Problem-Solving Tips and Understanding Pulleys

1. First, some problem-solving hint(s): Keep in mind that, in any situation where multiple objects are connected, they’re moving together somehow—they have the same (magnitudes of) velocity and acceleration. And conversely: Any object is made of parts that must each obey Newton’s Laws—and (as noted above) must have the same velocities and accelerations as all the other parts. OSU PH 211, Before Class #17

2. Focus: Notice Prep 6-7 problems 3b and 3c…. Don’t forget to do a free-body-diagram of each object in the system—even in simple-looking problems like this. FBD’s often don’t take long, but they reveal a lot. For example, in 3c… even though each cart is moving to the right, how is it accelerating? What’s happening? OSU PH 211, Before Class #17

3. A general discussion of strings, tension and pulleys—what are they, and what do they do? (See also section 7.4 in the textbook.)… – We will work only with ideal (mass-less) strings this term; they will connect masses without adding any mass of their own to the system. So they don’t require any force to accelerate; therefore, the tension at each point in such a string is the same. – This is true even when the ideal strings connect masses via one or more ideal pulleys. An ideal pulley is a mass-less wheel that re-directs the tension of a string wrapped along the wheel’s rim. The wheel is free to turn (without friction), but the string is assumed not to slip; it travels with the wheel’s rim. OSU PH 211, Before Class #17

4. Of course, a free-body diagram will still reveal what must be true about the forces acting on each of several objects connected by ideal strings and ideal pulleys. Example: One key use of a pulley is to “multiply” the tension in the string. Consider this situation, where the block is hanging at rest. How is FT.A, the tension in string A, related to the tension in string B? Do a free-body diagram of the lower pulley wheel. (It has negligible mass, so we can ignore the gravitational force on it, but not the tension forces!) String A FT.A String B block OSU PH 211, Before Class #17