Physics question on Work?

Question

1.) can work be negative? (i.e. if you go up 1 flight of stairs (10m) and then go back done net work is 0?)
2.) If the work done on an object doubles its kinetic energy, does it double its velocity? If not, by what ratio does it change the velocity?- is the answer 1/4?

Answer 1

Work can be negative. The definition of work is:

F*d*cosa

Where F is the magnitude of the force doing the work, d is the distance over which the force is applied, and 'a' is the angle between the direction of the force, and the direction of the displacement.

So if the force is in the opposite direction to the displacement, the angle between them is 180 degrees. cos 180 = -1, so the work is negative:

Work = F*d*cosa a=180
F*d*cos180 = F*d*(-1)= -(F*d)=Work

Of course F and d are always positive, since they are magnitudes.

In your example concerning the flight of stairs, you wouldn't need to think about negative work. Since you end up where you started, your total displacement is 0. Plug that into the work equation and you get: Work=F*d*cosa=F*0*cosa=0

Kinetic Energy= 0.5*m*v^2

Assuming your work doesn't change the mass, the velocity must change in such a way such that v^2 is twice as large. This is easily done, just multiply v by the square root of 2. If you multiplied it by 1/4, it would decrease the Kinetic Energy.

Answer 2

1) You are talking about `potential energy.The 0 of this energy depends on the plane of reference.Below this plane potential energy is negative.
2) The velocity increases by the factor sqrt(2)