Solution to problem 7.7.13 from the collection of Kepe O.E.

Problem 7.7.13: Given a graph of the speed v=v(t) of a point moving in a circle of radius 8 m. It is necessary to determine the moment of time t when the normal acceleration of the point is an = 0.5 m/s. Answer: 3.

Explanation: It is given that the point moves along a circle of radius 8 meters. The normal acceleration of a point is the acceleration directed towards the center of the circle. The modulus of normal acceleration of a point is expressed by the formula аn = v^2/R, where v is the speed of the point, R is the radius of the circle. Substituting the values, we get the equation: v^2/8 = 0.5. Having solved it, we find that v = 2 m/s. Knowing the speed, you can find the time during which the point travels a third of the way around the circle: s = vt = (2πR/3) / v = 8π/3 meters. We divide this distance by speed and get the answer: t = s/v = (8π/3) / 2 = 4π/3 seconds.

Solution to problem 7.7.13 from the collection of Kepe O.?.

This digital product is a solution to problem 7.7.13 from the collection of Kepe O.?. in physics. The solution is presented in a convenient and beautiful html format.

The solution to the problem includes explanations and detailed calculations that will help you solve this problem easily and accurately. It describes the movement of a point along a circle of radius 8 meters and determines the moment in time when the normal acceleration of the point is 0.5 m/s.

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Don't miss the opportunity to improve your knowledge and acquire a solution to problem 7.7.13 from the collection of Kepe O.?. today!

We present to your attention a digital product - a solution to problem 7.7.13 from the collection of Kepe O.?. in physics. This problem describes the movement of a point along a circle of radius 8 meters and requires determining the moment in time when the normal acceleration of the point is 0.5 m/s.

The solution to the problem is presented in a convenient and beautiful html format and includes detailed calculations and explanations that will help you easily and accurately solve this problem.

To solve the problem, we use the formula for the modulus of normal acceleration of a point, which is expressed as an = v^2/R, where v is the speed of the point, R is the radius of the circle. Using this formula, we obtain the equation: v^2/8 = 0.5, from which we find the speed of the point - v = 2 m/s.

Knowing the speed, we can find the time during which the point travels a third of the way around the circle: s = vt = (2πR/3) / v = 8π/3 meters. We divide this distance by speed and get the answer: t = s/v = (8π/3) / 2 = 4π/3 seconds.

By purchasing this digital product, you get access to useful information and can improve your knowledge in the field of physics. Don't miss the opportunity to improve your knowledge and acquire a solution to problem 7.7.13 from the collection of Kepe O.?. today!

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Solution to problem 7.7.13 from the collection of Kepe O.?. is associated with determining the moment of time t, when the normal acceleration of a point moving in a circle of radius 8 m with a speed v=v(t) is equal to 0.5 m/s.

To solve the problem, it is necessary to use the formula for the normal acceleration of a point, which is expressed through the product of the square of the speed of the point and the curvature of the trajectory of motion: аn = v^2 / R, where R is the radius of curvature of the trajectory of the point.

Since in this problem the radius of the circle (R = 8 m) and the desired value of the normal acceleration (an = 0.5 m/s) are known, we can create an equation by substituting the known values: v^2 / 8 = 0.5.

Solving this equation for speed v, we obtain: v = 2 m/s.

Thus, for the normal acceleration of a point to be equal to 0.5 m/s, its speed must be equal to 2 m/s. Let us find the moment of time t corresponding to this speed.

To do this, we use the equation of motion of a point along a circle: s = R * φ, where s is the length of the arc of a circle traversed by the point in time t, and φ is the angle of rotation of the circle during this time.

Since the speed of the point is constant and equal to 2 m/s, then s = v * t. It is also known from geometric considerations that the rotation angle is φ = s / R.

Substituting these values ​​into the equation of motion, we get: v * t / R = φ.

Since we are looking for the moment in time when the angle of rotation φ is equal to 2π (that is, the point has completed a full rotation), we can write the equation: v * t / R = 2π.

Substituting the known values, we get: t = 2π * R / v = 2π * 8 / 2 = 8π s ≈ 25.1 s.

Thus, the answer to problem 7.7.13 from the collection of Kepe O.?. is t = 8π s ≈ 25.1 s.

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