| Last revised 1999/09/22 |
39. Part (b) is a lot easier if you do part (a) analytically.
40. You need to apply F=ma to two different systems. What is the easiest system to use to get the joint acceleration of the two blocks?
54. No hint until I get a question that tells me what I need to hint about.
60. What kind of motion does the block undertake? How do you determine its acceleration? Remember to use the proper component of the forces. How do you determine its motion once you know the acceleration?
If you use a coordinate system with one axis aligned along the inclined plane and therefore with the other axis perpendicular to the plane, you will be able to avoid using the unknown normal force perpendicular to the plane.
73. What keeps the rope from falling?
Ropes generate forces by stretching. As a result a rope exerts whatever force is necessary to provide the motion (or lack of motion) specified by the situation. The force points along the rope, since otherwise the rope would bend, and a force on an object attached to a rope must always point toward the rope (you can't push with a rope). The force that is or would be exerted on an object inserted into the middle of a rope is called the tension in the rope. The tension is along the rope, and has a definite size but doesn't really have a sign, since the two sides of the object would be pulled in opposite directions.
Note that the force exerted on the block by the rope and the force exerted by the block on the rope are a Newton's-Third-Law pair, and so are equal in size. Properly speaking the force exerted on the block is the tension in the rope, but the magnitude of the two forces are necessarily equal.
VIII. See the box near the bottom of the second column on p. 90 of HRW.