A small mass m sides with negligible friction down an incline at an angle of 25.

Question

A small mass m sides with negligible friction down an incline at an angle of 25.76 degree with respect to the horizontal. It then drops down to a horizontal surface and bounces elastically back up as shown. The picture is to scale, it snows the position or the mass at equal time intervals starting from rest at U. The height of the mass at X is the same as at S. Click here to view the motion of the mass m. The size of the total force on m at R is at T. The speed of m at P is that at T. The size of the total force on m at Q is at X. The speed change between U and Q is between Q and V. The mechanical energy of m at T is that at X. The velocity of m at X is that at S

Explanation / Answer

at T there is gravity force. ( mg )

at point R, impulse acts that changes velocity more rapidly than gravity.

so Force at R is greater than T.

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as we go up speed decreases.

speed at P is less than at T.

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net force at Q is mgsin25.76 and net force at X is mg .

so force at Q is less than X.

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speed changes occurs accordingally ,

m (vf^2 - vi^2)   / 2 = mgh

vf^2 - vi^2 = 2gh

(vf - vi) ( vf + vi) = 2gh
for both cases h is same, but vf and vi are not same.

vf + vi is more form Q to V.

so change in less at Q and V/

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mechanical energy is conserved.

so equal.

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X and S are at same level .

so speed will be equal.

but at x, m is coming down.

at S, alos coming down .

so velocity equal.

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