### Educational Content on Kinetic Energy Calculations#### Problem (a)Consider a bicycle without its wheels, which has a mass of **8.19 kg**. Each wheel is modeled as a uniform solid disk with a mass of **0.820 kg** and a radius of **0.343 m**. Calculate the kinetic energy of the entire bicycle when it moves forward at a velocity of **2.90 m/s**.**Response Box**- Input provided: **37.88 J**- Feedback: "Your response differs from the correct answer by more than 10%. Double check your calculations."#### Problem (b)Before the wheel as we know it today, ancient civilizations used rollers to move heavy objects. Consider a scenario where a stone block with a mass of **819 kg** moves at a velocity of **0.290 m/s**, supported by two uniform cylindrical tree trunks, each with a mass of **82.0 kg** and a radius of **0.343 m**. Assume no slipping occurs between the block and rollers, or between the rollers and the ground. Your task is to determine the total kinetic energy of all the moving components.**Response Box**- Input required: **J (joules)**### Explanation of Concepts- **Kinetic Energy of an Object**: The energy that an object possesses due to its motion, calculated as: \[ KE = \frac{1}{2} mv^2 \] where \( m \) is mass and \( v \) is velocity.- **Kinetic Energy of a Rotating Object**: For an object rotating about an axis, such as a wheel or roller, the kinetic energy is given by: \[ KE = \frac{1}{2} I \omega^2 \] where \( I \) is the moment of inertia and \( \omega \) is the angular velocity.- **Uniform Solid Disk**: The moment of inertia \( I \) for a uniform disk is: \[ I = \frac{1}{2} m r^2 \] where \( m \) is the mass and \( r \) is the radius of the disk.- **No Slipping Condition**: This implies a relationship between linear velocity and angular velocity, where \( v = \omega r \).These problems require the application of these principles to find the total kinetic energy

(a) The moment of inertia of each wheel is, I=12m2r2=120.820 kg0.343 m2=0.0482 kg·m2 The angular…

(a) Without the wheels, a bicycle frame has a mass of 8.19 kg. Each of the wheels can be roughly modeled as a uniform solid disk with a mass of 0.820 kg and a radius of 0.343 m. Find the kinetic energy of the whole bicycle when it is moving forward at 2.90 m/s. 37.88 Your response differs from the correct answer by more than 10%. Double check your calculations. J (b) Before the invention of a wheel turning on an axle, ancient people moved heavy loads by placing rollers under them. (Modern people use rollers, too. Any hardware store will sell you a roller bearing for a lazy susan.) A stone block of mass 819 kg moves forward at 0.290 m/s, supported by two uniform cylindrical tree trunks, each of mass 82.0 kg and radius 0.343 m. No slipping occurs between the block and the rollers or between the rollers and the ground. Find the total kinetic energy of the moving objects.

(a) Without the wheels, a bicycle frame has a mass of 8.19 kg. Each of the wheels can be roughly modeled as a uniform solid disk with a mass of 0.820 kg and a radius of 0.343 m. Find the kinetic energy of the whole bicycle when it is moving forward at 2.90 m/s. 37.88 Your response differs from the correct answer by more than 10%. Double check your calculations. J (b) Before the invention of a wheel turning on an axle, ancient people moved heavy loads by placing rollers under them. (Modern people use rollers, too. Any hardware store will sell you a roller bearing for a lazy susan.) A stone block of mass 819 kg moves forward at 0.290 m/s, supported by two uniform cylindrical tree trunks, each of mass 82.0 kg and radius 0.343 m. No slipping occurs between the block and the rollers or between the rollers and the ground. Find the total kinetic energy of the moving objects.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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