A 1.50 kg solid, uniform sphere of radius 0.120 m is released from rest at point A in the figure below, its center of gravity a distance of 1.90 m above the ground. The sphere rolls without slipping to the bottom of an incline and back up to point B where it is launched vertically into the air. The sphere then rises to its maximum height \( h_{\text{max}} \) at point C.**Diagram Explanation:**- The diagram shows a slope starting from point A where the sphere is released with an initial velocity of \( v = 0 \).- The sphere rolls down to point B at the bottom of the incline and then moves vertically up to point C.- The initial vertical height at point A above the ground is 1.90 m.- The height of point B above the ground is 0.450 m.- The vertical distance to which the sphere rises at point C is marked as \( h_{\text{max}} \).**Questions:**(a) At point B, find the sphere's translational speed \( v_B \) (in m/s).\[ \_\_\_\_\_ \, \text{m/s} \](b) At point B, find the sphere's rotational speed \( \omega_B \) (in rad/s).\[ \_\_\_\_\_ \, \text{rad/s} \](c) At point C, find the sphere's rotational speed \( \omega_C \) (in rad/s).\[ \_\_\_\_\_ \, \text{rad/s} \](d) At point C, find the maximum height \( h_{\text{max}} \) of the sphere's center of gravity (in m).\[ \_\_\_\_\_ \, \text{m} \]

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A 1.50 kg solid, uniform sphere of radius 0.120 m is released from rest at point A in the figure below, its center of gravity a distance of 1.90 m above the ground. The sphere rolls without slipping to the bottom of an incline and back up to point B where it is launched vertically into the air. The sphere then rises to its maximum height h at point C. max

A 1.50 kg solid, uniform sphere of radius 0.120 m is released from rest at point A in the figure below, its center of gravity a distance of 1.90 m above the ground. The sphere rolls without slipping to the bottom of an incline and back up to point B where it is launched vertically into the air. The sphere then rises to its maximum height h at point C. max

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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Concept explainers

Angular speed, acceleration and displacement

Angular acceleration is defined as the rate of change in angular velocity with respect to time. It has both magnitude and direction. So, it is a vector quantity.

Angular Position

Before diving into angular position, one should understand the basics of position and its importance along with usage in day-to-day life. When one talks of position, it’s always relative with respect to some other object. For example, position of earth with respect to sun, position of school with respect to house, etc. Angular position is the rotational analogue of linear position.

Question

A 1.50 kg solid, uniform sphere of radius 0.120 m is released from rest at point A in the figure below, its center of gravity a distance of 1.90 m above the ground. The sphere rolls without slipping to the bottom of an incline and back up to point B where it is launched vertically into the air. The sphere then rises to its maximum height \( h_{\text{max}} \) at point C.

**Diagram Explanation:**

- The diagram shows a slope starting from point A where the sphere is released with an initial velocity of \( v = 0 \).
- The sphere rolls down to point B at the bottom of the incline and then moves vertically up to point C.
- The initial vertical height at point A above the ground is 1.90 m.
- The height of point B above the ground is 0.450 m.
- The vertical distance to which the sphere rises at point C is marked as \( h_{\text{max}} \).

**Questions:**

(a) At point B, find the sphere's translational speed \( v_B \) (in m/s).
\[ \_\_\_\_\_ \, \text{m/s} \]

(b) At point B, find the sphere's rotational speed \( \omega_B \) (in rad/s).
\[ \_\_\_\_\_ \, \text{rad/s} \]

(c) At point C, find the sphere's rotational speed \( \omega_C \) (in rad/s).
\[ \_\_\_\_\_ \, \text{rad/s} \]

(d) At point C, find the maximum height \( h_{\text{max}} \) of the sphere's center of gravity (in m).
\[ \_\_\_\_\_ \, \text{m} \]

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Step 4: c) Calculate the angular speed at C:

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Step 5: d) Calculate the maximum height:

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