Q: Are the answers for the multiple choice questions #34 and 38, Ch 8 correct? For #34, the bucket is just being dropped. There is friction and mass is negligable, so I do not understand why the answer isn't 9.8 m/s^2.
A: ??? there is friction? and the mass of the ROPE is negligeable, but it's still attached to the cylinder and crank, which need to be accelerated, all from the weight of the bucket. So the answer must be LESS than 9.8 m/s². I don't think you read the problem carefully. Don't let that happen on the exam!
Q: I also don't see how you get c. 6.5 m/s^2 for #38 when no numbers are given to you.....
A: This of course assumes gravity at 9.8 m/s², else you'd be right, not enough data. But in τ = I α = I (a/R) both τ (from gravity) and I are proportional to m, so m cancels; and you'll find that R also cancels. So the answer is just (factor) × g, where (factor) comes from the expression for I.
A:I agree the juxtaposition of these two problems is a bit confusing, since they do seem so similar. The difference is, the practice problem asks for the average force that the water exerts, whereas the book problem asks for the force experienced by the diver. The difference? Gravity also exerts a force, so the force of the water must be that of the diver plus the magnitude of the gravitational force (or minus that force, which is itself negative when up is positive).
A: From free-fall you know the energy with which it strikes. This is dissipated by the
resistive force from the ground AND by gravity (the latter being "negative
dissipation"), which you know; so that total force x the unkown distance = KE
you calculated in the first part. No one tells you the mass of the post, so one
must assume that negligible.
For 55, use work-energy. The initial potential energy becomes work of friction
(20 N x 100 m) + final energy. The latter gives you the speed.
8.57: contemplate ½Iw². I is proportional to M, so for the second flywheel is
half. w is doubled, so w² is 4 x as big. Makes an overall factor of 2. Again,
106 should be 10^6.
8.75: This one spells trouble. I think they want you to work it by conservation
of angular momentum, but actually K.E. and hence speed is conserved. So it's
either always or never 5 m/s. (Where would the energy come from to increase the
ball's speed?)
Q: I've been working on the webassign and there is one problem I cannot get even though I've been working on it for a few hours and even asked a few classmates. If you could help me it would be greatly appreciated:
Question:
A large 5.0 kg hoop of radius 3.0 m rolls without slipping.
If the hoop is given an angular speed of 3.5 rad/s while
rolling on the horizontal and allowed to roll up a ramp
inclined at 30° with the horizontal, how far (measured along
the incline) does the hoop roll?
So I formed the equation:
A: What are you doing wrong, you ask? One error is obvious even if you know nothing about the problem but just look at the equation: it's dimensionally wrong! Is that enough to let you solve it correctly?