Mechanical Energy in a Closed System

[Sisyphus]

Hello homework forum,

I am working on some mechanical energy questions right now for Physics class, and I have a quick question.

A mass (1.00 kg) is projected vertically upwards at a speed of 40.0 m/s. There is a frictional force of 5.0 N acting on the mass.

The question that's bothering me is one that is asking the speed of the mass at the instant that it lands again at the point of projection: since h=0 here, would the frictional energy be 0? (since the work done against friction is the product of the force of friction and displacement) making the Mechanical Energy equal to Kinetic Energy?

This is kind of counter-intuitive to me as it seems that even at the instant of impact, the mass would have been acting against friction. Or is it that at the moment that the mass comes back to its point of projection, the work done against friction transfers to kinetic energy (much like how potential energy is being transferred into kinetic energy while the object is falling)?

I hope someone can make sense of my question here.

 

[Tide]

If I understand the setup correctly then the force acting on the object as it rises is its weight plus the frictional force (acting downward) while on its descent the force is the weight minus the frictional force (again, acting downward). Can you use that to determine how high the onject rises and what its speed is at the time of impact with the ground?

 

[Sisyphus]

If I understand the setup correctly then the force acting on the object as it rises is its weight plus the frictional force (acting downward) while on its descent the force is the weight minus the frictional force (again, acting downward). Can you use that to determine how high the onject rises and what its speed is at the time of impact with the ground?

Thanks for giving me a new way of looking at the problem. I think I have it now. (I get a height of 54m and a final velocity of 22.8 m/s)