*57.  In attempting to pass the puck to a teammate, a hockey player gives it an initial speed of 1.7 m/s. However, this speed is inadequate to compensate for the kinetic friction between the puck and the ice. As a result, the puck travels only one-half the distance between the players before sliding to a halt. What minimum initial speed should the puck have been given so that it reached the teammate, assuming that the same force of kinetic friction acted on the puck everywhere between the two players?

 

Free Body Diagram

Since the normal force and the weight forces are perpendicular to the displacement, so they do no work.  Only the friction force does work.  There is no change in height, so there is no change in gravitational potential energy.  Finally kinetic energy at the end is zero.

 

 

 

 

 

So we have

Solve for v0

 

First pass we know and the puck goes a distance ½ the distance we want

 

And for the second pass

 

Now we are told, the friction force is constant and of course the mass of the puck does not change, so if we take a ratio of the speeds, we can cancel out the variables we do not know.

 

 

 

 

 

 

 

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This page last updated on January 11, 2020