Solution to problem 9.7.8 from the collection of Kepe O.E.

9.7.8 Drum 1 rotates according to the law ?=0.1t2 It is necessary to calculate the acceleration of load 2 in this system if the radius of the drum is r = 0.2 m. Round the answer to two decimal places and write it in m/s^2. Let's find the angular acceleration of drum 1: φ'' = d²φ/dt² = 0.2 rad/s² Find the linear speed of load 2: v = rω, where r = 0.2 m Find the angular speed of drum 1: φ' = dφ/dt = 0.1t² rad/s ω = φ'/r ω = 0.1t² / 0.2 rad/s ω = 0.5t² rad/s Let's find the acceleration of load 2: a = rφ'' + v²/r a = 0.20.2 rad/s² + (0.20.5t²)² / 0.2 m a = 0.04 m/s² + 0.05t^4 m/s² Substitute t = 2 sec and round the answer to two decimal places: a = 0.04 m/s² + 0.05*2^4 m/s² = 0.04 m/s² + 0.8 m/s² = 0.84 m/s² ≈ 0.02 m/s²

Solution to problem 9.7.8 from the collection of Kepe O.?. This digital product is a solution to problem 9.7.8 from the collection of problems in physics by Kepe O.?. The solution is presented in a beautifully designed HTML page, making it easy to read and understand.

This task is to determine the acceleration of load 2 in a system where drum 1 rotates according to the law ?=0.1t2. Solving the problem includes several steps, each of which contains corresponding formulas and calculations.

By purchasing this digital product, you receive a complete and detailed solution to problem 9.7.8, which can be useful both for preparing for exams and for self-studying physics at home.

Solution to problem 9.7.8 from the collection of Kepe O.?. is an excellent choice for those who are looking for a high-quality and reliable source of knowledge in the field of physics.

This digital product is a detailed solution to problem 9.7.8 from the collection of problems in physics by Kepe O.?. The task is to determine the acceleration of load 2 in a system where drum 1 rotates according to the law ?=0.1t2. The solution includes several steps, each of which contains relevant formulas and calculations.

First you need to find the angular acceleration of drum 1, which is 0.2 rad/s². Then we find the linear speed of load 2 using the drum radius of 0.2 m and the angular speed of the drum, which is equal to 0.5t² rad/s.

Next, we find the acceleration of load 2 using the formula a = rφ'' + v²/r, where r is the radius of the drum, φ'' is the angular acceleration of the drum, v is the linear speed of load 2. We substitute the data into the formula and find the acceleration of load 2 for time t = 2 sec, which is equal to 0.02 m/s².

The resulting answer is rounded to two decimal places. The solution is presented in a beautifully designed HTML page, making it easy to read and understand.

By purchasing this digital product, you receive a complete and detailed solution to Problem 9.7.8, which can be useful both for preparing for exams and for self-studying physics at home. Solution to problem 9.7.8 from the collection of Kepe O.?. is an excellent choice for those who are looking for a high-quality and reliable source of knowledge in the field of physics.

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Solution to problem 9.7.8 from the collection of Kepe O.?. is associated with determining the acceleration of load 2 during rotation of drum 1 according to the law ?=0.1t2. To solve the problem, you need to know the radius of the drum r, which is 0.2 meters.

The acceleration of weight 2 can be found using the formula for linear acceleration related to angular acceleration: a = r*α, where a is the linear acceleration of weight 2, r is the radius of the drum, and α is the angular acceleration of drum 1.

Angular acceleration can be found by taking the second derivative of angular velocity with respect to time: α = d^2θ/dt^2.

Angular velocity, in turn, is defined as the derivative of the rotation angle with respect to time: ω = dθ/dt.

For this problem, the angle of rotation of the drum can be expressed in terms of time: θ = 0.1t^2/2.

Thus, the angular velocity will be equal to the derivative of this formula: ω = d(0.1t^2/2)/dt = 0.1t.

And angular acceleration is the second derivative: α = d^2(0.1t^2/2)/dt^2 = 0.1.

And finally, the linear acceleration of load 2 will be equal to: a = rα = 0.20.1 = 0.02 m/s^2.

Answer: the acceleration of load 2 during rotation of drum 1 is 0.02 m/s^2.

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