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

When the spring is compressed a distance of 2x, the potential energy stored in the spring is (1/2)k(2x)^2 = 2kx^2, which is four times greater than the potential energy stored in the spring when it is compressed only a distance of x. Since potential energy is converted into kinetic energy as the box slides up the incline, the box will have twice as much kinetic energy just as it moves free of the spring, which means it will be traveling twice as fast as before (since kinetic energy is proportional to the square of the velocity). Therefore, choice B is the best choice.

A Box of Mass M Is Pressed Against (But Is