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Understanding Hooke's Law: The Foundation of Elasticity| Chapter 5 Physics 9th

HOOKE'S LAW   Introduction In physics, Hooke's Law is one of the fundamental principles governing how objects deform under external forces . Named after the 17th-century British physicist Robert Hooke, this law provides a crucial understanding of the behavior of elastic materials, such as springs and rubber bands. Whether stretching a rubber band or compressing a spring, Hooke's Law helps explain what happens when forces act on these materials. What is Hooke's Law: Hooke's Law states that the force F needed to extend or compress a spring by some distance x is proportional to that distance. Mathematically, it is expressed as: F= -kx Here k represents the spring constant, which is the measure of the stiffness of the spring, and x is the displacement from the displacement position.  The negative sign indicates that the force exerted by the spring is in the opposite direction of the displacement.  Understanding the Spring Constant: The spring constant k is a critical co

Torque or Moment of Force

 Torque or Moment of Force The turning effect of the force is called Torque. It is also known as Moment of Force.  Torque depends on: The magnitude of force. The perpendicular distance between point of application of the force and the pivot.  It is also called as Moment Arm. Now considering above equation, we have unit of torque is  Nm. Moments are described as Clockwise or Anti-clockwise in direction. Example Problems on Torque Example 01: A driver tightens the nut of the wheel using 2cm long spanner by exerting a force of 300N. Find the torque. Data: d= 2cm => 2/100= 0.02m F= 300N Torque =? Solution: Torque = F x d Torque = 300 x 0.02 Torque = 6Nm. Self-Assessment Question: What will be the moment of force? When 500N of force is applied on 40cm long spanner to tighten the nut? Data: d= 40cm = 0.4m F=500N Torque =? Solution: Torque = F x d Torque = 500 x 0.4 Torque = 200Nm. Example 02: A mechanic tightens the nut of the bicycle using a 15cm long spanner by exerting a force of 200N.

Determination of Force from its Rectangular Components | Chapter 4 Turning Effect of Forces| 9th Physics

 DETERMINATION OF FORCE FROM ITS RECTANGULAR COMPONENTS In this method, we are going to find the resultant force, its direction and the magnitude, when its rectangular components are given. Consider the figure given above. Let Fx and Fy are the rectangular/perpendicular components of the force F. Applying Head-to-Tail Rule we get, OR = OP + PR Since,  OR =F OP= Fx PR= Fy so,  F = Fx + Fy For Magnitude of Force: Applying Pythagoras theorem to the above figure we get,            Taking Square root on both the sides. For Direction: The direction of the force (F) with the x-axis can be found as,

Resolution of Force | Chapter 4 Turning Effect of Forces | 9th Physics

 Resolution of Force/ Rectangular Components of Force The process of splitting of vectors into mutually perpendicular  components is called Resolution of Force.  It is also known as rectangular components of forces.  F= Fx+Fy Now we can find the magnitudes of both of the rectangular components using trigonometric ratios, considering the given right-angled triangle. Now in order to solve problems related to the rectangular components of forces we have the following some of the values of the trigonometric ratios at different angles. Example 01: A man is pushing a wheelbarrow on a horizontal ground with a force of 300N making an angle of 60 with the ground. Find the horizontal and vertical components of the force. Data: F= 300N θ= 60 Degrees Fx=? Fy=? Solution: (i) Finding the horizontal component of Force: Fx= Fcos θ  Fx=(300).cos(60) Fx= (300)(0.5) Fx= 150 N (ii) Finding the Vertical Component of Force: Fy= Fsin θ  Fy=(300).sin(60) Fy= 300(0.866) Fy= 259.8N Result: The horizontal and ve

Trigonometric Ratios | Chapter 4 Turning Effect of Forces

 TRIGONOMETRIC RATIOS Definition:                             The ratio of any two sides of a right-angled triangle is known is Trigonometric Ratios.  There are total six trigonometric ratios are there out of which three are fundamental ratios and remaining three are said to be derived ratios. These six trigonometric ratios are given as under, Fundamental Ratios: 1. sin θ 2. cos θ 3. tan θ Derived Ratios: 4. cosec θ 5. sec θ 6. cot θ   Consider figure 1, we have following formulas of these trigonometric ratios, sin θ=Perpendicular/Hypotenuse cos θ= Base/ Hypotenuse tan θ= Perpendicular / Hypotenuse   Now remaining three are the reciprocals of the above fundamental formulas, cosec θ= 1/sin θ or Hyp/perpendicular sec θ=1/cos θ or hyp/base cot θ=1/tan θ or base/perpendicular Short Trick to Remeber these formulas, Some People have Curly Brown Hairs Through proper brushed Considering first sentence  Some stands for sine People stands for Perpendicular  Have for Hypotenuse Follow the video t