Test 1

The work W done by a system that expands against an external pressure is W=−P×ΔV, where ΔV is V final−V initial. Suppose the initial volume of a gas is 198 L, the work done by the gas is −2.0×104J and the pressure is 1.0 atm. Which of the following is needed to find the final volume of the gas?

a conversion from J / atm to L

Which of the following explains how to describe a vector? a. using magnitude and direction b. using an x- and y-coordinate system c. using unit vectors d. all of the above

all of the above

For each of the following diagrams estimate A→×B→. Which will result in the largest vector pointing out of the screen? Note that A→ and B→ each have the same magnitude in all of the figures.

c.

An object travels a distance d with acceleration aa over a period of time t according to the equation: d=(1/2)at^2. After 2.3 seconds with an acceleration of 9.8m/s^2, how far does an object travel?

d=(1/2)at^2=(1/2)(9.8m/s^2)(2.3s)^2 = 26m

Suppose you are told that 15 quarts (qt) = 14.2 liters (L). What is the conversion factor you would use to convert from quarts to liters? What is the conversion factor you would you use to convert liters to quarts?

quarts to liters: 14.2 L / 15 qt liters to quarts: 15 qt / 14.2 L

Which of the following uses a derived SI unit measurement?

speed

Which of the following quantities is not a vector?

speed (example: 70 miles per hour)

Which of the following best defines a second as an SI unit of time?

the amount of time that a cesium atom needs to vibrate a specific number of times

How many significant figures should be there for the product of 29×3.530m?

two significant figures

In order to understand vectors, you must understand some basic trigonometry. Which of the following correctly relates x, y, t and θ?

x=t cos θ; y=t sin θ tan θ=y/x; t= (x^2+y^2)^1/2

What is the correct value for θ and α in the given right triangle?

θ=36.9∘, α=53.1

Two vectors in the XY- plane are defined by the equations: A→=2i^−2j^ B→=3i^+j^ Which of the following answer choices related to the cross product of these two vectors or the measure of angle θ between the two vectors is not correct?

θ=45∘

The angle between two vectors is 175.0°. What is the scalar product of these two vectors if their magnitudes are 4.000 cm and 3.000 cm?

−11.95

Suppose you are told that 1 qt = 0.946 L. Which of the following statements is not correct?

(1qt/0.946L)(365)=365qt/L

Suppose you are told that the mass of an object is 1.283 kg. What is the implied range for the mass of this object?

1.282kg→1.284kg

Find the cross product of the following two vectors: A→=3i^−2j^ B→=2i^−j^

1k^

Suppose that vector A→ and vector B→ are defined in the following manner: A→=(2m)i^−(2m)j^ B→=(4m)i^+(2m)j^ What is the dot product of these two vectors?

4 m^2

Suppose you have $100 that you need to convert to Danish kroner. The conversion rate that day is 5.732 Danish kroner for one American dollar. The business that converts your money charges you a flat fee of 50 Danish kroner for the transaction. Use your knowledge of significant figures to decide which of the following shows the correct amount of Danish kroner that you should receive.

523.2 Danish kroner

What is the magnitude of vector A?

6.00 cm

Which of the following statements related to vectors is not correct?

A "one way" road sign is an example of a vector.

Given two vectors A→ and B→, which of the following is the correct method for adding A→ and B→? a. Move A→ parallel to itself placing the tail of A→ at the tail of B→, and then draw a vector from the tip of B→ to the tail of A→. b. Move B→ parallel to itself placing the tail of B→ at the tip of A→, and then draw a vector from the tail of A→ to the tip of B→. c. Move A→ parallel to itself placing the tail of A→ at the tip of B→, and then draw a vector from the tail of B→ to the tip of A→. d. Answers B and C

Answers B and C

The vector B→ is a scalar multiple of vector A→. The magnitude of B→ is three times the magnitude of A→. Which of the following vector equations describes the relationship between B→ and A→?

A→ =1/3B→

Suppose you are trying to solve for the cross product of two vectors in the XY-plane that are defined as A→=Axi^+Ayj and B→=Bxi^+Byj^. Which of the following statements about these vectors is not correct?

A→×(B→+C→) =( A→×B→)×(A→×C→)

Which of the following shows the correct equations for the cross product of two vectors?

A→×B→=(AyBz−AzBy)i^+(AzBx−AxBz)j^+(AxBy−AyBx)k^∣A→×B→∣=ABsinθ

Two vectors in the XY- plane are defined by the equations: A→=4i^+3j^ B→=3i^−4j Which of the following answer choices related to the cross product of these two vectors or the measure of angle θθ between the two vectors is not correct?

