4A Home Work Set 5


Work and kinetic energy


1.  You slide a box of books at constant speed up a frictionless ramp of angle theta, applying a force F directed up the slope.  How much work have you done when the box has risen a distance y vertically?  If theta = 30^o, F = 200N and y = 1m, what is the mass of the box?

2.  A force pointing in the x direction is given by F = F_o(x/x_o) where F_o and x_o are constants and x is the position.  Find an expression for the work done byu this force as it acts on an object moveing from x = 0 to x = x_o.

3.  You put your little sister (mass m) on a swing whose chains have lenght L and pull slowly back until the swing makes an angle ø with the vertical.  Show that the wrok you do is mgL(1 - cos ø).

4.  A 15-g ball is shot from a spring gun whose spring has a force constant of 600N/m.  The spring can be compressed 5 cm.  How high can the ball be shot if the gun is aimed vertically?  

5.  An Atwood's machine consists of two different masses, both hanging vertically and connected by an ideal string which passes over a pulley.  Let the masses be M₁ and M₂ and  M₂ = 2M₁.  Initially, M₁ is held fixed a distance y below M₂.  Find the speed of the blocks when they are the same elevation (that is, the same horizontal position, by then each block has moved y/2).  

6.  A small block is attached to a rubberlike material that exerts a froce F_x = -kx - ax² when it is stretched a distance x (x>0), where k and a are constants.  Find the work done on the block by the material when it is stretched from x = 0 to x = A.  

7.  A cord is used to lower verically a block of mass M a distance d at a constand downward acceleration of g/4.  Find the work done by the cord on the block.  

8.  A 30-g bullet initially traveling 500 m/s penetrates 12 cm into a wooden block.  What average force does it exert on the block?