8. A group of wildlife biologists needed to know how many frogs there were in a large pond. In order to make a reasonable estimate of this number, they captured 100
frogs from the pond and placed a band on one leg of each frog before releasing
them back into the pond.' Three weeks later, when 100 frogs were again captured,
there were 12 banded frogs and 88 unbanded frogs. What would you estimate to
be the total number of frogs in the pond? Explain your answer.

As you are trying to move a heavy box of mass m, you realize that it is too heavy for you to lift by yourself. there is no one around to , so you attach an ideal pulley to the box and a massless rope to the ceiling, which you wrap around the pulley. you pull up on the rope to lift the box. use g for the magnitude of the acceleration due to gravity and neglect friction forces. once you have pulled hard enough to start the box moving upward, what is the magnitude f of the upward force you must apply to the rope to start raising the box with constant velocity? express the magnitude of the force in terms of m, the mass of the box.