Physics 101 Lecture 7 Kinetic Energy and Work

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1 Phsics 101 Lecture 7 Kinetic Energ and Work Dr. Ali ÖVGÜN EMU Phsics Department

2 Wh Energ? q Wh do we need a concept of energ? q The energ approach to describing motion is particularl useful when Newton s Laws are difficult or impossible to use q Energ is a scalar quantit. It does not have a direction associated with it November 7, 016

3 What is Energ? q Energ is a propert of the state of a sstem, not a propert of individual objects: we have to broaden our view. q Some forms of energ: n Mechanical: n Kinetic energ (associated with motion, within sstem) n Potential energ (associated with position, within sstem) n Chemical n Electromagnetic n Nuclear q Energ is conserved. It can be transferred from one object to another or change in form, but cannot be created or destroed November 7, 016

4 Kinetic Energ q Kinetic Energ is energ associated with the state of motion of an object q For an object moving with a speed of v KE 1 mv q SI unit: joule (J) 1 joule 1 J 1 kg m /s November 7, 016

5 KE 1 mv Wh? November 7, 016

6 Work W q Start with 1 mv 1 mv 0 FΔ Work W q Work provides a link between force and energ q Work done on an object is transferred to/from it q If W > 0, energ added: transferred to the object q If W < 0, energ taken awa: transferred from the object November 7, 016

Definition of Work W q The work, W, done b a constant force on an object is defined as the product of the component of the force along the direction of displacement and the

7 Definition of Work W q The work, W, done b a constant force on an object is defined as the product of the component of the force along the direction of displacement and the magnitude of the displacement W ( F cosθ ) Δ n F is the magnitude of the force n Δ is the magnitude of the object s displacement!! n θ is the angle between F and Δ November 7, 016

8 Work Unit q This gives no information about n the time it took for the displacement to occur n the velocit or acceleration of the object q Work is a scalar quantit q SI Unit n Newton meter Joule mv n N m J n J kg m / s ( kg m / s ) m 1 1 mv0 ( F cosθ ) Δ W ( F cosθ ) Δ November 7, 016

9 Work: or -? q Work can be positive, negative, or ero. The sign of the work depends on the direction of the force relative to the displacement W ( F cosθ ) Δ n Work positive: W > 0 if 90 > θ> 0 n Work negative: W < 0 if 180 > θ> 90 n Work ero: W 0 if θ 90 n Work maimum if θ 0 n Work minimum if θ 180 November 7, 016

10 Eample: When Work is Zero q A man carries a bucket of water horiontall at constant velocit. q The force does no work on the bucket q Displacement is horiontal q Force is vertical q cos 90 0 W ( F cosθ ) Δ November 7, 016

11 Eample: Work Can e Positive or Negative q Work is positive when lifting the bo q Work would be negative if lowering the bo n The force would still be upward, but the displacement would be downward November 7, 016

Work Done b a Constant Force q The work W done on a sstem b an agent eerting a constant force on the sstem is the product of the magnitude F of the force, the magnitude Δr of the displacement of the

12 Work Done b a Constant Force q The work W done on a sstem b an agent eerting a constant force on the sstem is the product of the magnitude F of the force, the magnitude Δr of the displacement of the point of application of the force, and cosθ, where θ is the angle between the force and displacement vectors: W!! F Δr FΔr cosθ W I W III F! Δr! I 0 F! Δr! III FΔr F! Δr! II W II W IV FΔr F! Δr! IV FΔr cosθ November 7, 016

Work and Force q An Eskimo pulls a sled as shown. The total mass of the sled is 50.0 kg, and he eerts a force of 1.

13 Work and Force q An Eskimo pulls a sled as shown. The total mass of the sled is 50.0 kg, and he eerts a force of N on the sled b pulling on the rope. How much work does he do on the sled if θ 30 and he pulls the sled 5.0 m? W ( F cosθ ) Δ ( J N)(cos30! )(5.0m) November 7, 016

14 Work Done b Multiple Forces q If more than one force acts on an object, then the total work is equal to the algebraic sum of the work done b the individual forces W net W b individual forces n Remember work is a scalar, so this is the algebraic sum W net W W W ( F cosθ ) Δr g N F November 7, 016

