Tiêu đề PHYSICS PART- 3.pdf ✅

PHYSICS Class - C3 (Part - III) WORK POWER ENERGY WISE UP Dot product : Dot product of two vectors is defined as the product of their magnitudes and the cosine of the angle between the two. (OR) The dot product is the product of the magnitude of one of the vector quantities and the scalar component of second vector in the direction of the first vector: The scalar product of the two vectors, P⃗ and Q⃗ is defined as P⃗ ⋅ Q⃗ = |P⃗ ||Q⃗ |cos θ. Here θ is the angle between P⃗ and Q⃗ . The angle between the two vectors P⃗ and Q⃗ is given by cos θ = P⃗ ⋅Q⃗⃗ |P⃗ ||Q⃗⃗ | ∴ θ = cos−1 [ P⃗ ⋅Q⃗⃗ |P⃗ ||Q⃗⃗ | ] Examples of Scalar Product : a) The scalar product of force and displacement is called work done by that
force. i.e., W = F . S b) Dot product between force and velocity vectors gives power i.e., instantaneous power F ⋅S t = F⃗ ⋅ V⃗ Work : Work is said to be done by a force if the point of application of force undergoes displacement either in the direction of force or in the direction of component of force. When the displacement of the body makes an angle ' θ ' with the applied constant force, Then the work done by a constant force F is given by W = (component of force along the displacement) × (displacement ) = (Fcos θ)(S) = F ⋅ S • Work done is a scalar quantity • It's SI unit is J or kgm2 s −2 • It's CGS unit is erg or gcm2 s −2 • It's dimensional formula is [M1 L 2 T −2 ] • 1 J = 107 erg. Energy : Energy is the capacity to do work SI unit : joule CGS unit : erg It is a scalar physical quantity. Dimensional formula: [M1 L 2 T −2 ] Power: The work done in unit time is called power. Power = workdone time taken P = W t It's SI unit is 'watt' or 'W' or kgm2 s −3 It's dimensional formula is [M1 L 2 T −3 ]
It is a scalar quantity. 1 W = 1 J/s 1 horse power = 1hp = 746 W CONCEPT - I Work : Work is said to be done by a force if the point of application of force undergoes displacement either in the direction of force or in the direction of component of force. Work done by a constant force : 1. When the displacement of the body is in the direction of constant applied force, then the work done by the force is measured as the product of magnitude of force F and distance ' S ' through which the body moves. 2. When the displacement of the body makes an angle ' θ ' with the applied constant force, Then the work done by a constant force F is given by W = ( component of force along the displacement ) × (displacement ) = (Fcos θ)(S) = F . S
Work done is a scalar product (or) dot product of F and S WORK DONE BY VARIABLE FORCE If a particle is subjected to a varying force F but maintains a constant direction, the work done in moving the body from x1 to x2 is W1→2 = ∫x1 x2 Fdx Problem : A body covers a distance of 4 m under the action of force F = (17 − 4x) where ' x ' is the distance in meters. Find the work done by the force. Solution : W = ∫ Fdx = ∫0 4 (17 − 4x)dx = 17[x] − 4 [ x 2 2 ] = 17[4] − 2[4 2 ] = 36 J • Work done is a scalar quantity • It's SI unit is J or kgm2 s −2 • It's dimensional formula is [M1 L 2 T −2 ] • Work done by a constant force can be positive or negative or zero. i) If the displacement is in the direction of force or in the direction of component of force, work done is positive (⬚ as θ = 0 ∘ ) W = FScos θ = FScos 0 = FS Ex : When a person lifts a body, the work done by the force of lifting is positive (⬚ as θ = 0 ∘ ) ii) If the displacement is in the direction opposite to that of force or component of force, work done is negative (⬚ as θ = 180∘ ) Ex : When a person lifts a body, the work done by the force of gravity is negative (⬚ as θ = 180∘ )