Sliding down the sliding plane.

Please can anyone describe the motion of a block of mass mm sliding on smooth inclined plane of mass MM which can slide on the smooth ground. Here, gg is the acceleration due to gravity.

#Physics #Mechanics

Note by Shreyas S K
7 years, 2 months ago

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Comments

I cannot paste a diagram here but i hope you understand. Take a normal force NN perpendicular to mm. I will be solving the sum in the frame of reference of ground, so no pseudo force is required.

Let accelerations of mm be a(wrt.M)a( wrt. M) and that of MM be AA.

Note that the acceleration of mm wrt. ground in horizontal direction is (acosθA)(a cosθ - A). In vertical direction, it is asinθ.a sinθ.

Writing equations,

Nsinθ=MANsinθ = MA

MgNcosθ=ma sinθMg - N cos θ = ma~sinθ

Nsinθ=m(acosθA)Nsinθ = m ( acosθ - A)

Solving,

a=(M+m)gsinθM+msin2θ a = \dfrac{(M+m)gsinθ}{M + msin^{2}θ}

A=mgsinθcosθM+msin2θA = \dfrac{mgsinθcosθ}{M + msin^{2}θ}

Avineil Jain - 7 years, 1 month ago

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if we consider this system wrt wedge then we should take the pseudo force as it is in non inertial frame but you didnt considered it.....why????

Saurav Sharma - 7 years ago

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See my solution again, I have mentioned that i am solving it wrt ground frame!

Avineil Jain - 7 years ago

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@Avineil Jain got it thanks .........

Saurav Sharma - 7 years ago

Thank you very much

shreyas S K - 7 years ago

i dnt thnk so the horizontal acceleration is acos[tita]-A instead it is acos[tita]+A .as its a non inertial frame so pseudo force acts in opposite direction to the motion of the bigger block

Rohan Kumar - 7 years ago

f=ma+mg

sunitha bhadragiri - 7 years ago

please can any body help.......

shreyas S K - 7 years, 1 month ago

because of the gravity why its sliding and the shape of the triangle to

Ben-Rasher Sammain - 7 years ago

If we take wedge frame of reference, then there is a pseudo acceleration on the block of mass m to the right. Then use Normal and 'mg' downwards to find the acceleration.

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equations as Aveneil mentioned

Khan Academy can very well explain you this..

Kartik Sharma - 7 years, 1 month ago

I guess translatory motion

Zain Mehmood - 7 years ago

gsino. Other wise free fall

Sarvir Singh - 7 years ago

Well, I wish I could help, and also couldn't give you a diagram. First, we must make an agreement to the symbol and the sign, the positive sign and negative sign. Let the block mass m, an inclined plane M, an acceleration for block a, and an acceleration for M is A. We could look the entire objects or it's called a system. The equation will be Sigma Fx=ma, since it's m and a are system we could write as sigma Fx=(m+M)(a cos theta-A). why it should a cos theta? look at the picture, there's an arrow when the small mass are sliding, you could divide it into a cos theta and a sin theta (into a resultant) then you choose the angle is which have a relation to the plane. look again at the equations, it's said Fx, so we should look the acceleration which related to x-axis. then continue to the force, the only force which works on the plane is w sin theta, because there's no other force like friction (because the plane is smooth. so, comes the equation, mg sin theta=(m+M)(a cos theta-A). because you ask the motion of the block, so, a=[mg sin theta/m+M +A]1/cos theta.

Hoshea Simbolon - 7 years ago

Nsin[theta]=MA mgsin[theta]=MA A=mgsin[theta]/M THEN ACCORDING TO NON INERTIAL FRAME NET ACCELERATION OF m BLOCK IS A+a where a=gsin[theta] a[net]=mgsin[theta]/M+gsin[theta] a[net]=gsin[theta][m+M/M] i think this would be the correct ans for the question

Rohan Kumar - 7 years ago

Displacement of centre of mass will be vertically downward.

Ajay Kumar - 7 years ago

it undergoes a translational and linear motion

ayoade habibullah - 7 years ago

second equation will be : mg = ma sin (theta) + N cos (theta)

Hafiz-ur Rahim - 7 years ago

the best method to solve or to understand this type of motion is psuedo accerlation

suryansh tiwari - 7 years ago

Transitional

Ashu Solanki - 6 years, 11 months ago

Its depand upon inclination angle

kuldip bum - 6 years, 11 months ago

dude if plane is friction less then its acceleration will a=gsin(thita) so simple

Salman Zafar - 7 years ago
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