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, the potential energy stored in the spring when compressed by distance x is transferred to the kinetic energy of the box as it moves up the incline. Therefore, the initial potential energy of the spring (1/2)kx^2 is equal to the final kinetic energy of the box (1/2)mv^2, where v is the velocity of the box when it comes to rest at the highest point of the incline. 
If we use a spring of force constant 2k instead, then the potential energy stored in the spring when compressed by the same distance x would be (1/2)(2k)x^2=2(1/2)kx^2. Therefore, the final kinetic energy of the box would be twice as great as before because the potential energy supplied to the system has doubled. 
The speed of the box at the top of the incline will be determined by the conservation of energy as well since the height it reaches will be determined by its kinetic energy. Since kinetic energy is proportional to the square of the speed, the speed of the box when it comes to rest at the highest point of the incline will be proportional to the square root of its kinetic energy. Therefore, if the kinetic energy is doubled, the speed of the box will be multiplied by the square root of 2, which is approximately 1.41. Therefore, the speed of the box will be 1.41 times as great as before. 
Finally, if the final kinetic energy is twice as great as before and the potential energy was supplied by the same force over the same distance, then the box must have gone up twice as high as before. Therefore, all of the choices listed are correct.

A Box of Mass M Is Pressed Against (But Is