Irodov – Problems in General Physics

Fig. 1.30. Fig. 1.31.

A A

axi byj, where i and j are the unit vectors of the x and y axes,
and a and b are constants. Find out whether these fields are potential.
1.134. A body of mass in is pushed with the initial velocity vo
up an inclined plane set at an angle a to the horizontal. The friction
coefficient is equal to k. What distance will the body cover before it
stops and what work do the friction forces perform over this dis-
tance?
1.135. A small disc A slides down with initial velocity equal to
zero from the top of a smooth hill of height H having a horizontal
portion (Fig. 1.30). What must be the height of the horizontal por-
tion h to ensure the maximum distance s covered by the disc? What
is it equal to?
1.136. A small body A starts sliding from the height h down an
inclined groove passing into a half-circle of radius h/2 (Fig. 1.31).

Assuming the friction to be negligible, find the velocity of the body

at the highest point of its trajectory (after breaking off the groove).

1.137. A ball of mass m is suspended by a thread of length 1. With

what minimum velocity has the point of suspension to be shifted

in the horizontal direction for the ball to move along the circle about

that point? What will be the tension of the thread at the moment it

will be passing the horizontal position?

1.138. A horizontal plane supports a stationary vertical cylinder

of radius R and a disc A attached to the cylinder by a horizontal

thread AB of length /^0 (Fig. 1.32, top view). An initial velocity vo

B

Fig. 1.32.

B

Fig. 1.33.

is imparted to the disc as shown in the figure. How long will it

move along the plane until it strikes against the cylinder? The fric-

tion is assumed to be absent.

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