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 = 30o, F = 200N and y = 1m, what is the mass of the box?
2. A force pointing in the x direction is given by F = Fo(x/xo) where Fo and xo
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 = xo.
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 Fx = -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 running man has half the kinetic energy of a boy half his mass.
The man speeds up by 1.0m/s and then has the same kinetic energy
as the boy. What were the original speeds of (a) the man
and (b) the boy?
9. 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?