Recent content by runningninja

I apologize, my previous statement was incorrect. Since the mass is moving downward, the tension has to support the accelerations of both gravity and of the mass, and thus T = m(g+a). Your second statement is correct.

Because it is a one dimensional collision. The first object has to bounce backwards because there is no other place for it to go. Even if I omit the minus sign, I get 8/81 for the fraction.

Yes, t = mg - ma. But, for clarity, draw a free-body diagram of the block and sum your forces.

Homework Statement "A body of mass m, moving with velocity v, collides with a body of mass 2m at rest, in a head-on collision. The coefficient of restitution is 1/3. If the 2m body has a specific heat c, and if it is assumed that the two bodies share the heat generated in the collision equally...

Isn't 1 - sin2θ just cos2θ?

The new integral you made up is solvable however. Do a u substitution.

Assuming a standard coordinate system, the x component of the velocity still changes at a constant rate, meaning the x acceleration remains constant.

I don't know if you set up the integral correctly or not, but by factoring out a b you can do a nice trigonometric substitution for it. The math is a tad bit hairy, but if you are already doing differential equations, it shouldn't be too much of a problem.

You're thinking in the correct direction in terms of Newton's Laws, but there is a much easier way to approach this using energy (as voko said). Energy will give you the final distance from equilibrium, but you just need to figure out how to use impulse to solve for your initial energy.

We know that the first derivative represents the slope of the tangent line to a curve at any particular point. We know that the second derivative represents the concavity of the curve. Or, the first derivative represents the rate of change of a function, and the second derivative represents the...

Finding the critical points of a function means where the function's derivative is either zero or undefined. So when you get a set of critical points, you are solving for both where the derivative is 0 and/or undefined. Take the tangent function for example, which has a vertical asymptote every...

It should be possible to have a negative energy. Work can be negative (because it is Force times displacement, either of which can be negative), so the change in energy can be negative, which means you can have negative energy.

Would the restoring force then be the force of the water on the floe? How would that create simple harmonic motion?

The buoyancy force is defined as the difference in pressures on the top and bottom of an object submerged in a fluid. When an object is pushing on the top surface of a fluid from underneath, the force of surface tension begins to act downward on the object, preventing it from breaking the...

I agree with most of what was said above, except for the part about the derivations. I've gone through the mechanics part of the text, and much of the time the explanations were more clear than lecture. I suppose it depends on the person. The book is very much on the gregarious side though.