1. A force applied to an object is given, in Newtons, by the veetor =-45 N i-10
ID: 1879090 • Letter: 1
Question
1. A force applied to an object is given, in Newtons, by the veetor =-45 N i-10 N j+20Nk (a) Let us call the component of the force in the x-direction Fa, and the component in the y-direction Fy, and the component in the z-direction F. By visually inspecting the expression for the force above, find thevalues for F and F. (Let us callbthis the "inspection" a vector.) Fy of for finding the com (b) Find the same answers you found in part (a) abové using the "projection"IoN method. That is, show that the component of F in the x direction is given by the dot product of F with the unit vector i in the x direction. and similarly, show that F, F., and F,-F-k. (If you need a refresher on dot-products, see Chapter 1.10. This is also called a scalar product. The rules are that for two perpendicular unit vectors the dot product is zero, i.e. for example, i·j = 0, but the dot product of a unit vector with itself is 1, ie. for example 1-1 = 1 ) (c) Show that the magnitude of the vector can be determined from the product of the vector with itself, since 2 FF.F What is the magnitude of the force F in Newtons? (d) Write down an expression for a dimensionless u in this same direction as F. nit vector u that points (e) Use your answers to (c) and (d) to rewrite F as a product of the magni- tude of the force and a unit vector indicating which direction the force is acting 1.e. ú and distribute the terms, you get back Show that when you multiply F by the same expression for F that we started with at the beginning of this problemExplanation / Answer
Given,
F = -45 i - 10 j + 20 k
a)from the given vetcor,
Fx = -45 N ; Fy = -10 N ; Fz = 20 N
b)Fx = F.i
Fx = (-45 i - 10 j + 20 k).i = -45*1 = -45 N
Fy = (-45 i - 10 j + 20 k).j = -10 N
Fz = (-45 i - 10 j + 20 k).k = 20 N
c)F^2 = (-45 i - 10 j + 20 k).(-45 i - 10 j + 20 k)
F^2 = -45x-45 + -10x-10 + 20x20 = 2525
F = sqrt (2525) = 20.25 N
d)u(hat) = u/lul
u = -i -j + k
Hence, u = -i - j + k
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