Can\'t seem to figure out the answer for this question A small mass m slides wit

Question

Can't seem to figure out the answer for this question

A small mass m slides 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 shows the position of the mass at equal time intervals starting from rest at V. The height of the mass at P is the same as at X. Click here to view the motion of the mass m. The speed of m at Q is than that at P. The mechanical energy of m at R is that at X. The velocity of m at P is that at X. The size of the total force on m at P is at U. The speed change between V and U is between U and S. The size of the total force on m at T is at R.

Explanation / Answer

Applying Conservation of energy :i.e. Sum of K.E. and P,.E. is constant

1. Since height of P is less than Q, P.E. of Q is less than P. therefore K.E. and hence speed is less at P than Q

2. Mechanical Energy is equal

3. Since height of P & X are equal, hence P.E. of P & X are equal, hence K.E. and hence velocity are equal at P & X

4. At P. it is free fall i.e. mg, while at U: it is component of mg along plane which is less. Hence Total Force at P is greater than at U

5. Since height change between V & U is less than the Height change between U & S, speed change between V & U is less than between U & S

6. Net Force at T is less than at R

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