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Dr- Sonia Reda

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chapter 7 Kinetic energy and Work 7.2 What is energy 7.3Kinetic energy 7.4Work 7.5 Workandkinetic Energy 7.5 Work and kinetic Energy 7.6Work done by the gravitational force 7.7 Work done by a Spring force 7.8 Power 7.2 What is energy 7.3Kinetic energy 7.4Work 7.5 Workandkinetic Energy 7.5 Work and kinetic Energy 7.6Work done by the gravitational force 7.7 Work done by a Spring force 7.8 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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Dr- Sonia Reda What is Energy? 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.

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Dr- Sonia Reda Kinetic Energy Kinetic energy K is energy associated with the state of motion of an object. 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: 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.

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

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

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Dr- Sonia Reda Finding an Expression for Work we can use Eq to write, for components along the x axis, v 2 =v o 2 + 2a x d By multiplying the above Eq with ½ m

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Dr- Sonia Reda Finding an Expression for Work

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Dr- Sonia Reda Kinetic Energy Work-Kinetic Energy Theorem Change in KE work done by all forces K w

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Dr- Sonia Reda xixi xfxf = 1/2mv f 2 – 1/2mv i 2 = K f - K i K = K Work done by net force = change in KE Work-Kinetic Energy Theorem F x Vector sum of all forces acting on the body

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Dr- Sonia Reda Checkpoint 1 A particle moves along an x axis. Does the kinetic energy of the particle increase, decrease, or remain the same if the particles velocity changes A particle moves along an x axis. Does the kinetic energy of the particle increase, decrease, or remain the same if the particles 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?

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

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

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Dr- Sonia Reda (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:

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Dr- Sonia Reda mg F h Lift mass m with constant velocity Work done by me (take down as +ve) = F.(-h) = -mg(-h) = mgh Work done by gravity = mg.(-h) = -mgh ________ Total work by ALL forces ( W) = 0 What happens if I let go? = K Gravitation and work Work done by ALL forces = change in KE W = K

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Dr- Sonia Reda Work Done by a Spring Force The spring force given by Hookes Law: The work done by spring force:

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Dr- Sonia Reda Compressing a spring Compress a spring by an amount x Work done by me Fdx = kxdx = 1/2kx 2 Work done by spring -kxdx =-1/2kx 2 Total work done ( W) = 0 = K What happens if I let go? x F-kx

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Dr- Sonia Reda F f d Work done by me = F.d Work done by friction = -f.d = -F.d Total work done = 0 What happens if I let go?NOTHING!! Gravity and spring forces are Conservative Friction is NOT!! Moving a block against friction at constant velocity

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Dr- Sonia Reda 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? 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?

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Dr- Sonia Reda 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,

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Dr- Sonia Reda Power The rate at which work is done by a force is called the 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 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 We define the instantaneous power P as the instantaneous rate of doing work, so that W = F. Δx

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Dr- Sonia Reda The units of power

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Dr- Sonia Reda 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. 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.

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Dr- Sonia Reda (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.

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Dr- Sonia Reda (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.

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Dr- Sonia Reda

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