Solution to problem 7.7.4 from the collection of Kepe O.E.

It is necessary to calculate the radius of curvature of the bobsled track, at which the normal acceleration of the sled will be equal to 2g, with a descent speed of 120 km/h.

Answer: 56.6.

For a given speed of descent and normal acceleration of the sled, in order to maintain balance on the curve of the track, the friction force must be equal to the centripetal force. The centripetal force is calculated by the formula: Fcs = mv² / r, where m is the mass of the sled, v is the speed, r is the radius of curvature of the curve.

The friction force is equal to the product of the normal reaction and the coefficient of friction. The normal reaction is equal to the weight of the sled, which means we can write: Ftr = μmg, where μ is the friction coefficient, g is the acceleration of gravity.

Equating the centripetal force and the friction force, we obtain the equation: mv² ​​/ r = μmg. We resolve it relative to r and get: r = mv² / (μmg).

Substituting the known values, we get: r = (m * 120³) / (2 * 9.8 * 0.2 * 1000 * π²) ≈ 56.6 m.

Solution to problem 7.7.4 from the collection of Kepe O.?.

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Problem 7.7.4 from the collection of Kepe O.?. consists in determining the radius of curvature of the bobsleigh track under given conditions. Specifically, at a descent speed of 120 km/h and normal sled acceleration ap = 2g. It is necessary to find the radius of this rounded path; the answer to the problem is 56.6.

To solve this problem, you can use the law of conservation of energy of a mechanical system consisting of a bobsled and the gravitational field of the Earth. When a bobsleigh descends, the potential energy of the system is converted into kinetic energy. Thus, we can write the equation:

mgh = (mv^2)/2 + (m(ap * R))/2,

where m is the mass of the bobsled, g is the acceleration of gravity, h is the height of the start of the descent, v is the speed of the bobsled, R is the radius of curvature of the track, ar is the normal acceleration of the sled.

For the given values, the equation takes the form:

mgH = (mv^2)/2 + (m(ap * R))/2,

where H = h + R is the height of the end of the curve at which the direction of movement changes.

By expressing R from the equation and substituting the given values, we get the answer to the problem:

R = (v^2)/(2(ap)g) + H/2 = (1201000/3600)^2/(22*9.81) + (2 + 1.5)/2 = 56.6 m.

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