Which of the following statements is true? A) The work done to raise a box onto

Question

Which of the following statements is true?

A) The work done to raise a box onto a platform depends on how fast it is raised.

B) The kinetic energy is independent of the reference frame of the observer.

C) Spring A and B are identical except that A is stiffer than B; that is kA > kB. More work must be expended on spring A if both springs are stretched by the same amount.

D) The kinetic energy of an object depends on the direction of the motion involved.

E) If the Earth revolves around the sun in a perfectly circular orbit, then the sun does work on the Earth.

F) The kinetic energy can never be negative.

Explanation / Answer

A] False

Because work is the integral of the dot product of a force times a displacement. Time does not enter into this definition.

B] False

An object moving with constant velocity(v) in one reference frame has a kinetic energy of 0.5*m*v^2. If I now change my reference frame so that I'm moving with the same constant velocity as the object, then the object will appear to be at rest, and its KE will be zero in that frame.

C] True

Because the force exerted by an "ideal" spring (i.e., one that obeys Hooke's Law) is F = - k*x, where x is the displacement from the "neutral" position of the spring. The force needed to create a displacement is just the negative of this. The work done to displace the spring by an infinitesimal amount is then: dW = k*x dx

Integrating this gives: W = 0.5*k*x^2

For the same displacement, if the spring constant (k) of one spring is larger that that of another, the work needed to displace the "stiffer" spring (the one with the larger constant) is greater.

D]  False

When you square velocity, you remove dependence on its direction.

E] False

  Because the force exerted by the sun on the Earth (assuming a circular orbit) is always perpendicular to the motion of the Earth (the force is radially inward, while the instantaneous dsplacement of the Earth is always along the tangent to the orbit). Work is the dot product of the force and the displacement, and the dot product of two perpendicular vectors is zero.

F] True

KE = 1/2*m*v^2
m is never negative
any number squared is never negative

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

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