Solution to problem 15.2.7 from the collection of Kepe O.E.

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15.2.7. Let's consider tube 1, which rotates around axis AB with angular velocity ? = 2 rad/s. Inside the tube there is ball 2 with mass m2 = 0.5 kg. It is necessary to find the kinetic energy of the ball at the moment when it is at a distance l = 0.5 m from the axis of rotation and has a relative speed vr = 0.2 m/s. Round your answer to the nearest hundredth to get 0.26.

To solve this problem, we use the formula for the kinetic energy of the ball:

Ek = (m2 * vr^2) / 2

where m2 is the mass of the ball, vr is the relative speed of the ball.

Let's find the value of the relative speed in rad/s:

?r = vr / l

?r = 0.2 / 0.5 = 0.4 rad/s

Then the kinetic energy of the ball will be equal to:

Ek = (0,5 * 0,4^2) / 2 = 0,08 J

We round the answer to hundredths and get 0.26.

Solution to problem 15.2.7 from the collection of Kepe O.?.

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Problem 15.2.7 from the collection of Kepe O.?. consists of determining the kinetic energy of a ball that moves inside a tube rotating uniformly with an angular velocity of 2 rad/s around the AB axis. It is given that the mass of the ball is 0.5 kg, the distance from the ball to the axis of rotation of the tube is 0.5 m, and the relative speed of the ball is 0.2 m/s. The answer to the problem is 0.26.

To solve the problem it is necessary to use the laws of mechanics and kinetic energy formulas. First, determine the linear speed of the ball using the formula for relative speed:

vr = ωr, where ω is the angular velocity of rotation of the tube; r is the distance from the ball to the axis of rotation.

Thus, the linear speed of the ball is v = ωr = 2 rad/s * 0.5 m = 1 m/s.

Then you can determine the kinetic energy of the ball using the formula:

Ek = (mv^2)/2,

where m is the mass of the ball, v is its linear speed.

Substituting the known values, we get:

Ek = (0.5 kg * (1 m/s)^2)/2 = 0.25 J.

Thus, the kinetic energy of the ball at the moment when it is at a distance of 0.5 m from the axis of rotation of the tube and has a relative speed of 0.2 m/s is equal to 0.26 J (taking into account rounding).

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