| Last revised 1999/10/05 |
27. What is the normal force on the head of the mop? [The normal force is the perpendicular component of the force that the floor exerts on the mop.] Incidentally, a sponge (squeegee) mop might be a better visualization of this problem than the mop shown in the illustration in the text.
Don't forget to draw a force diagram.
36. A force diagram is crucial for this problem. The algebra for the problem is simple in principle but not in practice. You might want to use a symbolic-algebra program. Don't, however, be tempted into putting numbers into the equations immediately in order to make the algebra easier. If you get a symbolic answer for parts (a) and (b), you can write the answer to part (c) by inspection. Otherwise part (c) takes exactly as long as (a) and (b) taken together.
What determines whether the rod is in tension or compression: which mass is larger, which coefficient of friction is larger, or something else?
43. In this problem you get an equation where the unknown (x) is differentiated. The equation is simpler if you use v=dx/dt to write the entire equation in terms of v instead of x. There are two ways to approach the equation: (1) Divide the equation by v and integrate with respect to t [if you have had integration in math classes], or (2) substitute the general form
v = A e- B t
into the equation and determining B from the resulting algebraic equation. The constant A can be obtained using the information about the initial speed of the boat.
70. What is the value of the acceleration in this problem?
IX. The pulleys are supposed to be massless and frictionless. Under these conditions, the pulleys serve only to change the direction of the tension in the rope, not to change its magnitude. The tensions immediately left and right of each pulley have the same magnitude. So, what is the relation of the force exerted by the rope on the left-hand block to that exerted by the same rope on the middle block?
Do the tensions in the two ropes have to be the same?
X. Be careful. If you get a funny-looking result, think about what you have done. The correct answer is unexpected but obvious once you get it.
XI. The hint here is included in the problem.