Aptitude Test Problems in Physics Science for Everyone by S Krotov ( PDFDrive.com )

Solutions

1. Mechanics

1.1. Let us first assume that there is no friction.

Then according to the energy conservation law, the

velocity v of the body sliding down the inclined

plane from the height h at the foot is equal to the

velocity which must be imparted to the body for its

ascent to the same height h. Since for a body mov-

ing up and down an inclined plane the magnitude

of acceleration is the same, the time of ascent will

be equal to the time of descent.

If, however, friction is taken into consideration,

the velocity v 1 of the body at the end of the descent

is smaller than the velocity v (due to the work done

against friction), while the velocity v 2 that has to

be imparted to the body for raising it along the

inclined plane is larger than v for the same reason.

Since the descent and ascent occur with constant

(although different) accelerations, and the traversed

path is the same, the time t of descent and the

time t 2 of ascent can be found from the formulas

s=

viti

s— v2t2

2 ' 2 '

where s is the distance covered along the inclined

plane. Since the inequality 0 1 < v 2 is satisfied, it

follows that ti > t 2. Thus, in the presence of slid-

ing friction, the time of descent from the height h

is longer than the time of ascent to the same height.

While solving the problem, we neglected an

air drag. Nevertheless, it can easily be shown that

if an air drag is present in addition to the force of

gravity and the normal reaction of the inclined

plane, the time of descent is always longer than the