Solution to problem 7.7.3 from the collection of Kepe O.E.

7.7.3

Given: the point moves in a circle according to the equation s = 5t - 0.4t².

Find: time t when normal acceleration is a_p = 0.

Answer:

Normal acceleration is determined by the formula a_p = v²/r, where v is the speed and r is the radius of curvature.

To find the speed, we find the derivative of the equation s = 5t - 0.4t²:

v = ds/dt = 5 - 0,8t

The radius of curvature can be found from the relation r = v²/a_p:

r = v²/a_p = (5 - 0,8t)²/a_p

Substituting the expression for speed and normal acceleration into this expression for the radius of curvature, we obtain:

r = (5 - 0,8t)²/a_p = (5 - 0,8t)²/((v²)/r) = (5 - 0,8t)²/(25 - 4t + 0.64t²).

Condition a_p = 0 means that the radius of curvature is infinitely large, which means that the movement of the point becomes uniform, i.e. the speed does not change.

From the equation for speed v = 5 - 0.8t it follows that the speed does not change at t = 6.25. Let's check that at this moment the normal acceleration is zero:

a_p = v²/r = (5 - 0,8*6,25)²/((25 - 4*6,25 + 0,64*6,25²)) = 0.

Answer: time t, when normal acceleration is a_p = 0, equals 6.25.

Solution to problem 7.7.3 from the collection of Kepe O..

This product is a digital product, it is a solution to problem 7.7.3 from the collection of problems in physics by Kepe O.. The problem considers the motion of a point in a circle, described by the equation s = 5t - 0.4t². It is necessary to determine the time t when the normal acceleration a_p equals zero.

The solution to the problem is presented in the form of a beautifully designed html document, which allows you to conveniently study each stage of solving the problem. The user can easily find the necessary formulas and calculations, as well as get the answer to the problem.

By purchasing this digital product, you receive a ready-made solution to problem 7.7.3 from the collection of Kepe O.. in a convenient format that can be saved and used for independent study of the material or preparation for exams.

This product is a digital product, which is a solution to problem 7.7.3 from the collection of problems in physics by Kepe O.?. The problem considers the motion of a point in a circle, described by the equation s = 5t - 0.4t2, and it is necessary to determine the time t when the normal acceleration an is equal to zero.

The solution to the problem is presented in the form of a beautifully designed HTML document, which allows you to conveniently study each stage of solving the problem. The user can easily find the necessary formulas and calculations, as well as get the answer to the problem.

By purchasing this product, you receive a ready-made solution to problem 7.7.3 from the collection of Kepe O.?. in a convenient format that you can save and use for self-study or exam preparation. The answer to the problem is 6.25.

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Problem 7.7.3 from the collection of Kepe O.?. consists in determining the time t of motion of a point in a circle when the normal acceleration is zero. To solve the problem, the equation s = 5t - 0.4t^2 is given, which describes the dependence of the movement of point s on time t.

First you need to find the speed v and acceleration a of a point on a circle. The speed of a point v on a circle is defined as the derivative of its coordinate with respect to time: v = ds/dt. Differentiating this equation with respect to time, we obtain: v = ds/dt = 5 - 0.8t.

The acceleration of a point on a circle a is the sum of the normal acceleration an and the tangential acceleration at: a = √(an^2 + at^2). Normal acceleration determines the change in the direction of motion of a point, while tangential acceleration determines the change in its speed. Since the problem requires finding the time when the normal acceleration is zero, we can simplify the expression for acceleration: a = √(an^2). Then a = |d^2 s/dt^2|, where | | denotes the modulus of a number.

Differentiating the equation for speed with respect to time, we find the acceleration of the point: a = |d^2 s/dt^2| = |-0.8| = 0.8.

Thus, it is necessary to solve the equation a = 0, which gives the time value t = v/a = (5 - 0.8t)/0.8. Solving this equation, we get t = 6.25. Answer: 6.25.

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