VDU_Physics_1_008

Physics 1:  Mechanics:  Conservation of Energy

Javier Montenegro Joo

jmj@VirtualDynamics.Org

Conservation of Energy.-

(1) In the fig. , a block of 1 kg is at a height of 52 cm on a ramp by which it slides down. Determine: (a) the speed that acquires the block in the horizontal sector before hitting the spring. (b) The maximum distance the spring shrinks when pushed by the block. It is known that the spring stretches 60 cm when it is placed vertical and a trunk of 10 kg is hanged from it.

Solution.-

Initially as the block is at a certain height, there is only gravitational potential energy. Seeing that there is no friction, the initial potential energy is entirely turned into kinetic energy of the block while it slides on the horizontal before reaching the spring. Finally the kinetic energy of the block is invested in compressing the spring, so that at the end, the gravitational potential energy has been converted into elastic potential energy of the compressed spring.

(2) When a ball of 10 kg hangs from an upright spring, the spring stretches 60 cm. In the fig., the same spring rests on the floor, with one of its ends against the wall and the other end, which is compressed 25 cm, touches a block of 1 kg.  When the spring is freed the block slides on the floor and then it goes up the ramp. Determine (a) the speed of the block when it slides between the spring and the ramp (b) the maximum height the block reaches on the ramp.

Solution.-

In this case at the beginning there is only elastic potential energy of the compressed spring. Since there is no friction this potential energy is totally invested into kinetic energy while the block displaces on the horizontal. Finally the kinetic energy becomes gravitational potential energy.

(3) In the figure, a small block of mass m is initially at rest at the top of a semi-circular track of radius R. Next, the block slides down without friction on the track. For the moment the block passes by point B, determine: (a) the speed of the block (b) the force that exerts the track on the block.

Solution.-

If there is no friction, there is no rolling; hence the block slides down over the curved surface without rolling. Additionally since there is no fiction the energy is conserved. At point A all the energy is potential and at point B the energy has been transformed into kinetic and potential energies:

(4) A 1-kg block is 2-m above the upper end of a coil spring which has been vertically placed on the floor. When the block falls on the coil, this is compressed 10 cm.   Determine (a) the elastic constant of the coil. (b) The gravitational potential energy of the block invested in the compression of the coil. (c) In another experiment a block of 5 kg hangs from the same coil, determine the energy stored in the coil.

Solución

Initially the block is at a height ‘h’ above the upper extreme of the vertical spring. When the block falls down on the spring this is compressed a length ‘L’. Under these conditions the gravitational potential energy of the block has been invested in the elastic potential energy of the spring.

Gravitational potential energy = Elastic potential energy