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Reading Assignment 6.1: A. Push of the workers B.Friction C.Normal force D.Gravity E.Net force Workers of a moving company push a refrigerator over a distance of 5 m at a constant speed against a friction force of 200 N. Which of the following forces is doing work on the refrigerator? s=5.0 m

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What is work? Force: agent of change Work/energy: measure of change Agenda: 1.Constant force parallel to displacement 2.Constant force in angle with displacement 3.Variable force parallel to displacement 4.Variable force in variable angle with displacement

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1. Constant force parallel to displacement F s A 100-N force moves the box over a distance of 3 m. The force did 300 Nm or 300 J worth of work.

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1. Example Consider a bucket on a string, as shown. T – The tension in the string is 100 N, while the bucket is lifted to a height of 0.85 m. Calculate the work of the tension. – The bucket is now lowered back to the ground, while the tension in the rope is 80 N. What is the work of the tension? T

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2. Constant force in angle with displacement F s A 100-N force moves the box over a distance of 3 m while pulling at an angle of 30 degrees with horizontal. The force did 260 Nm or 260 J worth of work. 30 o Component of force in direction of displacement:

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2. Example Consider a 40-kg sled that is being pulled at constant speed by a force of 250 N at an angle of 20 above horizontal. Determine the work that is being done by all forces acting on the sled over a distance of 10 m.

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Consider a weightlifter holding a 500 pound- barbell above his head. The weightlifter does a) Positive work on the barbell. b) Negative work on the barbell. c) No work on the barbell.

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Reading Assignment 6.1: What is a scalar product? A.The product between two scalars, resulting in a vector. B.The product between two scalars, resulting in a scalar. C.The product between two vectors, resulting in a vector. D.The product between two vectors, resulting in a scalar.

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Force and displacement at an angle Scalar product between two vectors

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Scalar product In a plane: Work it out

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Work with scalar product - example Children slide a basket of toys with a mass of 10.0 kg from rest down a straight rope. The rope starts in a height of 4.00 m at a second-story window, and leads 8.00 m away from the house. – Write the force of gravity in form of (x,y) components. – Write the displacement vector s in form of (x,y) components. – Use the scalar product in order to calculate the work done by gravity. – The rope is providing a normal force in order to guide the bucket down the rope. How much work is the normal force doing?

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Consider two blocks stacked on a table. Someone pulls the bottom block to the right with a rope in such a way that both blocks accelerate to the right but no slipping occurs at the interface between the top and bottom blocks. Friction at the interface between the two blocks does A. Positive work on the top block. B. No work on the top block. C. Negative work on the top block. F

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Is the force of friction doing work?

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Walking on pavement

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Is the force of friction doing work? 15 20 The packages stay on the sled by means of static friction.

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3 - variable force parallel to displacement F x x F dx F Need to know F(x)

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Example for variable force The force of a spring is proportional to the distance at which the spring has been stretched or compressed away from equilibrium. We can phrase this observation as F= - kx, in which x is the distance from the equilibrium position, the constant k denotes the spring constant, and the minus sign indicates the fact that the force of the spring will always be directed back toward equilibrium. Determine the amount of work done by the spring, if it has a spring constant of 30 N/m if the spring has been stretched by 20 cm. 0 x F x F

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For which of these is the work done by the net force zero?

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Reading Assignment 6.2: Which of the following is the kinetic energy- work theorem? A B C D

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A 10-kg box receives a kick and an initial velocity of 3.5 m/s, and slides up an incline of 20 o. It comes to a stop after 1.2 m. Use the K-W theorem to determine the friction force on the box.

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When a person walks, the force of friction between the floor and the person's feet accelerates the person forward. The floor does a) Positive work on the person. b) Negative work on the person. c) No work on the person.

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