Aim: How can we describeAim: How can we describe resultant force (net force)? resultant force (net force)?

Identify some forces.Identify some forces. Identify the unit for force.Identify the unit for force.Explain the difference between mass and Explain the difference between mass and

weight.weight.A student has a mass of 75 kg. The A student has a mass of 75 kg. The

student weighs 831 newtons. Determine student weighs 831 newtons. Determine the acceleration due to gravity.the acceleration due to gravity.

Aim: How can we describeAim: How can we describe resultant force (net force)? resultant force (net force)?

List all vectors and units.List all vectors and units.

How can we describe forces acting How can we describe forces acting on an object?on an object?

Two or more forces that act on the same Two or more forces that act on the same object at the same time are calledobject at the same time are called

concurrent forcesconcurrent forces..Ex: Ex:

Combining forcesCombining forces

Resultant force (net force)Resultant force (net force) Is the single force that is equivalent to the Is the single force that is equivalent to the

combined effect of these concurrent forces.combined effect of these concurrent forces.Example 1: Example 1:

F1=10N

F2=5N

R = 15N Feq= -15N

The force vector needed to produce The force vector needed to produce equilibrium is the same length as the equilibrium is the same length as the resultant vector but it is pointing in the resultant vector but it is pointing in the opposite direction. (Fopposite direction. (Feqeq))

Example: 3 Example: 3 If forces act in opposite directions, the If forces act in opposite directions, the

angle between them is 180 degrees, the angle between them is 180 degrees, the resultant force is the smallest.resultant force is the smallest.

F1 = 3N F2 = 10N

F1 = 3NF2 = 10N

Combining forces Combining forces

Head-to-tail method – combine the head of one Head-to-tail method – combine the head of one vector to the tail of the other vector.vector to the tail of the other vector.

If two forces act in the same direction, the angle If two forces act in the same direction, the angle between them is 0 degrees and the resultant between them is 0 degrees and the resultant force is the sum of their magnitudes (R = Fforce is the sum of their magnitudes (R = F11+F+F22))

Ex2: Ex2: F1=10N

F2=3NF1=10N F2=3N

R = 13N

Sketch the Resultant force and Sketch the Resultant force and Equilibrium forceEquilibrium force

How can we sketch the equilibrium How can we sketch the equilibrium force?force?

The vector sum of the concurrent forces acting The vector sum of the concurrent forces acting on an object is called the on an object is called the net forcenet force F Fnet. net.

(Resultant force)(Resultant force) If the net force acting on the object is zero, the If the net force acting on the object is zero, the

object is in object is in equilibriumequilibrium. .

F1F2

F1

F2

RFeq

If two concurrent forces act at right angles If two concurrent forces act at right angles to each other, the head-to-tail method to each other, the head-to-tail method produces a right triangle.produces a right triangle.

F2

F1

F2

F1

R

When is resultant force is greater?When is resultant force is greater?When the two forces act in the same When the two forces act in the same

direction, 0 degree angle, they produce the direction, 0 degree angle, they produce the largest resultant force.largest resultant force.

When the two forces act in opposite When the two forces act in opposite directions, 180 degree angle, they produce directions, 180 degree angle, they produce the smallest resultant force.the smallest resultant force.

How can we analyze force vectors?How can we analyze force vectors?

1.1. Find the resultant force vector.Find the resultant force vector.

2.2. A 10 Newton force and a 4 Newton force A 10 Newton force and a 4 Newton force act concurrently on a point. As the angle act concurrently on a point. As the angle increases from 0increases from 0° to 180° what happens ° to 180° what happens to the resultant force?to the resultant force?

3N 7N

Triangular method of adding concurrent forces.Triangular method of adding concurrent forces. Leave the first force in the same position. Take the Leave the first force in the same position. Take the

second force and slide it to the head of the first force. second force and slide it to the head of the first force. (Head-to-tail method)(Head-to-tail method)

To find the resultant force: draw a line from the tail of the To find the resultant force: draw a line from the tail of the first force vector to the head of the last vector. first force vector to the head of the last vector.

