IIT JEE , AIEEE Forum - Physics , Mechanics - uwill surely be rated(if you expln correctly)

savvej

A car is speeding up on a horizontal road with an acceleration" a".Consider the following situations in the car:
(1) A ball is suspended from the ceiling through a string and is maintaining a constant angle with the vertical.Find this angle.
(2)A block is kept on a smooth inclince and does not slip on the incline.Find the angle of the incline with the horizontal.

what i have done is:
on the basis of the problem i drew free body diagrams as follows:(see below (1) and (2) )
for the first part:
with respect to ground(inertial frame)(here i have used "@" as theta)
Tsin @ = ma -----(1)
Tcos @ - mg = 0
.:Tcos @ = mg -----(2)
dividing (1) by (2),we get
tan @ = a/g
.: @ = tan^-1 a/g
the answer given is also the same.but is my method valid?

for the second part:
With reference to earth,
Nsin @ = ma --------(1)
similarly,
Ncos @ - mg =0 ------(2)
dividing (1) by (2) we get,
tan @ = a/g
@ = tan^-1 a/g
the answer given is also the same.but is my method valid?

splashprabhu

ya....everythin is right...wats d prob?

jus dat u hv used d pseudo force concept....n not d frame of ref of earth...

savvej

i have used frame of reference of earth only.why are u telling taht i have not used it

ramyani

1st part :
ur method is valid. I also did it in the same method.

ramyani

for the second part resolving the forces along the direction of R as y-axis, we get,

mgsinx=macosx

or, x= tan inverse(a/g)

here ma is the pseudo force as the car has an acceln a

ramyani

i assumed the angle of incline to be x

karthik2007

Your answers are perfect for both.

ramyani

u said " i have used frame of reference of earth only". Thats not correct.
u measured everything inside the car. The bob is inclined inside the accelerating car. The block is not slipping inside the accelerating car. So u used the frame of reference of accelerating car---a non-inertial frame of reference.
But u used newton's law. For that u used an imaginary force ---pseudo force--opposite to the direction of accelaration of the car.
Look into the 1st part.
u used
Tsin @ = ma -----(1)
But from ur figure Tsin@ is from left to right. The car is acclarating also from left to right. So u assumed some imaginary force m@ to act upon the bob from right to left --opposite to the direction of car's motion.
[ Assuming such a force m@ from right to left --opposite to the direction of car's motion , the accelarating car is mentally considered to be at rest. Then newton's law was applied.]

seifo_90

Yup ...Your answer is perfectly right.

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