Alevel數(shù)學(xué) | 揭秘萬(wàn)能參數(shù)方程求導(dǎo)法則

 

臨近5月份A-level大考，潘老師建議學(xué)生們梳理知識(shí)框架，從宏觀到微觀對(duì)知識(shí)點(diǎn)和易錯(cuò)點(diǎn)進(jìn)行整理，今天我們就針對(duì)Work(功)，Energy(能)和Power(功率)講解區(qū)分。

 

首先從定義方面進(jìn)行區(qū)分：

work做功 =force*distance 單位joules（J）

Kinetic energy動(dòng)能(K.E.)=(1/2)mv2,

Potential energy勢(shì)能(P.E.)=mgh

Work done=change in kinetic energy=(1/2)mv2-(1/2)mu2

Power is the rate of doing work, 單位watt(W),也就是1watt is 1 joule per second, Power在考題中經(jīng)常以kilowatt(kW)形式出現(xiàn)，所以Power=F*V.

 

接下來(lái)我們看一道真題：

A skier passes point A on a ski-run moving downhill at 6m/s, after descending 50m vertically the run begins to asend. When the skier has ascended 25m to point B her speed is 4m/s. The skier and her skis have a combined mass of 55kg, The total distance she travels from A to B is 1400m. The non-gravitational resistances to motion are constant and have a total magnitude of 12N, Calculate the work done by the skier.

 

 

分析：

首先分析動(dòng)能損失了多少，也就是初狀態(tài)-末狀態(tài)為正值，那么意味著動(dòng)能在損失；然后計(jì)算勢(shì)能的損失；然后計(jì)算動(dòng)能和勢(shì)能損失之和；克服阻力做功-能損失總和=滑雪人做功。

 

步驟：

Loss of K.E.=(1/2)mv2-(1/2)mu2=(1/2)*55*62-(1/2)*55*42=550

Loss of P.E.=mgh=55*9.8*(50-25)=13475

Total loss of energy=550+13475=14025

Work done against resistances=12*1400=16800

Work done by the skier=16800-14025=2775

 

以上就是功，能，功率典型題型，一方面同學(xué)們平時(shí)一定要注意積累題型，培養(yǎng)題感，多做題多對(duì)知識(shí)點(diǎn)做區(qū)塊化總結(jié)就能慢慢達(dá)到看到題就能了解出題人的意圖，希望今天的分享對(duì)大家能有所幫助，也歡迎同學(xué)們加入我們一起溝通和探討。