oef vecteurs --- Introduction ---

This modulus contains at this moment 10 simple exercises on vectors and their applications in physics on the following subjects:

Chiffres significatifs


( )

Relation entre trois vecteurs


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Mobile en rotation

Un mobile décrit un cercle de rayon R= m (représenté en jaune sur la figure), à vitesse uniforme V= m/s. A un instant donné, la position du mobile, , est représentée par le vecteur bleu , et sa vitesse, , par le vecteur rouge.
  • Calculer les coordonnées cartésiennes de et Ry(m) =
  • Calculer les coordonnées cartésiennes de et Vy(m) =
(On donnera les réponses avec 3 chiffres significatifs). An object is moving with a circular trajectory of radius R= m (represented in yellow in the figure) with a uniform velocity V= m/s. At a given instant, the position of the object, , is represented by the blue vector , and its velocity, , by the red vector.
  • Calculate the Cartesian coordinates of and Ry(m) =
  • Calculate the Cartesian coordinates of and Vy(m) =
(Please write the answers using 3 significant figures). 		xrange -1.5,1.5 yrange -1.5,1.5 arrow -1.5,0,1.5,0,10,black arrow 0,-1.5,0,1.5,10,black text black,1.4,-0.1,large,x text black,0.1,1.4,large,y text black,-0.1,-0.1,large,0 linewidth 2 circle 0,0,167,yellow fcircle cos(/180*3.1416),sin(/180*3.1416),12,black arrow 0,0,cos(/180*3.1416),sin(/180*3.1416),14,blue arrow cos(/180*3.1416),sin(/180*3.1416),1.22*cos((+35)/180*3.1416),1.22*sin((+35)/180*3.1416),14,red linewidth 1 arc 0,0,1.2,1.2,0,,blue text blue,cos(/2/180*3.1416),sin(/2/180*3.1416),large, text blue,cos(/2/180*3.1416)+0.3,sin(/2/180*3.1416)+0.05,small,O

Angle entre deux vecteurs (<90°)

Deux vecteurs unitaires ,
  • (représenté en )
  • et (représenté en ),
ont pour coordonnées cartésiennes les valeurs suivantes:
  • ax = et ay =
  • bx = et by =
A l'aide du produit scalaire, déterminer l'angle entre ces deux vecteurs. On donnera la réponse arrondie au degré le plus proche. Two unit vectors,
  • (represented by )
  • et (represented by ),
are defined by the following values of their Cartesian coordinates:
  • ax = and ay =
  • bx = and by =
Use the scalar product to determine the angle between these two vectors. Please give the answer rounded to the nearest degree.
= deg
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Angle entre deux vecteurs (>90°)

Deux vecteurs unitaires ,
  • (représenté en )
  • et (représenté en ),
ont pour coordonnées cartésiennes les valeurs suivantes:
  • ax = et ay =
  • bx = et by =
A l'aide du produit scalaire, déterminer l'angle entre ces deux vecteurs. On donnera la réponse arrondie au degré le plus proche. Two unit vectors ,
  • (represented by )
  • et (represented by ),
are defined by the following values of their Cartesian coordinates:
  • ax = and ay =
  • bx = and by =
Use the scalar product to determine the angle between these two vectors. Please round the answer to the nearest degree.
= deg
xrange -100,100 yrange -100,100 arrow -100,0,100,0,10,black arrow 0,-100,0,100,10,black text black,92,-10,large,x text black,10,95,large,y text black,-10,-10,large,0 arrow 0,0,80*,80*,14, arrow 0,0,80*,80*,14, arc 0,0,40,40,,,red text red,50*cos((+/2)/180*3.1416),50*sin((+/2)/180*3.1416),large,?

Projection d'un vecteur

Deux vecteurs , (représenté en bleu ) et (représenté en vert ) , ont pour coordonnées catésiennes les valeurs suivantes:
Ax = cm et Ay = cm
Bx = cm et By = cm
  • Quelle est la norme du vecteur ?
    A= cm
  • A l'aide du produit scalaire, déterminer la longueur du segment OH, projection de sur la direction de .
    OH = cm
On donnera les réponses avec 3 chiffres significatifs. Two vectors , (represented in blue ) and (represented in green ) , are define by the following value of their Cartesian units:
Ax = cm and Ay = cm
Bx = cm and By = cm
  • What is the norm of the vector?
    A= cm
  • Use the scalar product to determine the length of th OH segment, projection of on the direction of .
    OH = cm
Please give the answers with 3 significant figures. 		xrange -100,100 yrange -100,100 arrow -100,0,100,0,10,black arrow 0,-100,0,100,10,black text black,92,-10,large,x text black,10,95,large,y text black,5,-6,large,0 arrow 0,0,,,14,blue arrow 0,0,,,14,green dline ,,,,red text red,,,large,H

Combinaison de vecteurs

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p=
q=

Travail d'une force


     
A(,,)
  • B(,,)


    • (J)=

    Bloc sur un plan incliné

    • m= kg N.
    • .
    L=

    WF (kJ) =
    WP (kJ) =
    		xrange -1,10 yrange -1,10 line -1,0,10,0,black line 0,0,10*cos(*3.1416/180),10*sin(*3.1416/180),black arc 0,0,3,3,0,,red text red,2*cos((/2)/180*3.1416),3*sin((/2)/180*3.1416),large, text red,0.7+2*cos((/2)/180*3.1416),0.4+3*sin((/2)/180*3.1416),small,o fpoly blue,,,,,,,, linewidth 2 arrow ,,,-3,10,black copy +0.5,-2,-1,-1,-1,-1,P.gif arrow ,,+3*sin(*3.1416/180)*cos(*3.1416/180),+3*sin(*3.1416/180)*sin(*3.1416/180),10,black copy +0.3,+1.8,-1,-1,-1,-1,F.gif linewidth 1 dline ,,,,black

    Système de coordonnées direct /indirect




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