GREPhysics.NET: GR9677 #5

GR9677 #5

Problem

GREPhysics.NET Official Solution

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Mechanics $\Rightarrow$ }Centripetal Force

$\vec{F}_air$ acts in the direction as shown and the centripetal acceleration acts in the direction of $\vec{F}_A$ . Centripetal acceleration is a net force, however, and thus,

$\begin{eqnarray} \rightarrow_+ \sum F_x = 0 &=& -F_{air} +f_x \\ \uparrow_+ \sum F_y = -mv^2/r &=& f_y<br /> \end{eqnarray}$

$f_x$ is in the positive direction and $f_y$ is in the negative direction. Thus the force of the road is $\vec{F}_B$ .

Alternate Solutions

99percent
2008-11-06 06:20:59

Centripetal force is in the direction $\vec{F_A}$

Tires exert a force in the backward direction so that the car moves in the forward direction - By Newton's third law (Action-Reaction) - The road exerts an equal force in the forward direction, i.e., $\vec{F_C}$

the resultant of $\vec{F_A}$ and $\vec{F_C}$ will be in the direction $\vec{F_B}$

Bingo..!!

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Comments

99percent 2008-11-06 06:20:59	Centripetal force is in the direction $\vec{F_A}$ Tires exert a force in the backward direction so that the car moves in the forward direction - By Newton's third law (Action-Reaction) - The road exerts an equal force in the forward direction, i.e., $\vec{F_C}$ the resultant of $\vec{F_A}$ and $\vec{F_C}$ will be in the direction $\vec{F_B}$ Bingo..!! Reply to this comment
isina 2008-10-16 14:45:53	I do not completely agree with the answer on the grounds that it is not the only solution. Even if there is no wind force there is still force in +x direction. The reason that there is forward friction force is as follows: as the car moves in +x direction, its tires rotate in the reverse direction (at the point of contact their velocity vector points -x). So the friction of the road on the tires is actually to the opposite direction of the cars tires movement and on the same direction as the movement of the car. This results in a +x directed friction (hence the car moves). Reply to this comment
evanb 2008-06-30 11:50:46	Just a small typo: you need braces for $F_{air}$ so that it doesn't look like $F_air$ Reply to this comment
yosun 2005-11-10 02:00:50	BWHB: thanks for the typo-alert; it has been corrected. Reply to this comment
BWHB 2005-11-10 01:38:49	All the work is right but the answer is wrong. It's FB. Reply to this comment

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