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 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 U. The height of the mass at R is the same as at Q. Click here to view the motion of the mass m. The velocity of m at R is that at Q. The speed of m at T is that at S. The size of the total force on m at S is at X. The size of the total force on m at T is at V. The speed change between V and P is between U and V. The mechanical energy of m at S is that at R.

Explanation / Answer

a. Since the particle of the energy is constant hence R and Q are at the same height potential energy will be same obviouslt kinetic energy will also be same hence speed also same that means velocities are equal.

b. At s it only has the horizontal component whereas T has both horizontal and vertical component therefore T is greater than S.

c. The force on X is the component of gravity down the slope the remaining part is cancelled by force that is normal force at T the entire force of gravity takes place hence T is greater than X.

.d Since force F= dp/dt represents change in momentum at T is larger and v is smaller.thus T is greater than V.

e.s once the particle is under a constant acceleration so according to kinematic formula dv = a dt so time taken to travel from v to p is greater than from u to v .

f. sine thee is no friction in the system without non conservative forces energy is constant hence S=R

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