A box of mass m is pressed against (but is not attached to)an ideal spring of force constant k and negligible mass,compressing the spring a distance x.After it is released,the box slides up a frictionless incline as shown in the figure and eventually stops.If we repeat this experiment but instead compress the spring a distance of 2x
A)the box will go up the incline twice as high as before.
B)just as it moves free of the spring,the box will be traveling twice as fast as before.
C)just as it moves free of the spring,the box will be traveling four times as fast as before.
D)just as it moves free of the spring,the box will have twice as much kinetic energy as before.
E)just before it is released,the box has twice as much elastic potential energy as before.

Question

A box of mass m is pressed against (but is not attached to)an ideal spring of force constant k and negligible mass,compressing the spring a distance x.After it is released,the box slides up a frictionless incline as shown in the figure and eventually stops.If we repeat this experiment but instead compress the spring a distance of 2x 
A)the box will go up the incline twice as high as before. 
B)just as it moves free of the spring,the box will be traveling twice as fast as before. 
C)just as it moves free of the spring,the box will be traveling four times as fast as before. 
D)just as it moves free of the spring,the box will have twice as much kinetic energy as before. 
E)just before it is released,the box has twice as much elastic potential energy as before.

Quizplus · Accepted Answer

The potential energy stored in a spring is given by $U=\frac{1}{2}kx^2$. As the spring is compressed by a distance of 2x instead of x, the potential energy stored in it becomes $\frac{1}{2}k(2x)^2=2kx^2$. When the box is released, this potential energy is converted into kinetic energy. Since kinetic energy is directly proportional to the square of the velocity, if the potential energy is doubled, the velocity of the box just as it moves free of the spring will be $\sqrt{2}$ times greater than before. Therefore, the correct answer is B.

A Box of Mass M Is Pressed Against (But Is