VDU_Physics_1_012 Physics 1:  Mechanics:  Work and Energy

Javier Montenegro Joo

jmj@VirtualDynamics.Org

(1) In the sketch a force F pushes a 12 kg block upwards along the 10 m long tilted plane, whose coefficient of kinetic friction with the block is 0.25. It is observed that the velocities of the block are 2m/s at the base of the hill and, 3m/s at the top. Determine: (a) Energy invested on the change of velocity of the block (b) Energy consumed by friction (c) Energy invested on the elevation of the block (d) Work done by the force F. Solution.-

The block climbs the slope due to the work realized by the force F, which is invested to overcome the friction and the gravitational attraction of the block, additionally the block, arrives to the top with certain kinetic energy. (2) A 10 kg block goes up along the tilted plane that elevates 40o from the horizontal, with an initial speed of 15 m/s. After advancing 9m over the plane, the block speed is zero.  Determine: (a) Variation in kinetic energy, (b) Change in potential energy, (C) frictional force between block and plane, (d) kinetic friction coefficient between block and plane. Solution.- (3) A 3.5 kg brick is launched up along a ramp that elevates 55o from the horizontal, with an initial speed of 10 m/s. After advancing 4 m over the surface, the brick speed has gone down to zero.  Determine: (a) Height the brick would reach if there were no friction (b) Variation in kinetic energy of the brick, (c) Change in its potential energy, (d) frictional force between brick and ramp, (e) kinetic friction coefficient between brick and ramp. Solution.-

If there were no friction, all the initial kinetic energy of the brick would be invested in climbing the incline until a certain height Ho but, with friction this height must be shorter. When there is friction, the block goes up only a distance d = 4 m over the surface, when it loses all its energy. The difference in gravitational potential energy is lost to friction. 