Question

Two iceboats (one of mass m, one of mass 2m) hold a race on a frictionless,
horizontal, frozen lake. Both iceboats start at rest, and the wind exerts the same constant force on both iceboats.

A. the iceboat of mass m: it has twice as much KE as the other
B. the iceboat of mass m: it has 4 times as much KE as the other
C. the iceboat of mass 2m: it has twice as much KE as the other
D. the iceboat of mass 2m: it has 4 times as much KE as the other
E. they both cross the finish line with the same kinetic energy

WHY E??

1/2mv^2 = 1/2mv^2

1/2 (2m) v^2 = mv^2 ? so the with 2m has more KE ?? why not?

Answer 1

If we use F=ma , and F is the same(as defined by the question) and m is different,then the acceleration(a) of the boat with 2m mass will be half of the acc. of the m mass boat. This means that the 2m mass boat accelerates slower and has a slower speed.

Using Ek= 1/2 m v^2 , with double the mass(2m) , the boat has half the speed(1/2v)
So the boat with mass m will have (1/2mv^2) J of KE
The boat with mass 2m will have(1/2 (2m) (1/2v^2) J of KE. If you equate them together, they are the same. Therefore,the two boats cross the finish line with the same KE

the boat with mass m will have (1/2mv^2) = The boat with mass 2m will have(1/2 (2m) (1/2v^2) J

(1/2mv^2)= (1/2 (2m) (1/2v^2))