Solution to problem 15.5.5 from the collection of Kepe O.E.

Rotating crank 1 has an angular velocity? = 10 rad/s and drives wheel 2 weighing 1 kg, which can be considered a homogeneous disk. The moment of inertia of the crank relative to the axis of rotation is 0.1 kg • m2. The radius of the wheel is R = 3r = 0.6 m. It is necessary to determine the kinetic energy of the mechanism.

To solve the problem, it is necessary to find the angular speed of rotation of wheel 2. To do this, you can use the law of conservation of angular momentum, according to which the angular momentum of a closed system remains constant if it is not acted upon by external moments. Thus, the angular momentum of the crank must be equal to the angular momentum of the wheel.

The moment of inertia of the wheel can be found using the formula I = (mR^2)/2, where m is the mass of the wheel, R is its radius. Substituting the values, we obtain I = 0.3 kg • m2.

Taking into account the law of conservation of angular momentum, we can write the equation:

I1 ?1 = I2 ?2,

where I1 is the moment of inertia of the crank, ?1 is its angular velocity, ?2 is the angular speed of the wheel.

From here we find ?2 = I1 ?1 / I2 = 0.1*10 / 0.3 = 3.33 rad/s.

The kinetic energy of the wheel can be found using the formula:

E = (I2 ?2^2)/2 + (mR^2 ?2^2)/2,

where the first term corresponds to the kinetic energy of rotation of the wheel around its axis, and the second - the energy associated with its movement together with the crank.

Substituting the values, we get E = (0.33,33^2)/2 + (10.6^2*3.33^2)/2 = 17 J. Answer: 17.

Solution to problem 15.5.5 from the collection of Kepe O.?.

This digital product is a solution to problem 15.5.5 from the collection of Kepe O.?. in mechanics. The solution is completed by an experienced teacher and presented in PDF format.

Problem 15.5.5 is a classic mechanics problem and considers the motion of a wheel driven by a crank. The solution to the problem includes detailed calculations and a step-by-step explanation of the solution.

By purchasing this digital product, you receive a ready-made solution to the problem, which can be used to prepare for an exam or for a deeper understanding of the topic.

The PDF format allows you to conveniently read and print the solution to the problem, as well as store it on electronic devices.

Don't miss the opportunity to purchase a useful product for learning and developing your knowledge in the field of mechanics!

Cost: 100 rubles

The digital product you are purchasing is a solution to problem 15.5.5 from the collection by Kepe O.?. in mechanics. The problem considers the motion of a wheel driven by a crank and requires determining the kinetic energy of the mechanism.

The solution to the problem was completed by an experienced teacher and presented in PDF format. It includes detailed calculations and a step-by-step explanation of the solution.

To solve the problem, it is necessary to find the angular speed of rotation of the wheel using the law of conservation of angular momentum. Then, taking into account the moment of inertia of the wheel, you can find the kinetic energy of the mechanism using the formulas.

By purchasing this digital product, you receive useful material for preparing for an exam or for a deeper understanding of a mechanics topic. The PDF format allows you to conveniently read and print the solution to the problem, as well as store it on electronic devices.

The cost of a digital product is 100 rubles.

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solution to problem 15.5.5 from the collection of Kepe O.?.

A problem is given about a mechanism consisting of a crank and a wheel. The crank rotates with an angular velocity of 10 rad/s, driving a wheel with a mass of 1 kg and a radius of 0.6 m. The moment of inertia of the crank relative to the axis of rotation is 0.1 kg•m2. It is required to determine the kinetic energy of the mechanism.

To solve the problem, you need to calculate the kinetic energy of the wheel and crank and add them together. The kinetic energy of the wheel is determined by the formula K = (1/2)•m•v2, where m is the mass of the wheel, v is the speed of its movement. The wheel speed can be found by knowing the angular speed of rotation of the crank and the radius of the wheel: v = R•?, where R is the radius of the wheel, ? - angular speed of rotation of the crank. Thus, the kinetic energy of the wheel is equal to K1 = (1/2)•m•R2•?2.

The kinetic energy of the crank is determined by the formula K = (1/2)•I•?2, where I is the moment of inertia of the crank relative to the axis of rotation. Substituting the data from the condition, we obtain K2 = (1/2)•0.1•102 = 5 J.

Thus, the total kinetic energy of the mechanism is equal to K = K1 + K2 = (1/2)•m•R2•?2 + 5 J. Substituting numerical values, we obtain K = (1/2)•1•0.62•102 + 5 = 17 J. Answer: 17.

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