A→×B→=7k^

Consider the diagram of a toy train being pushed from behind at an angle θ relative to the horizontal. The equation for the work done on the train in this example is the scalar product A→⋅B→=ABcosθ. Which part of this expression accounts for the projection of vector B→ in the direction of vector A→?

B cos θ

Suppose a laboratory experiment lasted 4,532 seconds. Which of the following conversion factors would be used to figure out how many hours the experiment lasted?

Both 60 s / 1 min and 60 min / 1 hr

Think about the forces that are at work when you use a wrench, and about the cross product of two vectors: ∣A→×B→∣=ABsinθ. What does Bsinθ represent in this expression?

Bsinθ is the projection of the applied force vector B→ perpendicular to the direction of vector A→.

Which of the following does not correctly describe each given vector in terms of the unit vectors? (Note that each grid line is half of a unit.)

B→=−4j

The circumference of a circle is defined by the equation \( C=2 \pi r \), where \( \pi=3.14 \). Suppose that r = 0.0347 m. Which of the following correctly shows the circumference of the circle?

C = 0.218 m

Which of the following statements about SI distance units is not correct?

Converting a meter to feet is an example of a conversion involving two different SI units for distance.

If C→=A→+B→, then the magnitude of C→, or ∣C→∣, is the sum of the magnitudes of A→ and B→, or ∣A→∣+∣B→∣

False

How many significant figures are there in a measurement 0.30700 cm?

Five significant figures — every digit except the first 0.

The heat required to heat a glass of water is given by heat total=heat water + heat glass. You heat 500 g of water in a glass with a mass of 100 g from 20.0°C to 100.0°C. You know the following information: heat total=1.76×105J heat water=1.67×105J heat glass=(ΔT)(m glass)(c) where ΔTΔT is the change in temperature (T final−T initial), m glass is the mass of the glass, and c is the specific heat capacity of the glass. Which of the following is the unit of specific heat capacity? a. ∘C/g×J∘C/g×J b. J / g c. g/J×∘Cg/J×∘C d. None of the above.

None of the above.

Which of the following does not explain the use of SI units in physics?

SI units are more difficult to manipulate than old English system units (such as the foot and the pound).

Two vectors in the XY-plane are defined by the equations A→=2i^+5j^B→=−2i^+j^ Suppose you are asked to find the dot product of the two vectors, the cross product of the two vectors, and the measure of the angle θ between the two vectors. Which of the following statements related to any of these operations is not correct

The angle θ between the two vectors is 42∘.

The scalar or dot product of two vectors A→ and B→ is defined by the expression A→⋅B→=ABcosθ. Which of the following statements about the scalar product is not correct?

The angle θ is defined as the angle between either vector and the horizontal axis.

Which of the following statements about SI units is not correct?

The cgs system is not considered a standard SI system.

The SI unit for mass is the kilogram. Which of the following statements related to mass is not correct?

The definition of a kilogram is based on the mass of a certain number of carbon atoms.

A→=−1/2B→ Which of the following is incorrect?

The directions of A→ and B→ are the same

Which of the following statements about the dot product of the two vectors is not correct? Assume that one grid line is one unit.

The dot product of the two vectors is a positive value.

In physics (and in all science) standard units are used to ensure measurement uniformity. Which of the following fictitious units of measurement could not be considered a standard unit?

The pinkie: a distance unit equal to the exact length of the right pinkie finger on the current U.S. president.

Suppose that an environmental study determines that a town produces approximately 2,000 lb of trash each day. The study group decides to convert their findings to SI units, using the conversion 1 lb = 0.4536 kg. They report that the town produces 907.2 kg of trash each day. Which of the following is correct?

The study group used the correct conversion factor but did not account for significant digits.

Which of the following statements about the dot product of the two vectors is not correct?

The value of A to two significant figures is 7.2. The value of B to two significant figures is 3.5.

Which of the following statements about vector A→ is not correct?

The value of Ay is negative.

Which of the following answer choices related to the dot product of the two vectors is not correct?

The values Ax, Bx, Ay, and By are all greater than 0.

Which of the following best explains why physicists need to use standard units when making measurements?

To make accurate quantitative observations about the physical properties and behavior of things.

Consider the vectors A→ and B→ shown in the picture. Think about an example where B→ represents the force applied to a wrench, and A→ represents the wrench. Which of the following statements about these vectors is not correct?

To unscrew a bolt, a force in the direction parallel to the wrench must be applied. This force is a scalar with a magnitude B.

The order in which two vectors are added does not affect their sum; that is A→+B→=B→+A→

True

A toy train is moving on a track from right to left. You are told that work is the dot product of force and displacement. In what direction would you apply a force so that you do the most negative work on the train?

You would apply a force that is in the left to right direction.