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A string is attached to the rim of a small hoop of radius r = 8.00x10-2 m and mass m = 0.180 kg and then wrapped several times around the rim. If the free end of the string is held in place and the hoop is released from rest and allowed to drop, as shown in the figure (Figure 1), calculate the angular speed and the translational speed of the rotating hoop after it has descended h = 0.750 m. Use g = 9.80 m/s? for the acceleration due to gravity. What are the initial and final kinetic energies (K; and K ) of the hoop? Express the initial and final kinetic energies symbolically in terms of the final velocity v and variables given in the problem introduction, separated by a comma. • View Available Hint(s) Π ΑΣφ ?

A string is attached to the rim of a small hoop of radius r = 8.00x10-2 m and mass m = 0.180 kg and then wrapped several times around the rim. If the free end of the string is held in place and the hoop is released from rest and allowed to drop, as shown in the figure (Figure 1), calculate the angular speed and the translational speed of the rotating hoop after it has descended h = 0.750 m. Use g = 9.80 m/s? for the acceleration due to gravity. What are the initial and final kinetic energies (K; and K ) of the hoop? Express the initial and final kinetic energies symbolically in terms of the final velocity v and variables given in the problem introduction, separated by a comma. • View Available Hint(s) Π ΑΣφ ?

College Physics
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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The coorect answer should have variable m in it

### Learning Goal: To practice Problem-Solving Strategy 9.1 on Rotational Energy. A string is attached to the rim of a small hoop with a radius \( r = 8.00 \times 10^{-2} \, \text{m} \) and mass \( m = 0.180 \, \text{kg} \) and then wrapped several times around the rim. If the free end of the string is held in place and the hoop is released from rest and allowed to drop, as shown in Figure 1, calculate the angular speed and the translational speed of the rotating hoop after it has descended \( h = 0.750 \, \text{m} \). Use \( g = 9.80 \, \text{m/s}^2 \) for the acceleration due to gravity. #### Figure - **Description:** The figure (labeled as Figure 1) is currently unavailable in this view. ### Part C **Question:** What are the initial and final kinetic energies (\( K_i \) and \( K_f \)) of the hoop? **Task:** Express the initial and final kinetic energies symbolically in terms of the final velocity \( v \) and variables given in the problem introduction, separated by a comma. - **Input Box:** The text box allows for symbolic input of \( K_i \) and \( K_f \). This exercise involves applying the concepts of rotational motion and energy conservation to solve for unknown quantities related to a rotating hoop.
Transcribed Image Text:### Learning Goal: To practice Problem-Solving Strategy 9.1 on Rotational Energy. A string is attached to the rim of a small hoop with a radius \( r = 8.00 \times 10^{-2} \, \text{m} \) and mass \( m = 0.180 \, \text{kg} \) and then wrapped several times around the rim. If the free end of the string is held in place and the hoop is released from rest and allowed to drop, as shown in Figure 1, calculate the angular speed and the translational speed of the rotating hoop after it has descended \( h = 0.750 \, \text{m} \). Use \( g = 9.80 \, \text{m/s}^2 \) for the acceleration due to gravity. #### Figure - **Description:** The figure (labeled as Figure 1) is currently unavailable in this view. ### Part C **Question:** What are the initial and final kinetic energies (\( K_i \) and \( K_f \)) of the hoop? **Task:** Express the initial and final kinetic energies symbolically in terms of the final velocity \( v \) and variables given in the problem introduction, separated by a comma. - **Input Box:** The text box allows for symbolic input of \( K_i \) and \( K_f \). This exercise involves applying the concepts of rotational motion and energy conservation to solve for unknown quantities related to a rotating hoop.
The diagram illustrates the initial and final states of an object in motion. - **Initial State:** The object, depicted as an orange circle, is positioned at a higher point. - **Final State:** The circle moves downward to a lower point. An arrow labeled "h" represents the vertical height between the initial and final states. This diagram helps demonstrate concepts such as gravitational potential energy and energy conservation as the object moves from a higher to a lower point.
Transcribed Image Text:The diagram illustrates the initial and final states of an object in motion. - **Initial State:** The object, depicted as an orange circle, is positioned at a higher point. - **Final State:** The circle moves downward to a lower point. An arrow labeled "h" represents the vertical height between the initial and final states. This diagram helps demonstrate concepts such as gravitational potential energy and energy conservation as the object moves from a higher to a lower point.
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