Find the work done by the force field F(x,y)=x^2-xy in moving a particle along the quarter-circle r(t)=cos t+sin t, 0≤ t≤ π2.相关知识点: 试题来源: 解析 Since x=cos t and y=sin t, we haveF(r(t))=cos ^2t-cos tsin t and r'(t)=-sin t+cos tTherefore the...
【题目】Find the work done by the force field F in moving an object from p to o.F(x,y)=e^^(-x) " -xe^(-x) -j; P(0,1), Q(2,0) 相关知识点: 试题来源: 解析 【解析】F(x,y)=e^(-y_i)-xe^(-y) W=∫_c^r⋅|a| Sinceθ/(θ_y)(e^(-y))=-e^(-y)=θ/(...
Answer to: Find the work done by the force of F(x) newtons along the x-axis from x = a meters to x = b meters. F(x) = x\sqrt{100 - x^2},\ a = 0,\ b...
Answer to: Find the work done by the force field F(x,y) = x\sin y i + yj on a particle that moves along the parabola y = x^2 from (-2,4) to...
Find the work done by the force field {eq}\mathrm{F} {/eq} in moving an object from {eq}P {/eq} to {eq}Q {/eq}. {eq}\displaystyle \vec F(x, y) = 2y^{\frac{3}{2}}\vec i + 3x \sqrt y\vec j, \; P(1, 1), \; Q(...
【题目】Find the work done by the force fieldF(x,y)=x2i-zyj in moving a particle along the quarter-cirle r(t)=costi+sint j 0≤t≤π/(2) 相关知识点: 试题来源: 解析 【解析】Since x=cost and y=sint, we haveF(r(t) = cos2ti- costsintj and r'(t) = -sinti+ costjT he...
【题目】Find the work done by the force fieldF(x,y)=x2i+yej on a particle that moves along the parabola x=y^2+1 from (1,0) to (2,1). 相关知识点: 试题来源: 解析 【解析】Choosing y as the parameter, the curve c is parametrized by x=y2+1,y=y, 0≤y≤1 . T hen(2y,...
According to definition, Work done by a force on an object in moving it from one position to another is given by {eq}Work=Force\times Distance {/eq}. In Calculus, work done on a particle across a curve is given by integration of force on that path ...
Answer to: Find the work done by the force field F(x,y,z) = x^3 i + y^2 j+ z k in moving an object along the line segment C from the origin...
Problem #4: Find the work done by the forceF=3xyi+6y2jacting along the piecewise-smooth curve consisting of the line segments from(-3,3)to(0,0)and from(0,0)to(3,6). Problem #4: Submit Problem #4for Grading ...