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,
Initial potential energy of the spring = Final kinetic energy of the box
1/2 kx² = 1/2 mv²
If the spring constant is doubled, then the new potential energy of the spring is
1/2 (2k)x² = 2(1/2 kx²) = 2 times the initial potential energy.
Therefore, when the box is released, it will have twice the initial kinetic energy and will move up the incline to a new height h'.
1/2 (2k)x² = 1/2 mv² + mgh'
On solving for h', we get
h' = 2x
As the box moves up to a height twice the initial height, its speed will be given by,
v' = √(2gh') = √(2g(2x)) = 11ea83ea_699f_884f_aeff_f1072fcdf62d_TB6394_11 times the initial velocity.

A Box of Mass M Is Pressed Against (But Is