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TRANSCRIPT
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Forces in Equilibrium
The principle of the forces in equilibrium states, “ When forces act upon an object , the object is said to be in a state of equilibrium when the resulting force acting on the object is zero ( no net force acting upon it) ” When the equilibrium is reached, then the object is in two states, that is (i) remains stationary (if the object is stationary) (ii) moves at a constant velocity ( if the object is moving)
Based on , F = ma atau a = F m
When the equilibrium of forces is achieved, then, F = 0 , hence a =0 Thus a = 0 , it means the object remains stationary or moves at a constant velocity.
Newton’s Third Law of Motion
Newton’s third law of motion states , “ To every action there is an equal but opposite direction” Examples Forces in Equilibrium (a)
Weight = Normal reaction (b)
Weight = Tension (c)
Buoyant force = Weight
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(d)
Weight = Normal reaction
(e)
Weight = Normal reaction Pulling force = Frictional force
(f)
Weight = Lifting force Driving force = Dragging force
(g)
Weight = Normal reaction Engine thrust = Air resistance + Frictional force
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(h)
Buoyant force = Weight of load + Weight of helium gas Two Forces in Equilibrium
P + Q = 0 We can rewritten into P = – Q
Example 1 Figure shows a stationary wooden block of mass 2 kg resting on a table.
Calculate (a) the weight of the wooden block (b) the normal reaction Solution
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Three Forces in Equilibrium
P + Q + R = 0
When three forces in equilibrium the triangle of forces in one direction (in order) Example 2 The following figure shows a steel sphere of mass 12 kg suspended from a length of rope which is pulled to the side by a horizontal force of M. The tension of another rope is N.
(a) Draw a triangle of forces. (b) Calculate the value of (i) M (ii) N Solution
Resultant force Force is a vector quantity and hence it has magnitude and direction. Two or more forces which act on an object can be combined into a single force called the resultant force. If two forces are in same line, vector addition is easy. We simply add the forces if both pull or push together; subtract them if one is in the opposite direction. If they are at an angle, the resultant force can be determined by the triangle method and the parallelogram method.
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Parallelogram method :
In this method the tail of the first vector is joined to the tail of second vector and then draw a parallelogram. The diagonal represents the resultant force. Triangle method:
In this method the tip of the first vector is joined to the tail of second vector and then draw a line to complete the triangle. The third side represents the resultant force. Example 3 Find the resultant force for the following figure:-
Solution:
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Example 4
The figure shows a trolley is pulled by two forces What is the magnitude and the direction of the resultant force acting on the trolley. Solution Example 5 Figure shows a boat is pulled by two forces. Calculate the magnitude of the resultant force acting on the trolley.
Solution:
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Resolution of forces A force can be resolved into two components, that is, (i) the horizontal component, Fx and (ii) the vertical component , Fy
Fx = F cos q Fy = F sin q
· q is an angle between the force F to the horizontal line · the sign of the force depend on the quadrant where the force , F is placed
For an object on a inclined plane, the weight,W of the object can be resolved into two components ; (i) parallel to inclined plane, A (ii) perpendicular to inclined plane,B
A = W sin q B = W kos q
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Example 6 Find the values of Px and Py for the following figures.
Solution: Example 7
Figure shows a stationary wooden block of mass 50 g which is placed on a inclined plane that is at an angle of 40o to the horizontal. What is the magnitude of the weight parallel to the inclined plane.
Solution: