For a short time, a motor of the random-orbit sander drives the gear \( A \) with an angular velocity of \( \omega_A = 40(t^3 + 6t) \, \text{rad/s} \), where \( t \) is in seconds. This gear is connected to gear \( B \), which is fixedly connected to the shaft \( CD \). The end of this shaft is connected to the eccentric spindle \( EF \) and pad \( P \), which causes the pad to orbit around shaft \( CD \) at a radius of 15 mm. (Figure 1)**Part A**Determine the magnitude of the velocity of the spindle \( EF \) when \( t = 2.3 \, \text{s} \) after starting from rest. Express your answer to three significant figures and include the appropriate units.Input field: \[ v_E = \text{Value} \, \text{Units} \]\[ \text{Submit Button} \]\[ \text{Request Answer} \]**Part B**Determine the magnitudes of the tangential and normal components of acceleration of the spindle \( EF \) when \( t = 2.3 \, \text{s} \) after starting from rest.Express your answers in meters per second squared to three significant figures separated by a comma.Input field: \[ (a_E)_t, (a_E)_n = \]\[ \text{m/s}^2 \]\[ \text{Submit Button} \]\[ \text{Request Answer} \]**Provide Feedback Link****Figure Explanation**The diagram in Figure 1 shows a side view of the sander’s mechanism. The gear \( A \) drives the mechanism, connected to a gear system leading to a spindle \( EF \). Various distances and dimensions, such as the radius of the orbit (15 mm) and gear sizes (e.g., 60 mm, 40 mm, 10 mm), are shown to illustrate the gear connections and mechanical layout. The pad \( P \) orbits at the specified radius and is part of the eccentric spindle's motion.

For a short time a motor of the random-orbit sander drives the gear A with an angular velocity of WA-40(+³+6t) rad/s, where t is in seconds. This gear is connected to gear B, which is fixed connected to the shaft CD. The end of this shaft is connected to the eccentric spindle EF and pad P, which causes the pad to orbit around shaft CD at a radius of 15 mm. (Figure 1)

For a short time a motor of the random-orbit sander drives the gear A with an angular velocity of WA-40(+³+6t) rad/s, where t is in seconds. This gear is connected to gear B, which is fixed connected to the shaft CD. The end of this shaft is connected to the eccentric spindle EF and pad P, which causes the pad to orbit around shaft CD at a radius of 15 mm. (Figure 1)

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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For a short time, a motor of the random-orbit sander drives the gear \( A \) with an angular velocity of \( \omega_A = 40(t^3 + 6t) \, \text{rad/s} \), where \( t \) is in seconds. This gear is connected to gear \( B \), which is fixedly connected to the shaft \( CD \). The end of this shaft is connected to the eccentric spindle \( EF \) and pad \( P \), which causes the pad to orbit around shaft \( CD \) at a radius of 15 mm. (Figure 1)

**Part A**

Determine the magnitude of the velocity of the spindle \( EF \) when \( t = 2.3 \, \text{s} \) after starting from rest.

Express your answer to three significant figures and include the appropriate units.

Input field:
\[ v_E = \text{Value} \, \text{Units} \]
\[ \text{Submit Button} \]
\[ \text{Request Answer} \]

**Part B**

Determine the magnitudes of the tangential and normal components of acceleration of the spindle \( EF \) when \( t = 2.3 \, \text{s} \) after starting from rest.

Express your answers in meters per second squared to three significant figures separated by a comma.

Input field:
\[ (a_E)_t, (a_E)_n = \]
\[ \text{m/s}^2 \]
\[ \text{Submit Button} \]
\[ \text{Request Answer} \]

**Provide Feedback Link**

**Figure Explanation**

The diagram in Figure 1 shows a side view of the sander’s mechanism. The gear \( A \) drives the mechanism, connected to a gear system leading to a spindle \( EF \). Various distances and dimensions, such as the radius of the orbit (15 mm) and gear sizes (e.g., 60 mm, 40 mm, 10 mm), are shown to illustrate the gear connections and mechanical layout. The pad \( P \) orbits at the specified radius and is part of the eccentric spindle's motion.

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