To find the equilibrium force: draw the same size line as To find the equilibrium force: draw the same size line as the resultant force but 180the resultant force but 180°° from the resultant force. from the resultant force.

F2

F2

F1

R

F1

ExamplesExamplesDraw the resultant force for the following Draw the resultant force for the following

vectors.vectors.

F1

F2

F2

R

P P

F1

ExamplesExamples

F1

F2

F3

F1

F2

F3

R

Equilibrium forceEquilibrium force The vector sum of the concurrent forces acting on an The vector sum of the concurrent forces acting on an

object is called the object is called the net forcenet force F Fnet. net. (Resultant force)(Resultant force) If the net force acting on the object is zero, the object is If the net force acting on the object is zero, the object is

in in equilibriumequilibrium. . The force vector needed to produce equilibrium is the The force vector needed to produce equilibrium is the

same length as the resultant vector but it is pointing in same length as the resultant vector but it is pointing in the opposite direction. (Fthe opposite direction. (Feqeq))

F1

F2

F1

F2

RFeq

If two concurrent forces act at right angles If two concurrent forces act at right angles to each other, the head-to-tail method to each other, the head-to-tail method produces a right triangle.produces a right triangle.

F2

F1

F2

F1

R

Let’s calculate the resultant force Let’s calculate the resultant force vector using Pythagorean theoremvector using Pythagorean theorem

cc2 2 = a= a22 + b + b22

Use physics terms: Use physics terms: 222 )40()30( NNR

22

21

2 FFR

F2 = 40N

F1= 30N

R

222 1600900 NNR 22 2500NR

22 2500NR

NR 50

Using the same example in the previous slide. What Using the same example in the previous slide. What is the is the angleangle of the resultant force. (The angle is of the resultant force. (The angle is located next to the tail of the resultant force)located next to the tail of the resultant force)

Using Soh Cah Toa, find angle theta. (hint: Toa)Using Soh Cah Toa, find angle theta. (hint: Toa)

adjacent

OppositeTan

F2 = 40N

F1= 30N

R = 50N

θ

1

2

F

FTan

33.130

40

N

NTan

33.1Tan

53)33.1(1Tan

Aim: How can we analyze force Aim: How can we analyze force vectors and components?vectors and components?

Calculate the resultant force and the Calculate the resultant force and the angle. Sketch and label the equilibrium angle. Sketch and label the equilibrium force.force.

10N

5N

Example: Find the resultant force and the angle.Example: Find the resultant force and the angle.

22

21

2 FFR

2222 125)10()5( NNNR

22 125NR

NR 1.11

1

2

F

FTan

25

10

N

NTan

2Tan

4.63

)2(1Tan

F2 = 10N

F1= 5N

R = ?

θ

R = 11.1N

Aim: How can we analyze force Aim: How can we analyze force vectors?vectors?

1)1) Sketch the resultant force and Sketch the resultant force and equilibrium force.equilibrium force.

2)2) Calculate the magnitude of the Calculate the magnitude of the equilibrium force.equilibrium force.

7N2N

1) Which pair of vectors produce the 1) Which pair of vectors produce the greatest resultant force?greatest resultant force?

2) Which pair of vectors produce the least 2) Which pair of vectors produce the least resultant force? resultant force?

The diagram below represents a force The diagram below represents a force vector A, and resultant vector, R.vector A, and resultant vector, R.

Where should we draw vector B?Where should we draw vector B?Recall: The resultant vector goes from Recall: The resultant vector goes from

start to end.start to end.

A

R

B

The diagram below represents a force The diagram below represents a force vector A, and resultant vector, R.vector A, and resultant vector, R.

Where should we draw vector B?Where should we draw vector B?

A

R

B

Force vector componentsForce vector components

A person is pulling a sled with a 100-A person is pulling a sled with a 100-newton force at a 30newton force at a 30° angle with the ° angle with the horizontal. horizontal.

1) Sketch a picture1) Sketch a picture2) Calculate the horizontal force.2) Calculate the horizontal force.3) Calculate the vertical force.3) Calculate the vertical force.4) As the angle decreases, describe the 4) As the angle decreases, describe the

horizontal force and vertical force.horizontal force and vertical force.