VDU_Physics_1_013

# ## Physics 1:  Mechanics:  Energy invested against friction

Javier Montenegro Joo

## jmj@VirtualDynamics.Org

(1) A block of mass m initially at rest at the top of a semi-circular track of radius R, slides down over the frictionless surface from A to B. The surface from B to C has friction and the block reaches a maximum height h there. Determine: (a) Velocity at the bottom (b) the energy lost due to friction. Solution.-

The total available energy is the potential energy at the top at point A:  E = Ep = mgR

((a)  (a) At the bottom at point B, the potential energy is zero and all the available energy has been converted to kinetic energy, then (2) A spring of elastic constant k is placed at the end of a horizontal track. There exists friction Uk   along the distance L between A and B and, there is no friction from B to C. The block of mass m slides over the track towards the spring and, when passing by point A it has a velocity Vo.  Determine: (a) Velocity of the block when passing by point B. (b) The maximum deformation (shrinkage) of the spring when it is pressed by the block. Solution.-

Since there is friction, the block loses part of its original kinetic energy when displacing from A to B. The remaining of the energy, this is, the (kinetic) energy at point B is used to compress the spring. A block initially at rest at a height ‘h’ on a ramp slides down without friction. Once at the bottom of the ramp the block is on a horizontal rough ground which offers a frictional force  (constant ‘Uk’)  to the block, next the block slides along the horizontal ground until friction stops it. Find: (a) the velocity of the block as soon as it gets to the horizontal ground (b) the distance covered by the block on the ground.

Solution.-

In the sketch below, since the ramp offers no friction between A and B the block slides down freely and all its initial gravitational potential energy transforms to kinetic energy at B. Between B and C the block displaces consuming its energy against the friction, finally the block stops at C where all its energy has been consumed by friction. 