forces & the effects pt ii

7/27/2019 Forces & the Effects Pt II

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Forces & The Effects Pt

II

Calculations of Vector, Turning,

Balance, Pressure & Density


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Calculating Vectors

Vectors are the directionthat a force is applied in.

Two vectors acting in thesame direction can beadded together toproduce a sum orresultant vector whichcan be used to replaceboth vectors and producethe same effect.


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The two forces, Fx and Fy are acting on an object. To

calculate their sum, Fx is drawn in one direction. Fy is thendrawn at right angles to the end of Fx. The length of thelines is representative of the force exerted. In this case Fxcould equal 4N and Fy could equal 2N.

Both sides are connected using a third line which representsthe sum or resultant drawn from the start of Fx to the endof Fy. The scale drawing could then be used to calculate the

length of the sum which would equal the force in N, orPythagoras theorem (a + b = c) could be used tocalculate the hypotenuse or F. However, this can only beused when the forces are acting at 90 to each other, whichnot always be the case.


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Resultant Force = O

Two equal forces acting in theopposite direction will cancel each

other out, by creating equilibrium. Thismeans the object will remainstationary or, if it is already moving,

will continue to do so in the samedirection and at the same speed.


5/13

In the picture,the weightlifter

has the force ofgravity workingto pull the weightdown towardsthe Earth. He

must thereforeexert an upwardcontact force ofequal size tokeep the weightin the air.


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Resultant Force > O

If the resultant force is > O, then the object isaffected by the force.

If the object was stationary, then it will begin to

move in the direction of the force. If the object is already moving, it will accelerate or

decelerate or change direction depending on theforce.

For a system in equilibrium the sum of the verticalcomponents will be equal to the sum of thehorizontal components.

For an object affected by force the equation is F =m x a


8/13

In the example of thepool balls, the cuedelivers a force to astationary cue ball,which then travels inthe direction of theforce, until it hitsanother ball, whichalso exerts a force onthe cue ball andcauses it todecelerate. At the

same time the forcedelivered by the cueball will cause theother ball to move.


9/13

Tension

Tension is the result of two vectors workingindependently of each other.

The two separate effects of a vector can be foundby splitting the vector in two. This is called the

resolution of a vector. If a telephone pole is being held in place by a

cable, there is both a horizontal and vertical forcebeing applied to the pole. Tension is being appliedin both directions, there fore we have tension in thecable (T), tension in the vertical component (Tv)and tension in the horizontal component (Th).

Therefore Th + Tv = T. But to find the magnitude,Th = Tsin and Tv = Tcos, where is the anglebetween the vector and the vertical component(the angle between the vector and the horizontal

component will be 90- .


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Example

A car is being towed with a ropeinclined at 20 to the horizontal. The

tension in the rope is 350N. Work outthe horizontal and vertical componentsof the tension in the rope.


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Moments

A turning force is known as a moment and has onlytwo possible directions, clockwise andcounterclockwise.

The moment of a force is dependent on two things the size of the force and the perpendiculardistance between the force line and the pivot (axisof rotation).

Therefore the moment of a force = force xperpendicular distance. This is also called torqueand is measured in Nm.

Moments can also be balanced. The principle ofmements states that for an object to be balancedthe sum of the clockwise moments is equal to thesum of the anticlockwise moments.


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If we imaginethat the

diagramrepresents alever in amachine, the

force will beexerted whenthe lever isturned in aclockwisedirectionaround thepivot.


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Example

A wrench is being used to tighten abolt. Suppose a 10 N force was

applied to the wrench handle 25 cmfrom the pivot point. Calculate thetorque being applied by the wrench to

the bolt.

forces & the effects pt ii

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