A box of mass m is pressed against (but is not attached to) an ideal spring of f

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 3x ]

Answers:

just before it is released, the box has three times as much elastic potential energy as before.

just as it moves free of the spring, the box will be traveling three times as fast as before.

just as it moves free of the spring, the box will have twice as much kinetic energy as before.

the box will go up the incline twice as high as before.

just as it moves free of the spring, the box will be traveling four times as fast as before.

Explanation / Answer

(a) just before it is released, the box has three times as much elastic potential energy as before.-No

elastic potential energy=0.5*k*x^2

if x=3x

elastic potential energy will be 9 times

(b)just as it moves free of the spring, the box will be traveling three times as fast as before-Yes

when it separates from spring

kinetic energy=0.5*m*v^2

from conservation of energy

0.5mv^2=0.5kx^2

if x=3x

then v will also be 3v

(c)just as it moves free of the spring, the box will have twice as much kinetic energy as before.-No

initial kinetic energy=0.5mv^2

final kinetic energy=0.5m*9v^2

so it will be 9 times

(d)the box will go up the incline twice as high as before.-No

by conservation of energy

initially

0.5*mv^2 =mgh=>h=0.5v^2/g

finally

0.5*m*9*v^2=mgh=>h=4.5v^2/g

so it will be 9 times

(d)just as it moves free of the spring, the box will be traveling four times as fast as before-No

it will travel 3 times as fast

Only (b) is correct

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.