Solution to problem 7.8.16 from the collection of Kepe O.E.

7.8.16

There is a point moving in a circle of radius r = 200 m. From the initial rest position, the point moves with a constant tangential acceleration a? = 1 m/s2. It is necessary to determine the total acceleration of the point at time t = 20 s.

Answer: 2.24.

Based on the conditions of the problem, the point moves along a circle of radius r = 200 m and has an initial rest position. The tangential acceleration of a point is equal to a? = 1 m/s2. It is necessary to find the total acceleration of the point at time t = 20 s.

To solve the problem, we use the formula for calculating the total acceleration of a point, which is the vector sum of tangential acceleration and centripetal acceleration:

a = sqrt(at^2 + ac^2),

where at is tangential acceleration, ac is centripetal acceleration.

Since a point moves in a circle, its centripetal acceleration is equal to:

and = v^2/r,

where v is the speed of the point.

To determine the speed of a point at time t = 20 s, we use the formula for calculating speed for uniformly accelerated motion:

v = at * t.

Thus, the speed of the point at time t = 20 s is equal to:

v = 1 * 20 = 20 m/s.

Substituting the values ​​into the formula for centripetal acceleration, we get:

and = (20^2) / 200 = 2 м/с^2.

Now you can calculate the total acceleration of the point:

a = sqrt((1^2) * (20^2) + (2^2)) = 2.24 m/s^2.

Thus, the total acceleration of the point at time t = 20 s is equal to 2.24 m/s^2.

Solution to problem 7.8.16 from the collection of Kepe O.?.

This digital product is a solution to problem 7.8.16 from the collection of Kepe O.?. in physics. The problem is formulated as follows: a point moves along a circle of radius r = 200 m from a state of rest with constant tangential acceleration a? = 1 m/s2. It is necessary to determine the total acceleration of the point at time t = 20 s.

In this digital product you will find a detailed solution to this problem using the appropriate formulas and a step-by-step explanation of each step of the solution. All calculations are presented in a clear form with a beautiful html design, which makes the material easier to understand.

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This product is a solution to problem 7.8.16 from the collection of Kepe O.?. in physics. The problem describes the movement of a point along a circle of radius 200 m, starting from a state of rest, with a tangential acceleration of 1 m/s². It is necessary to determine the total acceleration of the point at time t=20 s. In the product you will find a detailed description of the solution to the problem with a step-by-step explanation of each step and the use of the corresponding formulas. All calculations are presented in a clear form with a beautiful design, which makes the material easier to understand. This product can be used as an assistant for schoolchildren and students, as well as for anyone interested in physics and wanting to improve their knowledge in this area. By purchasing this product, you will receive a high-quality solution to the problem with a convenient design, which can be used to improve your performance and prepare for exams. The answer to the problem is 2.24 m/s².

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Problem 7.8.16 from the collection of Kepe O.?. is formulated as follows:

There is a point that begins to move along a circle of radius r = 200 m from rest and with constant tangential acceleration a? = 1 m/s². It is necessary to find the total acceleration of the point at time t = 20 s.

To solve the problem, you can use the formula for the total acceleration of a point that moves in a circle with constant angular acceleration:

a = sqrt(a_t^2 + a_r^2),

where a_t is the tangential acceleration of the point, a_r is the radial acceleration of the point.

The tangential acceleration of a point can be found using the formula:

a_t = r * alpha,

where r is the radius of the circle and alpha is the angular acceleration.

Angular acceleration can be found from the formula:

alpha = v / r,

where v is the speed of the point.

The speed of a point on a circle can be found using the formula:

v = omega * r,

where omega is the angular velocity.

Angular velocity can be found from the formula:

omega = phi / t,

where phi is the angle traversed by the point during time t.

The radial acceleration of a point is equal to the acceleration of the center of the circle and is directed along the radius of the circle. Since the point moves in a circle at a constant speed, the radial acceleration is zero.

By substituting all known values ​​into the formulas, you can find the total acceleration of the point at time t = 20 s. The answer should be 2.24 m/s².

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