Question

已知兩恒力F₁=(3，4)，F₂=(6，-5)作用于同一質(zhì)點(diǎn),使之由點(diǎn)A(20,15)移動(dòng)到點(diǎn)B(7,0).試求：

(1)F₁、F₂分別對(duì)質(zhì)點(diǎn)所做的功；

(2)F₁、F₂的合力F對(duì)質(zhì)點(diǎn)所做的功.

Answer 1

解析：設(shè)物體在力F作用下位移為s,則所做的功為W=F·s.

=(7,0)-(20,15)=(-13,-15).

(1)W₁=F₁·=(3,4)·(-13,-15)=-99(焦耳).

W₂=F₂·=(6,-5)·(-13,-15)=-3(焦耳).

(2)W=F·

=(F₁+F₂)·［(3,4)+(6,-5)］·(-13,-15)=(9,-1)·(-13,-15)=-102(焦耳).