Chapter 19 Problem 11

This is a question for discussion. There is no right or wrong answer, but some responses may be more reasonable than others. Here or some of my thoughts:

(a) After the first rubber band, additional bands stretched the same amount and pulling in the same direction have the same incremental effect on the acceleration of the block. Forces acting in the same direction on the mass can be added algebraicly, except for the first force which is counterbalanced by some mysterious opposition.

(b) There seems to be a force (friction) which must be overcome before the block can be accelerated by the stretched bands. The opposing frictional force appears to increase with the applied force until the force of less than two but more than one stretched band is applied and the block starts to accelerate. The opposing force then seems to remain fairly constant once the acceleration starts. (This is a complex question.)

(c) It would seem from the graph that there is no accelration with one band stretched by the standard amount.

(d) If we assume that the slope of the graph is due to the mass and that the friction doesn't depend on velocity or acceleration then another surface might cause the intercept to move one way or the other.

Chapter 19 Problem 30 solution

In order to keep the boat in the canal, the acceleration at right angles to the canal must be zero. Therefore the net force on the boat at right angles to the canal must be zero too. That assumes that the boat's velocity is initially straight down the canal. The boy's force must have its y component exactly opposite the net y component of the two men's forces. Any component of the boy's force along the x axis will not help to balance y component of the men's net force but will increase the magnitude of the boy's force. Thus the least force the boy can exert to keep the boat in the canal will be along the -y direction with magnitude -186 N.

There is a net force of the men and boys pulling the boat forward which may be balanced by water resistance.