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Vectors and Scalars

A scalar is a quantity that is completely specified by its magnitude and has no direction. A scalar can be described either dimensionless, or in terms of some physical quantity. Examples of scalars are: mass, volume, distance, energy, and time.

Scalar quantities can be manipulated by the laws of arithmetic applicable to natural numbers. For example if I add 20 grams of sugar to a recipe and then add 20 grams more the result is 40 grams of sugar in the recipe. If I buy a liter (1000ml) bottle of water and drink 250 ml, the amount left over is 750 ml.

A vector is a quantity that specifies both a magnitude and a direction. Such a quantity may be represented geometrically by an arrow of length proportional to its magnitude, pointing in the assigned direction. Examples of vectors are: displacement, velocity, acceleration, force and electric field. Vectors can be added in simple ways that scalars can. For example: A plane flies south at 500 miles/hour. A wind blows from the east at 100 miles/hour occurs. The resultant speed is not 600 miles/hour or 400 miles per hour.


The resultant (red arrow) can be calculated using the Pythagorean Theorem

R= sqrt (100^2 + 500^2)

R= 509.9 mi/hr.

The direction of the plane can be calculated using the cosine function.

tan = 100/500 = 11.31 degrees

(Note: diagram is not drawn to scale)



1. ___ _ is an example of a scalar quantity
a) velocity
b) force
c) volume
d) acceleration

2. ___ is an example of a vector quantity
a) mass
b) force
c) volume
d) density

3. A scalar quantity:
a) always has mass
b) is a quantity that is completely specified by its magnitude
c) shows direction
d) does not have units

4. A vector quantity
a) can be a dimensionless quantity
b) specifies only magnitude
c) specifies only direction
d) specifies both a magnitude and a direction

5. A boy pushes against the wall with 50 pounds of force. The wall does not move. The resultant force is:
a) -50 pounds
b) 100 pounds
c) 0 pounds
d) -75 pounds

6. A man walks 3 miles north then turns right and walks 4 miles east. The resultant displacement is:
a) 1 mile SW
b) 7 miles NE
c) 5 miles NE
d) 5 miles E

7. A plane flying 500 MI/hr due north has a tail wind of 45 MI/hr the resultant velocity is:
a) 545 miles/hour due south.
b) 455 miles/hour north.
c) 545 miles/hr due north.
d) 455 MI/hr due south

8. The difference between speed and velocity is:
a) speed has no units
b) speed shows only magnitude, while velocity represents both magnitude (strength) and direction
c) they use different units to represent their magnitude
d) velocity has a higher magnitude

9. The resultant magnitude of two vectors

a) Is always positive
b) Can never be zero
c) Can never be negative
d) Is usually zero

10. Which of the following is not true.
a) velocity can be negative
b) velocity is a vector
b) speed is a scalar
d) speed can be negative


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