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بسم الله الرحمن الرحيم Dr- Sonia Reda

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**Kinetic energy and Work**

chapter 7 Kinetic energy and Work By Dr\ Sonia Reda Dr- Sonia Reda

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**chapter 7 Kinetic energy and Work**

What is energy 7.3 Kinetic energy 7.4 Work 7.5 Work and kinetic Energy 7.6 Work done by the gravitational force 7.7 Work done by a Spring force Power

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**Outline Chapter 7 Work and Kinetic energy**

Work done by a net force results in kinetic energy Some examples: gravity, spring, friction

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**However, this definition is too vague to be of help to us now.**

What is Energy? The term energy is so broad that a clear definition is difficult to write. Technically, Energy is a scalar quantity associated with the state (or condition) of one or more objects. However, this definition is too vague to be of help to us now. Dr- Sonia Reda

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Kinetic Energy Kinetic energy K is energy associated with the state of motion of an object. For an object of mass m whose speed v is well below the speed of light, Kinetic energy K is: Unit for Kinetic energy is: Kinetic energy is a scalar quantity. Dr- Sonia Reda

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Work Work W is energy transferred to or from an object by means of a force acting on the object. Energy transferred to the object is positive work, Energy transferred from the object is negative work. Dr- Sonia Reda

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Properties of Work Only the force component along the object’s displacement will contribute to work. The force component perpendicular to the displacement does zero work. A force does positive work when it has a vector component in the same direction displacement, A force does negative work when it has a vector component in the opposite direction. Work is a scalar quantity. Dr- Sonia Reda

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**Finding an Expression for Work**

we can use Eq to write, for components along the x axis, v2 =vo2 + 2axd By multiplying the above Eq with ½ m Dr- Sonia Reda

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**Finding an Expression for Work**

Dr- Sonia Reda

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**Work-Kinetic Energy Theorem**

Change in KE work done by all forces Chap 7.3 DK Dw Dr- Sonia Reda

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**Vector sum of all forces acting on the body**

Work-Kinetic Energy Theorem SF x Vector sum of all forces acting on the body xf xi Work and Energy 7.3 Work and Kinetic energy Note that in the slide F is the net force acting on the body. = 1/2mvf2 – 1/2mvi2 = Kf - Ki = DK Work done by net force = change in KE Dr- Sonia Reda

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Checkpoint 1 A particle moves along an x axis. Does the kinetic energy of the particle increase, decrease, or remain the same if the particle’s velocity changes (a) from −3 m/s to −2 m/s and (b) from −2 m/s to 2 m/s? (c) In each situation, is the work done on the particle positive, negative, or zero? Dr- Sonia Reda

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Example 7-3 During a storm, a crate of crepe is sliding across a slick, oily parking lot through a displacement while a steady wind pushes against the crate with a force The situation and coordinate axes are shown in Fig. 7-5. (a) How much work does this force do on the crate during the displacement? . Dr- Sonia Reda

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**Work done by the wind force on crate :**

(a) How much work does this force from the wind do on the crate during the displacement? SOLUTION: Work done by the wind force on crate : The wind force does negative work, i.e. kinetic energy is taken out of the crate. Dr- Sonia Reda

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(b) If the crate has a kinetic energy of 10 J at the beginning of displacement , what is its kinetic energy at the end of ? SOLUTION: Dr- Sonia Reda

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**Work done by ALL forces = change in KE**

Gravitation and work Work done by me (take down as +ve) = F.(-h) = -mg(-h) = mgh h Work done by gravity = mg.(-h) = -mgh F ________ Total work by ALL forces (W) = mg =DK Lift mass m with constant velocity This example resolves the situation when there are 2 forces, which are equal and opposite. The change in KE is zero. Work done by ALL forces = change in KE DW = DK What happens if I let go? Dr- Sonia Reda

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**Work Done by a Spring Force**

The spring force given by Hooke’s Law: The work done by spring force: Dr- Sonia Reda

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**Compressing a spring =DK What happens if I let go?**

Compress a spring by an amount x F -kx x Work done by me Fdx = kxdx = 1/2kx2 Work done by spring -kxdx =-1/2kx2 Here also the two forces are equal and opposite Total work done (DW) = =DK What happens if I let go? Dr- Sonia Reda

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**Moving a block against friction at constant velocity**

d Work done by me = F.d Work done by friction = -f.d = -F.d Total work done = Here again the two forces are equal and opposite The force here (friction) is different from the gravity force or the spring force. Friction is NOT a conservative force What happens if I let go? NOTHING!! Gravity and spring forces are Conservative Friction is NOT!! Dr- Sonia Reda

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Sample Problem 7-8 In Fig. 7-11, a cumin canister of mass m = 0.40 kg slides across a horizontal frictionless counter with speed v = 0.50 m/s. It then runs into and compresses a spring of spring constant k = 750 N/m. When the canister is momentarily stopped by the spring, by what distance d is the spring compressed? Dr- Sonia Reda

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SOLUTION: We assume the spring is massless. Work done by the spring on the canister is negative. This work is : Kinetic energy change of the canister is : Therefore, Dr- Sonia Reda

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**Power The rate at which work is done by a force is called the power.**

The average power due to the work done by a force during that time interval as We define the instantaneous power P as the instantaneous rate of doing work, so that W = F . Δx Dr- Sonia Reda

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The units of power Dr- Sonia Reda

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Sample Problem 7-10 Figure 7-14 shows constant forces and acting on a box as the box slides rightward across a frictionless floor. Force is horizontal, with magnitude 2.0 N; force is angled upward by 60° to the floor and has magnitude 4.0 N. The speed v of the box at a certain instant is 3.0 m/s. Dr- Sonia Reda

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(a) What is the power due to each force acting on the box at that instant, and what is the net power? Is the net power changing at that instant? SOLUTION: The kinetic energy of the box is not changing. The speed of the box remains at 3 m/s. The net power does not change. Dr- Sonia Reda

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**(b) If the magnitude of is, instead, 6**

(b) If the magnitude of is, instead, 6.0 N, what now is the net power, and is it changing? SOLUTION: There is a net rate of transfer of energy to the box. The kinetic energy of the box increases. The net power also increases. Dr- Sonia Reda

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THANK شكـراً YOU Dr- Sonia Reda

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Kinetic energy Vector dot product (scalar product) Definition of work done by a force on an object Work-kinetic-energy theorem Lecture 10: Work and kinetic.

Kinetic energy Vector dot product (scalar product) Definition of work done by a force on an object Work-kinetic-energy theorem Lecture 10: Work and kinetic.

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