PHYSICS QUESTIONS- ENERGY PROBLEMS (DIAGRAMS INCLUDeD!)?

Question

hey everyone ive got some physics probs that i need answers too to study from in the future, i tried scanning the page but it didnt work properly so i made them all up on paint, i did the best i could so try and work with it =]

thanksss in advance

links:

1. http://i34.photobucket.com/albums/d130/MATTRAINES/q2.jpg?t=1164668205

2. http://i34.photobucket.com/albums/d130/MATTRAINES/q3.jpg?t=1164668225


3. http://i34.photobucket.com/albums/d130/MATTRAINES/q4.jpg?t=1164668264


4. http://i34.photobucket.com/albums/d130/MATTRAINES/q5.jpg?t=1164668771

Answer 1

1) use conservation of energy:

1/2*m*vb^2=1/2*m*va^2+m*g*h

m=2
va=4
g=9.8
h=6
v=sqrt(16+2*9.8*6)
=11.56 m/s

2.
Same concept
m*g*(bounce)=1/2*m*va^2+m*g*(drop)
mass divides out
bounce=va^2/(2*g)+drop
va=6
g=9.8
drop=4
bounce=36/(2*9.8) + 4
=5.84 m

3) since the mass isn't moving it's offset the 300N force

4)
Again, use conservation of energy
Note that the change in potential energy will subtract from the kinetic energy of the start

1/2*m*vc^2=1/2*m*va^2-m*g*delta-h
the mass divides out
va=8
delta-h=2
g=9.8
vc=sqrt(64-2*9.8*2)
=4.98

j

Answer 2

because the pressure varies as a function of x, you'll favor to do an integration to remedy this. also, take careful note that Fx is in the "minus-x" direction, i.e. it really is DECELERATING the body. (a) Your calculation of the kinetic power at x=3 looks perfect: KE(3) = (a million/2)*m*v^2 = (a million/2)*2*(8^2) = sixty 4 J Fx = -6x The power removed from the body is in the kind of work, because it strikes alongside the axis. dW = F*dx = -6x*dx In shifting from x=3 to x=4, the artwork further is: W = critical from 3 to 4 of (-6x*dx) = -6x^2/2 = -3x^2 evaluated at 3 to 4 W = -3*(4^2) + 3*(3^2) = -3*(16 - 9) = -21 J KE(4) = KE(3) - 21 J = sixty 4 - 21 = 40 3 J the cost will be derived: KE = (a million/2)*m*v^2 v = sqrt( 2*KE/m) = sqrt( 2*40 3/2) = 6.6 m/s (b) The KE at v = 5 m/s is: (a million/2)*m*v^2 = 25 J So, the replace in KE is: sixty 4 - 25 = 39J, or... the artwork further to the body in decelerating it really is -39 J. This time, enable "x" stay because the better decrease of the blend: W = critical from 3 to x (-6x*dx) = -3x^2 evaluated from 3 to x W = -3*x^2 + 27 = -39 J -3x^2 = -39 - 27 = -sixty six x^2 = 22 x = sqrt(22) = 4.7 m