Solved University-Physics Problems

Physics 1:  Mechanics:  Energy invested against friction 

Javier Montenegro Joo


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(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.


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.


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.



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[3] 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.  


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.


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