# work - Mechanics and Modern Physics Dr. Bernd Stelzer PHYS...

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Dr. Bernd Stelzer Mechanics and Modern Physics PHYS 120 SFU Fall 2010 Dr. Bernd Stelzer

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Introducing Work October 25, 2010 Goal: Complete the concept of energy and its conservation. The bobsleigh team is increasing the sled’s kinetic energy by pushing it forward . They do work on the sled, (i.e. transfer energy) PHYS120 2
Work October 25, 2010 A net force acting on an object as it is displaced along a path ds is doing work on the object. W = F s i s f d s SI unit of Work: [Nm] = 1Joule = 1J PHYS120 3 E.g. Energy is transferred from person to spring as the person stretches the spring. For a constant force parallel to displacement: W = F ⋅ Δ x

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Scalar Vector Product (Dot Product) October 25, 2010 В A B = A cos θ B = AB cos A B = ( A x ˆ i + A y ˆ j ) ( B x ˆ i + B y ˆ j ) A B = A B B = AB A = A x B x ˆ i ˆ i + ( A x B y + A y B x ) ˆ i ˆ j + A y B y ˆ j ˆ j A B = A x B x + A y B y The scalar vector product (dot product) is the sum of the products of the components ˆ i x y ˆ i ˆ j = 0 ˆ i ˆ i = ˆ j ˆ j = 1 Orthogonality ˆ j A B = AB cos PHYS120 4
Scalar Vector Product (Dot Product) October 25, 2010 A = 3 ˆ i + 3 ˆ j B = 4 ˆ i ˆ j A B = A x B x + A y B y = 3 4 + 3 ( 1) = 9 A B = AB cos θ = A x 2 + A y 2 B x 2 + B y 2 cos = 18 17 cos = 9 В =59 o PHYS120 5

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Scalar Vector Product (Dot Product) October 25, 2010 PHYS120 6
Pulling a box across the floor October 25, 2010 A constant force results in work along a straight line displacement. Maximum work is done if the force F is parallel to the displacement No work is done if the force and displacement are perpendicular PHYS120 7 W = F d x x i x f = Fdx cos θ x i x f = F cos dx x i x f = F cos Δ x

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Dr. Bernd Stelzer Mechanics and Modern Physics PHYS 120 SFU Fall 2010 Dr. Bernd Stelzer
Recap - Work October 25, 2010 Goal: Complete the concept of energy and its conservation. The bobsleigh team is increasing the sled’s kinetic energy by pushing it forward . They do work on the sled, (i.e. transfer energy) PHYS120 9

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Work Kinetic Energy Theorem October 25, 2010 F s = ma s = m dv s dt dv s dt = dv s ds ds dt = v s dv s ds F s = mv s dv s dy mv s dv s = F s ds mv s dv s v i v f = F s ds s i s f 1 2 mv s 2 v i v f = 1 2 mv sf 2 1 2 mv si 2 = F s ds s i s f K f K i = F d s s i s f Δ K = W Newton’s 2 nd Law: Using chain rule: Work Kinetic energy theorem In general, more than one force can act on a system: Δ K = W net W net = W i i F net = F i i PHYS120 10