Forces applied to a spring-loaded gas pedal

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The discussion revolves around calculating the force applied to a spring-loaded gas pedal and understanding the related forces acting at point O. The calculated force T exerted on the pedal is determined to be 4.7N, using torque balance equations where the moment of external forces equals zero. Participants express confusion regarding the second question about the force R, which seems to refer to the reaction force at the pivot O, but its specifics, such as direction and magnitude, are unclear. The term "density" for R is questioned, suggesting a possible translation issue. Overall, the main focus is on understanding the mechanics of the gas pedal's forces and clarifying the terminology used in the problem.
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TL;DR Summary: An accelerator pedal is located steadily on our line at point O, the spring AB is perpendicular to the accelerator pedal, keeping it balanced at an angle of 45 degrees. a = 45* the weight of the accelerator pedal is 10N and it is loaded on G. OG = 10 cm OB = 15 cm.
Question = Calculate the intensity of the force T applies to the accelerator pedal.
Question = Determine the direction, side, and density of R from point O.

For the firtst question i did like that =
As the pedal is in balance the sum of the moment of
external forces are zero
M(P)+M(T)+M(R)=0
M(R)=0 because it meets the axis of rotation
So M(P)+M(T)=0
If we choose a positive direction towards P
M(P)=P.dp or dp = OG.cosalpha=OGcos45°
M(T)=-T.OB
T=OGxcos45°xP/OB=10x10xcos45°/15
T=4.7N

But i'm not sure sor i can't do the second one.
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Hello @Theexploer ,
:welcome: ##\qquad## !​

So this is a ##G## ,
1707945734347.png
right ? :wink:

But who is ##T## ? And ##P## ?

And did you render the complete problem statement ?

##\ ##
 
Yes, it's a G wich is the point of gravity, T is the tension and P is the Gas Pedal wich have a mass of 10N.

so i rendered the complete problem statement.
 
Theexploer said:
T=OGxcos45°xP/OB=10x10xcos45°/15
Let me asssume this translates as follows:
## OG## is a given distance, 0.1 m
x is 'multiply'
##P## is not the gas pedal but the weight of the gas pedal, 10 N

Theexploer said:
we choose a positive direction towards P
Does that mean ##P## = +10 N ? (i.e. down is positive) ?


##OG \cos 45^\circ## is the perpendicular distance of ##P## wrt ##O##
The 45 degrees is the angle AOB (not the other one, BAO)

##OG \cos 45^\circ P## is the torque you call M(P)
it's acting in clockwise direction (which you consider positive, right ?)

and M(T) is the torque the spring exerts. It's acting in counter-clockwise direction (so ##T## is pointing up?)
It is pointing perpendicular to OB, so the torque is ##M(T) = -T \ \text{OB}##

And the torque balance ##M(P)+M(T)=0## yields ##T= OG \cos 45^\circ P/ \text{OB}##

In a more conventional notation (torque as a vector and with y+ = up):

1707956983913.png


##\vec \tau_\text {left} +\vec \tau_\text {right} = 0 \Rightarrow ## ## \vec{\text {OG}} \times \vec mg ## ##+ \vec {\text {OB}} \times \vec T = 0 \Rightarrow## ## |OG|\, mg\sin\theta_1+ |OB|\, T\sin\theta_2 =0 ##
[edit] fixed typo
And I confess I have no idea what is asked in part 2. 'Density of ##R##' ? R doesn't occur in the story ...

##\ ##
 
Last edited:
Theexploer said:
T=4.7N
Looks right.
But I don't understand the second question either. Is it a translation? Is R defined anywhere?
 
I think R is the reaction force acting on the pedal at the pivot O. They want the magnitude ("density"?) and direction of this force. I don't have any idea what "side" of R means. The wording does appear to be a translation.
 
TSny said:
I don't have any idea what "side" of R means.
Maybe "direction, side, and density" means angle to the horizontal, to the left or to the right, and magnitude.
 
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BvU said:
Let me asssume this translates as follows:
## OG## is a given distance, 0.1 m
x is 'multiply'
##P## is not the gas pedal but the weight of the gas pedal, 10 N


Does that mean ##P## = +10 N ? (i.e. down is positive) ?


##OG \cos 45^\circ## is the perpendicular distance of ##P## wrt ##O##
The 45 degrees is the angle AOB (not the other one, BAO)

##OG \cos 45^\circ P## is the torque you call M(P)
it's acting in clockwise direction (which you consider positive, right ?)

and M(T) is the torque the spring exerts. It's acting in counter-clockwise direction (so ##T## is pointing up?)
It is pointing perpendicular to OB, so the torque is ##M(T) = -T \ \text{OB}##

And the torque balance ##M(P)+M(T)=0## yields ##T= OG \cos 45^\circ P/ \text{OB}##

In a more conventional notation (torque as a vector and with y+ = up):

View attachment 340350

##\vec \tau_\text {left} +\vec \tau_\text {right} = 0 \Rightarrow ## ## \vec{\text {OG}} \times \vec mg ## ##+ \vec {\text {OG}} \times \vec T = 0 \Rightarrow## ## |OG|\, mg\sin\theta_1+ |OB|\, T\sin\theta_2 =0 ##

And I confess I have no idea what is asked in part 2. 'Density of ##R##' ? R doesn't occur in the story ...

##\ ##
Thanks for your help
 
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