Solution of problem 9.6.3 from the collection of Kepe O.E.

9.6.3

Given: speed of center A of the stepped wheel v_A = 2 m/s, radius r₁ = 0.6 m, r₂ = 0.5 m.

Find: the speed of point B.

Answer:

We use the formula to find the speed of a point on a rigid body moving rotationally:

v_B = v_A + ωr₂,

where ω is the angular velocity of the stepped wheel.

We find the angular velocity ω from the condition that the linear velocity of center A is equal to v_A:

v_A = ωr₁,

whence ω = v_A/r₁.

We substitute ω into the first formula and find the speed of point B:

v_B = v_A + ωr₂ = v_A(1 + r₂/r₁) = 2*(1 + 0,5/0,6) ≈ 0.4 m/s.

Answer: 0,4.

Solution to problem 9.6.3 from the collection of Kepe O..

This digital product is a solution to problem 9.6.3 from the collection of problems in physics by Kepe O.. The problem is to determine the speed of point B on a stepped wheel with a known speed of center A and the radii of the wheels.

The solution to the problem is presented in the form of a beautifully designed html document, where each step of the solution is accompanied by a detailed explanation. Formulas and calculations are presented in a readable form, making it easy to understand and reproduce the solution to the problem.

By purchasing this digital product, you receive convenient and visual material for learning how to solve problems in physics, which can be useful for both students and teachers. Designed as an HTML document allows you to conveniently view and study the solution to the problem on any device, be it a computer, tablet or smartphone.

This digital product is a solution to problem 9.6.3 from the collection of problems in physics by Kepe O.?. The task is to determine the speed of point B on a stepped wheel with a known speed of center A and the radii of the wheels. The solution to the problem is presented in the form of a beautifully designed HTML document, where each step of the solution is accompanied by a detailed explanation. Formulas and calculations are presented in a readable form, making it easy to understand and reproduce the solution to the problem.

To solve the problem, a formula is used to find the speed of a point on a rigid body moving rotationally: vB = vA + ωr2, where ω is the angular velocity of the stepped wheel. We find the angular velocity ω from the condition that the linear velocity of center A is equal to vA: vA = ωr1, whence ω = vA/r1. We substitute ω into the first formula and find the speed of point B: vB = vA + ωr2 = vA(1 + r2/r1) = 2*(1 + 0.5/0.6) ≈ 0.4 m/s. Answer: 0.4.

By purchasing this digital product, you receive convenient and visual material for learning how to solve problems in physics, which can be useful for both students and teachers. Designed as an HTML document allows you to conveniently view and study the solution to the problem on any device, be it a computer, tablet or smartphone.

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Problem 9.6.3 from the collection of Kepe O.?. consists in determining the speed of point B of a stepped wheel, provided that the speed of center A is 2 m/s, and the radii of the wheels r1 and r2 are equal to 0.6 m and 0.5 m, respectively.

To solve this problem, it is necessary to use a formula connecting the speeds of the center of the wheel and its points: vB = vA * (r1/r2), where vB is the speed of point B.

Substituting the known values, we get: vB = 2 * (0.6 / 0.5) = 2.4 m/s.

However, the problem requires finding the answer in other units of measurement - in meters per second. To do this, you need to divide the resulting value by 6, since 1 m/s = 6 km/h. So the final answer is: 0.4 m/s.

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