The frequency of the pendulum is independent of the mass on the end. (c)
This means that it doesn't matter if you hang a piece of spaghetti or a school bus from the bottom end. If there is no air resistance, and no friction at the top end, and the string has no mass, then the time it takes the pendulum to swing from one side to the other <u><em>only</em></u> depends on the <u><em>length</em></u> of the string.
If my math is right its A) 7
because 189 divided by 27 is 7
The work done will be equal to the potential energy of the piano at the final position
P.E=m.g.h
.consider the plank the hypotenuse of the right triangle formed with the ground
.let x be the angle with the ground=31.6°
.h be the side opposite to the angle x (h is the final height of the piano)
.let L be the length of the plank
sinx=opposite side / hypotenuse
= h/L
then h=L.sinx=3.49×sin31.6°=0.638m
weight w=m.g
m=w/g=3858/10=385.8kg
Consider Gravity g=10m/s2
then P.E.=m.g.h=385.8kg×10×0.638=2461.404J
then Work W=P.E.=2451.404J
were solving for v velocity of the ball after it has hit the bottle. a. momentum ->p=mv->ball + bottle momentum during hit = ball + bottle momentum after hit-> ball (.5*21)+ bottle (.2*0) (it's 0 because the the bottle is standing still) = ball after hit (.5*v)+bottle after hit (.2*30) -> 10.5+0=.5v+6 ->4.5=.5v->v=9m/s
b. if bottle was heavier the ball would be slower so final velocity would decrease
