The limiting velocity of a solid sphere of radius a and density ρ falling freely in a medium of density ρ ' and the co-efficient of viscosity μ where a body falling in a relatively dense fluid, is acted on by three forces; a resistive force R , a buoyant force B , and its weight w due to gravity.

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Answer 1

Question

Chapter 2.3, Problem 29P

(a)

To determine

The limiting velocity of a solid sphere of radius a and density ρ falling freely in a medium of density ρ' and the co-efficient of viscosity μ where a body falling in a relatively dense fluid, is acted on by three forces; a resistive force R, a buoyant force B, and its weight w due to gravity.

(b)

To determine

An expression for e, such that E has been adjusted, so the droplet is stationary where a field of strength E exerts a force Ee on a droplet with charge e

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By considering appropriate series expansions, e². e²²/2. e²³/3. .... = = 1 + x + x² + · ... when |x| < 1. By expanding each individual exponential term on the left-hand side the coefficient of x- 19 has the form and multiplying out, 1/19!1/19+r/s, where 19 does not divide s. Deduce that 18! 1 (mod 19).

Proof: LN⎯⎯⎯⎯⎯LN¯ divides quadrilateral KLMN into two triangles. The sum of the angle measures in each triangle is ˚, so the sum of the angle measures for both triangles is ˚. So, m∠K+m∠L+m∠M+m∠N=m∠K+m∠L+m∠M+m∠N=˚. Because ∠K≅∠M∠K≅∠M and ∠N≅∠L, m∠K=m∠M∠N≅∠L, m∠K=m∠M and m∠N=m∠Lm∠N=m∠L by the definition of congruence. By the Substitution Property of Equality, m∠K+m∠L+m∠K+m∠L=m∠K+m∠L+m∠K+m∠L=°,°, so (m∠K)+ m∠K+ (m∠L)= m∠L= ˚. Dividing each side by gives m∠K+m∠L=m∠K+m∠L= °.°. The consecutive angles are supplementary, so KN⎯⎯⎯⎯⎯⎯∥LM⎯⎯⎯⎯⎯⎯KN¯∥LM¯ by the Converse of the Consecutive Interior Angles Theorem. Likewise, (m∠K)+m∠K+ (m∠N)=m∠N= ˚, or m∠K+m∠N=m∠K+m∠N= ˚. So these consecutive angles are supplementary and KL⎯⎯⎯⎯⎯∥NM⎯⎯⎯⎯⎯⎯KL¯∥NM¯ by the Converse of the Consecutive Interior Angles Theorem. Opposite sides are parallel, so quadrilateral KLMN is a parallelogram.

By considering appropriate series expansions, ex · ex²/2 . ¸²³/³ . . .. = = 1 + x + x² +…… when |x| < 1. By expanding each individual exponential term on the left-hand side and multiplying out, show that the coefficient of x 19 has the form 1/19!+1/19+r/s, where 19 does not divide s.

Answer 2

Question

Chapter 2.3, Problem 29P

(a)

To determine

The limiting velocity of a solid sphere of radius a and density ρ falling freely in a medium of density ρ' and the co-efficient of viscosity μ where a body falling in a relatively dense fluid, is acted on by three forces; a resistive force R, a buoyant force B, and its weight w due to gravity.

(b)

To determine

An expression for e, such that E has been adjusted, so the droplet is stationary where a field of strength E exerts a force Ee on a droplet with charge e

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 3

Question

Chapter 2.3, Problem 29P

(a)

To determine

The limiting velocity of a solid sphere of radius a and density ρ falling freely in a medium of density ρ' and the co-efficient of viscosity μ where a body falling in a relatively dense fluid, is acted on by three forces; a resistive force R, a buoyant force B, and its weight w due to gravity.

(b)

To determine

An expression for e, such that E has been adjusted, so the droplet is stationary where a field of strength E exerts a force Ee on a droplet with charge e

Expert Solution & Answer

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Check out a sample textbook solution

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Answer 4

Question

Chapter 2.3, Problem 29P

(a)

To determine

The limiting velocity of a solid sphere of radius a and density ρ falling freely in a medium of density ρ' and the co-efficient of viscosity μ where a body falling in a relatively dense fluid, is acted on by three forces; a resistive force R, a buoyant force B, and its weight w due to gravity.

(b)

To determine

An expression for e, such that E has been adjusted, so the droplet is stationary where a field of strength E exerts a force Ee on a droplet with charge e

Expert Solution & Answer

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Check out a sample textbook solution

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Answer 5

Chapter 2.3, Problem 29P

(a)

To determine

The limiting velocity of a solid sphere of radius a and density ρ falling freely in a medium of density ρ' and the co-efficient of viscosity μ where a body falling in a relatively dense fluid, is acted on by three forces; a resistive force R, a buoyant force B, and its weight w due to gravity.

(b)

To determine

An expression for e, such that E has been adjusted, so the droplet is stationary where a field of strength E exerts a force Ee on a droplet with charge e

Answer 6

Chapter 2.3, Problem 29P

(a)

To determine

The limiting velocity of a solid sphere of radius a and density ρ falling freely in a medium of density ρ' and the co-efficient of viscosity μ where a body falling in a relatively dense fluid, is acted on by three forces; a resistive force R, a buoyant force B, and its weight w due to gravity.

Answer 7

Chapter 2.3, Problem 29P

(a)

To determine

The limiting velocity of a solid sphere of radius a and density ρ falling freely in a medium of density ρ' and the co-efficient of viscosity μ where a body falling in a relatively dense fluid, is acted on by three forces; a resistive force R, a buoyant force B, and its weight w due to gravity.

Answer 8

(b)

To determine

An expression for e, such that E has been adjusted, so the droplet is stationary where a field of strength E exerts a force Ee on a droplet with charge e

Answer 9

(b)

To determine

An expression for e, such that E has been adjusted, so the droplet is stationary where a field of strength E exerts a force Ee on a droplet with charge e

Answer 10

Expert Solution & Answer

Answer 11

Expert Solution & Answer

Answer 12

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Answer 13

The limiting velocity of a solid sphere of radius a and density ρ falling freely in a medium of density ρ' and the co-efficient of viscosity μ where a body falling in a relatively dense fluid, is acted on by three forces; a resistive force R, a buoyant force B, and its weight w due to gravity.

An expression for e, such that E has been adjusted, so the droplet is stationary where a field of strength E exerts a force Ee on a droplet with charge e

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