45kJ"/></div> <div>vastustusvoimat tekevät 45 kilojoulen suuruisen työn liu'un aikana, liikkeen suunnan vastaisesti</div> <br/> <br/> <br/> <br/> 14-7<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=m%3D73kg" alt="m=73kg"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=h_a%3D8%7B%2C%7D0m" alt="h_a=8{,}0m"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=v_a%3D2%7B%2C%7D5%5Cfrac%7Bm%7D%7Bs%7D" alt="v_a=2{,}5\frac{m}{s}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=v_l%3D%3F" alt="v_l=?"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=s%3D35m" alt="s=35m"/><br/> <div><img src="https://math-demo.abitti.fi/math.svg?latex=F%3D-55N" alt="F=-55N"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=g%3D9%7B%2C%7D81%5C%20%5Cfrac%7Bm%7D%7Bs%5E2%7D" alt="g=9{,}81\ \frac{m}{s^2}"/></div> <div>potentiaalienergian nollataso mäen alla eli</div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=h_l%3D0m" alt="h_l=0m"/></div> <div>potentiaali- ja liike-energia muuttuvat mäessä sisäenergiaksi</div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=%5Cfrac%7B1%7D%7B2%7Dmv_a%5E2%2Bmgh_a%2BFs%3D%5Cfrac%7B1%7D%7B2%7Dmv_l%5E2" alt="\frac{1}{2}mv_a^2+mgh_a+Fs=\frac{1}{2}mv_l^2"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=v_l%5Capprox10%7B%2C%7D51%5C%20%5Cfrac%7Bm%7D%7Bs%7D%5Capprox11%5C%20%5Cfrac%7Bm%7D%7Bs%7D" alt="v_l\approx10{,}51\ \frac{m}{s}\approx11\ \frac{m}{s}"/><br/> <br/> <br/> 14-8<br/> <div>valitaan potentiaalitaso mäen alle<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=h_l%3D9%7B%2C%7D5m" alt="h_l=9{,}5m"/></div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=v_a%3D18%5C%20%5Cfrac%7Bm%7D%7Bs%7D" alt="v_a=18\ \frac{m}{s}"/></div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=W%3D750N" alt="W=750N"/></div> <img src="https://math-demo.abitti.fi/math.svg?latex=m%3D1200kg" alt="m=1200kg"/><br/> <br/> <img src="https://math-demo.abitti.fi/math.svg?latex=E_%7Bp%7B%2C%7Da%7D%2BE_%7Bk%7B%2C%7Da%7D%2BW%3DE_%7Bp%7B%2C%7Dl%7D%2BE_%7Bk%7B%2C%7Dl%7D" alt="E_{p{,}a}+E_{k{,}a}+W=E_{p{,}l}+E_{k{,}l}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=mgh%2B%5Cfrac%7B1%7D%7B2%7Dmv_a%5E2%2BW%3Dmgh%2B%5Cfrac%7B1%7D%7B2%7Dmv_l%5E2" alt="mgh+\frac{1}{2}mv_a^2+W=mgh+\frac{1}{2}mv_l^2"/><br/> <div><img src="https://math-demo.abitti.fi/math.svg?latex=%5Csqrt%7B%5Cfrac%7B600%5Ccdot18%5E2%2B750N-1200%5Ccdot9%7B%2C%7D81%5Ccdot9%7B%2C%7D5m%7D%7B600%7D%7D%3Dx" alt="\sqrt{\frac{600\cdot18^2+750N-1200\cdot9{,}81\cdot9{,}5m}{600}}=x"/></div> <div>x on auton nopeus mäen päällä</div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=x%3D11%7B%2C%7D78388...%5C%20%5Cfrac%7Bm%7D%7Bs%7D" alt="x=11{,}78388...\ \frac{m}{s}"/><!--filtered attribute: style="display: inline;"--></div> <div>liike-energia mäen päällä</div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=%5Cfrac%7B1%7D%7B2%7Dmv%5E2%3D%5Cfrac%7B1%7D%7B2%7D%5Ccdot1200kg%5Ccdot%5Cleft(11%7B%2C%7D78388...%5C%20%5Cfrac%7Bm%7D%7Bs%7D%5Cright)%5E2%3D7070%7B%2C%7D332382...J%5Capprox7%7B%2C%7D1k" alt="\frac{1}{2}mv^2=\frac{1}{2}\cdot1200kg\cdot\left(11{,}78388...\ \frac{m}{s}\right)^2=7070{,}332382...J\approx7{,}1k"/></div> <div>autolla on 7,1 kilojoulen verran liike-energiaa mäen päällä</div> <div> </div> <div> </div> <br/> <br/> </div> 2019-12-03T13:37:00+02:00