1. Recall that the equation for torque could be written as =rFsin. We can also w

Question

1. Recall that the equation for torque could be written as =rFsin. We can also write the equation for torque in vector form: =r x F. Compute the torque about the origin for the force F=-mgj acting on a particle at r=xi+yj.

2. A particle is given a displacement  s = (2m)iˆ (5m) ˆj along a straight line. During this displacement, a constant force  F = (3Nt)i + (4Nt)j acts on the particle. Find (a) the work done by the force and (b) the component of the force in the direction of the displacement. Recall that: W=Fs.

Explanation / Answer

1)
torque = r x F.
r=xi+yj.
F=-mgj
torque =(xi+yj)x(-mgj)=(-mgx )k +(0)=(-mgx)k
[
note that ixj =k;jxk=i;kxi=j;ixi=0;jxj=0;kxk=0
]
2)
a)

workdone = F.s
=((3Nt)i^ + (4Nt)j^).((2m)iˆ - (5m)j^ )
=6-20
=-14 N.m
[
i.i=1;j.j=1;k.k=1;i.j=j.k=k.i=0
]

b)

component of force in a particular direction is obtained by the dot product of force with unit vector in that particular direction

component of force in the direction of displacement is : F.s/|s|

=-14/sqrt(2^2+5^2)

=-14/sqrt(29)

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