Homework Statement
Suppose we have a lake and a layer of ice on top such that the bottom of the lake is maintained at a constant temperature T_{bot} which is above the freezing point of water, and top of the ice is maintained at the air temperature T_{air} which is below the freezing point of...
I don't believe that r is the solution of a quadratic. I actually made a mistake in post #3 which I later corrected. I originally wrote F_c=dm*w*R^2 and corrected it to F_c=dm*w^2*R. When I used the first formula I got a solution with a quadratic as well, which leads me to believe you did not...
Clearly the tension T is a function of the radius R, the natural radius R_0, and k. Naively I guess that T=k(R-R_0) and doing the math I get
R=2*pi*kR_0/(2*pi*k-mw^2)
Interestingly this is of a similar form to the answer I gave to the first problem.
Now my only assumption is T=k(R-R_0)...
Drawing a circle and doing using some geometry we find the radial force is F_r=2Tsin(dθ/2), which is also equal to the centripetal force on the element: F_c=dm*w^2*R. Thus it suffices to find the tension T, presumably in terms of the spring constant k. I'm not sure how to do this...
Homework Statement
Consider a spring of natural length L_0 with constant k which rests on a horizontal frictionless surface. The spring is attached at one end to a fixed post and at the other end to a mass m. Suppose the spring is rotating around the post in a circle with angular velocity w...
Upon further reflection, this makes sense. The motion of m2 can be thought of as rotation about the center of mass plus translation of the center of mass. When the rod is horizontal, the velocity vector due to rotational motion is perpendicular to the ground. But the translation of the center of...
Are you sure about this? I got the same result myself but I thought I must have done something wrong because it is too simple. The masses have to matter, surely,...
Actually, the horizontal impulse given at the top is assumed to be very small, so that it's initial angular velocity is zero. So you don't have to worry about the system becoming airborne before m2 hits the ground.
Now, I still don't think your answer is right, because according to you...
Homework Statement
Consider the following classic problem: we have a rod in the vertical position with a pivot at its midpoint and a spring attached to the bottom of the rod, perpendicular to the rod. The is rotated through a small angle theta to the vertical, and released. Find the period of...
I am trying to proceed using your hints, but I must say I am quite confused by what you are saying.
Ok so first we are looking at different theta's. My theta is the angle of the rod to the horizontal, and if I understand correctly, your theta is the angle of the rod to the vertical?
If we...