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

Question

A small mass m slides with negligible friction down an incline at an angle of 25.76° 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 S. The height of the mass at P is the same as at X. Click here to view the motion of the mass m.

• The size of the total force on m at Q is (greater than, less than, equal to) at V.
• The speed of m at X is  (greater than, less than, equal to)  that at R.
• The velocity of m at X is  (greater than, less than, equal to) that at P.
• The speed change between T and U is  (greater than, less than, equal to) between S and T.
• The mechanical energy of m at Q is (greater than, less than, equal to)  that at P.
• The size of the total force on m at R is  (greater than, less than, equal to)  at T.

Explanation / Answer

The force acting on mass M is same at all points i.e., mg. Therefore force at Q and V is same in quantity.

The speed m is greater at X than at R

Velocity P and X are equal

Speed change between T and U is greater than S and T

Mechanical at all points is same (Conservation of energy). Hence energy at Q and P are equal.

The size of total force at all points is gravitational only. Hence size of total force on M at R equal to T

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