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 use a spring having force constant 2k
A) the box will go up the incline twice as high as before.
B) just as it moves free of the spring, the kinetic energy of the box will be twice as great as before.
C) just as it moves free of the spring, the speed of the box will be times as great as before.
D) All of the above choices are correct.
E) None of the above choices is correct.

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 use a spring having force constant 2k 
A) the box will go up the incline twice as high as before. 
B) just as it moves free of the spring, the kinetic energy of the box will be twice as great as before. 
C) just as it moves free of the spring, the speed of the box will be times as great as before. 
D) All of the above choices are correct. 
E) None of the above choices is correct.

Quizplus · Accepted Answer

According to the conservation of energy principle, the initial potential energy stored in the spring is converted into the kinetic energy of the box as it moves up the incline. Therefore, the speed of the box when it moves free of the spring depends on the initial potential energy and the mass of the box, but not on the force constant of the spring.

However, the maximum height reached by the box depends on both the initial potential energy and the force constant of the spring. Thus, if the force constant of the spring is doubled, the maximum height reached by the box will also be doubled.

Since the kinetic energy of the box is proportional to the square of its speed, if the maximum height reached by the box is doubled, the speed of the box when it moves free of the spring will increase by a factor of sqrt(2), or approximately 1.41.

Therefore, all of the above choices are correct.

A Box of Mass M Is Pressed Against (But Is