Q: Given two vectors $$\vec{A}_1 = 2\vec{i} + 3\vec{j} + 4\vec{k}$$ and $$\vec{A}_2 = -1\vec{i} + 0\vec{j} + 2\vec{k}$$, what is their dot product?

$$2 \times (-1) + 3 \times 0 + 4 \times 2 = 6$$

Question 1

A weather balloon is released and floats in the atmosphere. According to Archimedes' principle, what determines the magnitude of the upward buoyant force acting on the balloon?

Accepted Answer

The weight of the air displaced by the balloon

Question 2

Which of the following correctly expresses Newton's Second Law for a particle moving in three dimensions?

Accepted Answer

$$\vec{F} = m \dfrac{d^2$\vec{x}}{dt^2$}$$

Question 3

A block is fully submerged in water. If the block has a volume of $$0.02\ \mathrm{m}^3$$ and the density of water is $$1000\ \mathrm{kg/m}^3$$, what is the magnitude of the buoyant force acting on the block? (Use $$g = 9.8\ \mathrm{m/s}^2)$$

Accepted Answer

$$196\ \mathrm{N}$$

Question 4

Which of the following is the correct formula for pressure exerted by a force $$F on an $$area $$A$$?

Accepted Answer

$$p = \dfrac{F}{A}$$

Question 5

A vector $$\vec{V}_1 = 3\vec{i} + 4\vec{j} + 12\vec{k}. $$What is the magnitude of $$\vec{V}_1$$?

Accepted Answer

$$\sqrt{3^2$ + 4^2$ + 12^2$} = 13$$

Question 6

A force of $$50\ \mathrm{N} is $$applied perpendicular to a surface of area $$0.25\ \mathrm{m}^2. $$What is the pressure exerted on the surface?

Accepted Answer

$$200\ \mathrm{Pa}$$

Question 7

Which of the following statements about pressure inside a fluid at rest is correct?

Accepted Answer

Pressure is the same in every direction at a given location

Question 8

Given two vectors $$\vec{A}_1 = 2\vec{i} + 3\vec{j} + 4\vec{k}$$ and $$\vec{A}_2 = -1\vec{i} + 0\vec{j} + 2\vec{k}$$, what is their dot product?

Accepted Answer

$$2 	imes (-1) + 3 	imes 0 + 4 	imes 2 = 6$$

Question 9

A particle moves $$80\ \mathrm{cm}$$ south in $$0.12\ \mathrm{s}$$ and then $$60\ \mathrm{cm}$$ west in $$0.08\ \mathrm{s}. $$What is the magnitude of its average velocity?

Accepted Answer

$$500\ \mathrm{cm/s}$$

Question 10

Which of the following is a scalar quantity?

Accepted Answer

Mass

Question 11

The SI unit for pressure commonly used in atmospheric science is:

Accepted Answer

Hectopascal (hPa)

Question 12

Which operation between two vectors results in a scalar?

Accepted Answer

Dot product

Question 13

A vector $$\vec{V} = x\vec{i} + y\vec{j} + z\vec{k}. $$What is the formula for its magnitude?

Accepted Answer

$$\sqrt{x^2$ + y^2$ + z^2$}$$

Question 14

Which of the following best describes kinetic energy for a non-rotating object of mass $$m$$ and speed $$v$$?

Accepted Answer

$$E_k = \dfrac{1}{2} m v^2$

Question 15

Which of the following is NOT a base SI unit?

Accepted Answer

Hertz

Question 16

A force $$\vec{F}$$ acts on a mass $$m$$ causing an acceleration $$\vec{a}. $$Which equation correctly relates these quantities?

Accepted Answer

$$\vec{F} = m \vec{a}$$

Question 17

Which of the following is true about the direction of pressure inside a fluid at rest?

Accepted Answer

It acts equally in all directions

Question 18

If a vector $$\vec{A} = 5\vec{i} - 2\vec{j} + 3\vec{k} is $$multiplied by a scalar $$2$$, what is the resulting vector?

Accepted Answer

$$10\vec{i} - 4\vec{j} + 6\vec{k}$$

Question 19

Which of the following best describes potential energy?

Accepted Answer

Energy due to position relative to other objects

Basic Physical Concepts in Atmospheric Thermodynamics and Dynamics

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