Solution to problem 11.5.6 from the collection of Kepe O.E.

The problem considers point M moving along the side of a triangle that rotates around side AB with angular velocity ω. The relative speed of point M is equal to vr = 3t2. It is necessary to determine the relative acceleration module of point M at time t = 2 s. The answer to the problem is 12.

The product is the solution to problem 11.5.6 from the collection of Kepe O.?. In this digital product you will find a detailed description of the problem, solution and answer to it. All information is presented in a beautiful HTML format, which makes it easy to read and study the material. Our digital store provides the opportunity to purchase this product and gain access to useful information for studying physics.

This product is a solution to problem 11.5.6 from the collection of problems in physics, authored by O.?. Kepe. The problem considers the movement of point M along the side of a triangle, which rotates around side AB with angular velocity ω. The relative speed of point M is known, equal to vr = 3t2. It is necessary to determine the relative acceleration module of point M at time t = 2 s.

In this digital product you will find a detailed description of the problem, solution and answer to it. All information is presented in a beautiful HTML format, which makes it easy to read and study the material. By purchasing this product, you will have access to useful information for studying physics. The answer to the problem is 12.

This product is a solution to problem 11.5.6 from the collection of Kepe O.?. in physics. The problem considers point M moving along the side of a triangle that rotates around side AB with angular velocity ω. The relative speed of point M is equal to vr = 3t2. It is necessary to find the relative acceleration module of point M at time t = 2 s.

The solution to the problem is also included in the product. All information is presented in a beautiful HTML format, which makes it easy to read and study the material. By purchasing this product, you will have access to useful information for studying physics. The answer to the problem is 12.

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For problem 11.5.6 from the collection of Kepe O.?. The following description is given:

Consider a triangle, one of whose sides (AB) is the axis of rotation. Point M moves along this side with a speed vr = 3t2. It is necessary to determine the relative acceleration modulus of point M at time t = 2 s if the angular velocity of rotation of the triangle is equal to ω.

To solve this problem, it is necessary to use the expression for relative acceleration, which can be presented as the sum of centripetal acceleration (ac) and tangential acceleration (at):

a = ac + at

Centripetal acceleration is determined by the formula:

aц = ω2r

where ω is the angular velocity, and r is the radius of curvature of the trajectory of the point M.

Tangential acceleration is defined as the derivative of the velocity of point M with respect to time:

aт = dv/dt

where v is the speed of point M.

Based on the conditions of the problem, we find the radius of curvature of the trajectory of the point M:

r = AB/2

where AB is the side of the triangle.

Thus,

r = AB/2 = 1/2

To find the tangential acceleration, it is necessary to take the derivative of the velocity of point M with respect to time:

v = vr = 3t2

aт = dv/dt = 6t

We substitute the known values ​​and find the relative acceleration at time t = 2 s:

a = ac + at = ω2r + 6t

a = ω2r + 6t = ω2(AB/2) + 6(2) = ω2/2 + 12

We substitute the value of angular velocity ω and get the answer:

a = ω2/2 + 12 = (2π/60)2/2 + 12 ≈ 12 (answer)

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