Answer to Question #170846 in Mechanics | Relativity for saddam

Question #170846

. A particle moving in the xy plane undergoes a displacement (2.0i+3.0j) m as a constant force F (5.0i+ 2.0) acts on the particle. a) Calculate the magnitudes of the displacement and the force b) Calculate the work done by c) Calculate the angle between the force and displacement.


1
Expert's answer
2021-03-12T09:17:47-0500

Displacement, d=2i+3j2i+3j

Force, F= 5i+2j5i+2j


(a) Magnitude of Displacement, d=(2)2+(3)2=4+9=13|d|=\sqrt{(2)^2+(3)^2}=\sqrt{4+9}=\sqrt{13}


Magnitude of force, F=(5)2+(2)2=25+4=29|F|=\sqrt{(5)^2+(2)^2}=\sqrt{25+4}=\sqrt{29}


(b) Work done, W=F.d=(2i+3j).(5i+2j)=10+6=16jouleW=F.d=(2i+3j).(5i+2j)=10+6=16 joule


(c) As we know W=FdcosθW=|F||d| cos\theta


16=13.29cosθ16=\sqrt{13}.\sqrt{29} cos\theta


cosθ=1613.29=0.824cos\theta=\dfrac{16}{\sqrt{13}.\sqrt{29}}=0.824


θ=cos1(0.824)=34.5\theta=cos^{-1}(0.824)=34.5^{\circ}


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