Solution to problem 18.2.10 from the collection of Kepe O.E.

18.2.10

It is necessary to determine how the possible movements of points B of drum 1 and load 2 of the differential gate are related, provided that the radii are equal to R = 2r = 20 cm. The answer is number 4.

To solve the problem it is necessary to use geometric considerations. Let us denote by s1 and s2 the movements of points B and the load, respectively. Then, taking into account that the radii are equal to R, we get:

s1 = 2πR,

s2 = πR.

Thus, the ratio of s1 to s2 will be equal to:

s1/s2 = (2πR)/πR = 2.

So, the ratio of possible displacements is 2, which corresponds to the answer 4 obtained in the problem.

Solution to problem 18.2.10 from the collection of Kepe O..

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Problem 18.2.10 from the collection of Kepe O.?. consists in determining the relationship between possible movements ?sB of point B of drum 1 and ?s2 of load 2 of the differential gate. To solve the problem, it is necessary to take into account that the radii R are equal to 20 cm, and also that R = 2r.

To solve the problem, you can use the formula for calculating the path traveled by a point on a circle, which looks like this:

s = R * α,

where s is the path traveled by a point on the circle, R is the radius of the circle, α is the angle through which the point on the circle has turned.

In order to determine the relationship between possible movements ?sB and ?s2, it is necessary to calculate the corresponding angles α1 and α2 through which points B and load 2 rotated, respectively. Since the radii R are equal to 20 cm, then for point B the angle α1 is equal to ?sB / 20 cm, and for load 2 the angle α2 is equal to ?s2 / 20 cm.

Thus, the relationship between possible movements ?sВ and ?s2 can be determined by the formula:

?sВ / ?s2 = α1 / α2 = (?sВ / 20 cm) / (?s2 / 20 cm) = ?sВ / ?s2 = 4.

So, the answer to problem 18.2.10 from the collection of Kepe O.?. is 4.

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