a car of mass m is moving on a horizontal circular path of radius r At an instant its speed is v and is increasing at the rate a Then prove that the coefficient of friction between the ground and car is not less than a/g
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μmgsinθ=ma
μmgcosθ=mv2/R
sinθ=a/μg
-1≤sinθ≤1
-1≤a/μg≤1
μ>a/g... and μ≈(a/g)+ for θ→90°
and see that for that θ... v→0 at that instant if r is fixed...
actually v2/r→0 ...
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1Abhishek if u(mg)sintheta =ma
then how can the body accelerate with acceleration a
because here here we are saying that the resistive frictional force is equal to the accelerating force
Please explain where i am wrong
3consider an apple be in free fall from a height H.wat is the acc of the apple da
33ma and μmgsinθ are not opposing forces...
F=ma..
here Force is μmgsinθ providing acc 'a'
hence μmgsinθ=ma
1Abhishek, isn't u(mg)sintheta acting in opposite direction to the motion of the car according to your diagram
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Why cars accelerate??
Consider car is accelerating in forward direction in straight path.. as shown... wheel is moving in direction as shown.....
Now wheel is rotating by engine to make v=ωR friction has to decrease ω and increase v as engine is providing α to increase ω...
so friction acts on tires as shown.. so on car friction acts in forward direction...
This is common misconception that friction acts on car in backward direction only...
In which direction friction acts on car..
1. When car is accelerated..
engine provides α and hence ω increases .. hence ωR>v hence to make it pure rolling friction acts in forward direction...
(You might have seen car just standing at one place and wheels rotating before starting a car... there friction is less so it takes time to make v=ωR
2. when car is moving steadily..
v=ωR.. no friction acts..
3. when car is stopped (brakes are applied..)
case just opposite of 1.. friction in backward direction...
You can think like this also..
Since engine provide internal force for the car it cannot accelerate it..there has to be an external force...which is friction only... so.. whenever car is accelerated friction must act in forward direction and when it is stopped or deaccelerated friction must do this so acts in backward direction...
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