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1. Fluid Mechanics of a metal cube

What is the title of the book?
2. Fluid Mechanics of a metal cube

I think the same. Are you sure this is the correct answer?
3. Relativistic Velocity Transformations

No, you can't have a speed greater than c. In relativity, you must use Lorentz's velocity transformation equations.
4. Fluid Mechanics of a metal cube

That extra force you mention is in fact the weight of the cube.
5. Inclined plane with spring underneath.

To find the difference in height, try 1.6 m - (0.18 m) sen 40°. Calculate gravitational energy and equate it to elastic potential energy.
6. Inclined plane with spring underneath.

The height h doesn't depends of inclination; it is measured from the ground. From the drawing you made, it is clear that not all gravitational potential energy goes into compressing the spring, if you take ground as a point of 0 gravitational potential energy. Try to find the difference in...
7. Inclined plane with spring underneath.

A spring is comprensed or stretched along only one axis. That said, it seems that the confusion here is what must we use as x. If 12 cm (0.12 m) is the compressed lenght, then x = 0.12 m. But if 0.12 m is the final lenght of the spring, x would be instead 18 cm. One question: is the spring...
8. Kinetic and Potential Energy on Ramps

Part of the kinetic energy is lost due to friction, and part is converted to gravitational potential energy. Ef - Ei = -Fd = mgh - (1/2)mv^2
9. Rotational equilibrium question

Right, the rope makes an angle of 100° with the body. With this in mind, you can draw a component vector that begins from the body and goes up to the tip of the tension vector, in such way that the component is perpendicular to the body. You have then a 90°-80°-10° triangle, from which you can...
10. Using hookes law to find impulse

Find the function F that defines force (it is a sine or cosine, from what you told). Integrate it over the time interval from 0 to 2 seconds.
11. Two cylinders rolling without slipping

Yes, friction forces are applied at different distances from the axis. That said, the torque is greater for cilinder A, and it comes first. One question: is the lower part of cilinder B contributing to normal force? If it isn't, the problem is now solved.
12. Two cylinders rolling without slipping

I got it. The difference in the radius of cilinder A and the radius of the bits of cilinder B should account for the difference in angular speed...
13. Two cylinders rolling without slipping

But, if the inner surfaces that are in contact to the two sides (bases) of the cilinder are not frictionless, there would be a reduction of the torque... And it would also reduce kinetic energy... Anyway, ignoring that, all seems to indicate that they come at the same time.
14. Two cylinders rolling without slipping

But, if the inner surfaces that are in contact to the two sides (bases) of the cilinder are not frictionless, there would be a reduction of the torque... And they would also reduce kinetic energy... Anyway, all seems to indicate that they come at the same time.
15. Two cylinders rolling without slipping

If both cilinders have the same normal force (which is evenly distributed in the bits), then the friction force is the same, and they come to the floor at the same time. Cilinder B could be lower than A, but I think we can ignore this.
16. Angular velocity of cylinder

Try to ignore translation. It seems that there is just a rotation, since the axis doesn't move.
17. Impulse, momentum and efficiency to find height formula

Gneill, I think that efficiency here refers to energy; in other words, only 82% initially available energy is useful, and the other 18% is converted to other forms of energy.
18. Impulse, momentum and efficiency to find height formula

I would calculate kinetic energy (it is not the same as the potential energy, since the efficiency is less than 100%). Then, I would find speed, and later calculate the speed after the inelastic collision. Then, I would use conservation of energy.
19. Two cylinders rolling without slipping

Mmm... do the cilindrical bits have mass? If they don't, then they would not affect the moment of inertia... If you have some diagram or picture you can upload, if would greatly help in understanding the problem :)
20. Angular velocity of cylinder

You must apply parallel-axis theorem to find the moment of inertia (since the axis doesn't pass through the center of mass). Take in account the displacement of the center of mass and the rotational and translational kinetic energies when applying conservation of energy. Remember this equation...
21. Compute acceleration and tension in the cord

Another way to solve this problem is to use just two directions for forces. It may sound crazy, but I have seen this procedure in two or more textbooks. The positive direction would the direction of motion (the direction of falling of the 12-kg block). This way, if m1 is the 12-kg block, and...
22. Relative time space travel

C = 3 x 10^8 m/s. Remember this: the difference in ages will be the difference in the proper time and dilated time.
23. Box being pushed up an inclined plane

To find the components of the weight, draw an angle formed by the vector of weight and a line perpendicular to and under the surface. This angle is equal to the angle of inclination of the plane. Make the x axis parallel to the surface, so the y axis would be perpendicular to the surface and...
24. Simple angular speed problem

If angular momentum doesn't change, then the product of the initial angular speed and moment of inertia is equal to the product of the final angular speed and final moment of inertia.
25. Need to find the net force and the average force .

The heat would be all the kinetic energy lost (neglecting sound) when the bullet comes to rest.
26. Need to find the net force and the average force .

Mmmm... I have just tried to solve this problem using the equation of kinematics I gave and the work-kinetic energy theorem and both gave me that the average force is 32000 N. Do you know what is the correct answer (from the textbook, if you took the problem from one)? About using momentum...
27. Need to find the net force and the average force .

That would be possible only if the acceleration is constant. I suppose it isn't, so the work-kinetic energy theorem seems to be the only option.
28. Need to find the net force and the average force .

Try using this equation: 2ax = (vf)^2 - (vi)^2. Find the acceleration. Use Newton's second law to calculate force. This is the only possible solution I can see. Note: use above equation only if a is constant. I like your approach using work-kinetic energy theorem. One point: the force...
29. Calculating Moment of Inertia of a cube

Ok, the only possible way (at least for me) is performing a triple integral. This integral, however is easy to solve, but a bit tedious. Make r^2 = x^2 + y^2. Integrate dm = p dV over the region ocupied by the cube (the limits of integration are 0 to L for all three axis). Remember that dV = dx...
30. Simple angular speed problem

The reduction of mass makes the moment of inertia smaller. If angular momentum is conserved, how do you think would angular speed change? It is easy to tell it taking in account what I said above.