Review ComponentsReview Components

Do Now:Do Now:

Draw a vector that is 40 m/s at 40° Draw a vector that is 40 m/s at 40° North of WestNorth of West What is the x component of the velocity What is the x component of the velocity

and the y component of the velocity?and the y component of the velocity? Solve both graphically (with an Solve both graphically (with an

appropriate scale) and by using trigappropriate scale) and by using trig

Quick ExperimentQuick Experiment

► If two forces act on an object, how can If two forces act on an object, how can the forces be arranged to get the the forces be arranged to get the maximum force? The minimum force? A maximum force? The minimum force? A force in between the maximum and the force in between the maximum and the minimum?minimum?

Work with your partner. Choose an object on Work with your partner. Choose an object on your desk. Each partner applies a force with your desk. Each partner applies a force with your force producer (finger). Figure answer.your force producer (finger). Figure answer.

ResultantResultant

►A single vector that represents the A single vector that represents the same affect as the addition of 2 or same affect as the addition of 2 or more vectorsmore vectors

►Represented as a dashed lineRepresented as a dashed line

Two Vectors in the Same Two Vectors in the Same Direction MathematicallyDirection Mathematically

►0° angle between them0° angle between them►Add the magnitudes of the vectors Add the magnitudes of the vectors

togethertogether►The resultant is the The resultant is the maximummaximum value value

possiblepossible

Aim: How can we add two Aim: How can we add two vectors together acting on a vectors together acting on a

point?point?

A girl walks 200 m East and then walks A girl walks 200 m East and then walks another 400 m East. Draw a scaled another 400 m East. Draw a scaled representation.representation.

Scale:Scale:

1 cm = 100 m1 cm = 100 mResultant = 600 m

Two Vectors in Opposite Two Vectors in Opposite Directions MathematicallyDirections Mathematically

►180° angle between the vectors180° angle between the vectors►Subtract the magnitude of the two Subtract the magnitude of the two

vectorsvectors►The direction of the resultant is the The direction of the resultant is the

same as the direction of the larger same as the direction of the larger vectorvector

►The resultant is the The resultant is the minimumminimum value value possiblepossible

A boy runs 50 m West and then runs 20 A boy runs 50 m West and then runs 20 m East.m East.

What distance did the boy run?What distance did the boy run?

70 m70 m

What is the boy’s resultant What is the boy’s resultant displacement?displacement?

Scale:Scale:

1 cm = 10 m1 cm = 10 mResultant = 30 m

Range of Possible ValuesRange of Possible Values

►When two vectors are added together, the When two vectors are added together, the resultant can be between the maximum resultant can be between the maximum value (when the angle is 0°) and the value (when the angle is 0°) and the minimum value (when the angle is 180°)minimum value (when the angle is 180°)

►Example: Is 9 N a possible value when the Example: Is 9 N a possible value when the forces of 30 N and 20 N act concurrently forces of 30 N and 20 N act concurrently on an object?on an object? No: the range of values is 50 N maximum and No: the range of values is 50 N maximum and

10 N minimum. 9 N falls outside of that range.10 N minimum. 9 N falls outside of that range.

A 5 N force directed North and a 3 N A 5 N force directed North and a 3 N force directed East act concurrently force directed East act concurrently (acts on the same point at the same (acts on the same point at the same time)time)

Draw the two vectors Draw the two vectors (Hint: start with a set of (Hint: start with a set of axes)axes)

Scale:Scale:

1 cm = 1 N1 cm = 1 N

N

S

W E

►Make a parallelogramMake a parallelogram►The resultant is The resultant is

constructed from the constructed from the origin of the two origin of the two vectors to the vectors to the opposite corneropposite corner

►Measure the Measure the magnitude with the magnitude with the ruler and the angle ruler and the angle with the protractorwith the protractor

5.7 cm = 5.7 N5.7 cm = 5.7 N59° North of East59° North of East

N

S

W

Adding Two Vectors at Right Adding Two Vectors at Right Angles MathematicallyAngles Mathematically

►Magnitude is obtained through the Magnitude is obtained through the Pythagorean TheoremPythagorean Theorem

aa22 + b + b22 = R = R22

(3 N)(3 N)22 + (5 N) + (5 N)22 = R = R22

9 N9 N22+ 25 N+ 25 N22 = R = R22

34 N34 N22 = R = R22

R = 5.8 NR = 5.8 N

N

S

W

5 N

3 N

►The angle is obtained through The angle is obtained through SOHCAHTOASOHCAHTOA

N

S

W

5 N

3 N

adj

opptan

N

N

3

5tan

67.1tan o59

θ

North of East

Solve the following problems Solve the following problems mathematically and graphically using an mathematically and graphically using an

appropriate scaleappropriate scaleA moterboat can move with a velocity of 4 A moterboat can move with a velocity of 4

m/s. What is the resultant velocity if:m/s. What is the resultant velocity if:

The boat is traveling with a current of 2.5 m/s The boat is traveling with a current of 2.5 m/s south?south?

The boat is traveling against a current of 2.5 The boat is traveling against a current of 2.5 m/s south?m/s south?

The boat is trying to move perpendicularly The boat is trying to move perpendicularly (west) across a stream that is flowing south (west) across a stream that is flowing south with a current of 2.5 m/s?with a current of 2.5 m/s?