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 T. The height of the mass at X is the same as at V. Click here to view the motion of the mass m.


(options are: less than, greater than, equal to)


• The speed change between T and S is (blank) between S and R.

• The speed of m at X is (blank) that at Q.

• The size of the total force on m at P is (blank) at U.

• The mechanical energy of m at P is (blank) that at V.

• The size of the total force on m at S is (blank) at P.

• The velocity of m at X is (blank) that at V.

Answer 1

• The speed change between T and S is greater between S and R.

• The speed of m at X is  greater that at Q.

• The size of the total force on m at P is less at U.

• The mechanical energy of m at P is equal to that at V.

• The size of the total force on m at S is greater at P.

• The velocity of m at X is equal to that at V.

What is mechanical energy?

The mechanical energy is the sum of kinetic energy and the potential energy of an object at any instant of time.

M.E = KE +PE

Given is 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 shows the position of the mass at equal time intervals starting from rest at T. The height of the mass at X is the same as at V.

Between T to S and S to R, the mass is under constant acceleration. Time taken to move from T to S is greater than S to R. Thus, the speed change between T and S is greater than between S and R.

At Q, there is only a horizontal velocity component, but at X. the speed will be greater and has both vertical and horizontal component. Thus, the speed of m at X is greater than that at Q.

Force is given as the rate of change of momentum with time. At U, change in momentum is large compared to P. Thus, the size of the total force on m at P is less at U.

There is no friction acting on the system. So the energy remains conserved. Mechanical energy at P = V.

The force on mass m at S is only the gravity force. The remaining forces are cancelled by the normal force. Thus, size of the total force on m at S is greater at P.

The energy is conserved at each point of motion of mass. If X and V are at same height, they have same potential energy and so their kinetic energy. Thus, velocity of m at X is equal to that at V.

Learn more about mechanical energy.

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