15 Work and Multiple Forces q Suppose µ k 0.00, How much work done on the sled b friction, and the net work if θ 30 and he pulls the sled 5.0 m? F net, N mg F sinθ N mg F sinθ 0 W fric ( f µ NΔ µ ( mg F sinθ ) Δ k k (0.00)(50.0kg 9.8m / s cos180 N J k! sin 30 ) Δ! )(5.0m) f k Δ W net W 90.0J F W fric W N J W g J 0 0 November 7, 016

16 Kinetic Energ q Kinetic energ associated with the motion of an object 1 KE mv q Scalar quantit with the same unit as work q Work is related to kinetic energ 1 mv 1 mv 0 F netδ Wnet KEf KEi ΔKE November 7, 016

17 November 7, 016

18 Work-Kinetic Energ Theorem q When work is done b a net force on an object and the onl change in the object is its speed, the work done is equal to the change in the object s kinetic energ n Speed will increase if work is positive n Speed will decrease if work is negative Wnet KEf KEi ΔKE W net 1 mv 1 mv 0 November 7, 016

19 Work and Kinetic Energ q The driver of a kg car traveling on the interstate at 35.0 m/s slam on his brakes to avoid hitting a second vehicle in front of him, which had come to rest because of congestion ahead. After the breaks are applied, a constant friction force of N acts on the car. Ignore air resistance. (a) At what minimum distance should the brakes be applied to avoid a collision with the other vehicle? (b) If the distance between the vehicles is initiall onl 30.0 m, at what speed would the collisions occur? November 7, 016

20 Work and Kinetic Energ q q (a) We know 3 v0 35.0m / s, v 0, m kg, fk Find the minimum necessar stopping distance W net W fric W g f k WN Wfric 1 Δ 0 mv0 1 1 mv 3 3 ( N ) Δ ( kg)(35.0m / s Δ 76. 6m f 1 mv ) i 3 N November 7, 016

21 Work and Kinetic Energ q q q 3 (b) We know Δ 30.0m, v0 35.0m / s, m kg, fk Find the speed at impact. Write down the work-energ theorem: 1 1 Wnet Wfric fkδ mv f mvi v f v0 fkδ m 3 v f ( 35m / s) ( )( N)(30m) 745m / s kg 3 N v f 7.3m / s 3 v0 35.0m / s, v 0, m kg, fk November 7, N

22 Work Done a Spring qspring force F k November 7, 016

23 qf 0 Spring at Equilibrium November 7, 016

24 Spring Compressed November 7, 016

25 lim Δ 0 f 0 i f FΔ Fd i f f W F d kd i i k d ma 1 k f W kd k k i 1 1 i f Work done b spring on block Fig. 7.9, p. 173

26 Measuring Spring Constant q Start with spring at its natural equilibrium length. q Hang a mass on spring and let it hang to distance d (stationar) q From F k mg k mg d so can get spring constant. 0 November 7, 016

27 Scalar (Dot) Product of Vectors q The scalar product of q two rvectors r is written as A n It is also called the dot product r r A A cos θ n θ is the angle between A and q Applied to work, this means r r W FΔ rcosθ F Δ November 7, 016

28 Dot Product q q q The dot product sas something about how parallel two vectors are. The dot product (scalar product) of two vectors can be thought of as the projection of one onto the direction of the other.!! A A cosθ! A i Acosθ A Components A!! A A A ( A cosθ )! θ A! A( cosθ ) November 7, 016

29 Projection of a Vector: Dot Product q q q The dot product sas something about how parallel two vectors are. The dot product (scalar product) of two vectors can be thought of as the projection of one onto the direction of the other.!!! A A cosθ! A i Acosθ A Components π/ A!! A A A i j 0; i i 1; i k j Projection is ero A! 0; j 1; j k k k 1 0 November 7, 016

30 November 7, 016 Derivation q How do we show that? q Start with q Then q ut q So A A A A!! k j i A k j A A i A!! ) ( ) ( ) ( ) ( ) ( k j i A k k j i j A k j i A i k j i A k j A A i A!! 1 1; 1; 0 0; 0; k k j j i i k j k i j i A A A k A k j j A i A i A!!

31 Scalar Product!! q The vectors A i 3 j and i j q Determine the scalar product A!!? A!! A A (-1) q Find the angle θ between these two vectors A A A " " A cosθ A θ cos ! ( 1) 5 November 7, 016

32 P: November 7, 016

33 P3: P4: P5: November 7, 016

34 P6: P7: P8: November 7, 016

35 P9: P10: November 7, 016

Physics 111 Lecture 6 Work-Energy -Power Dr.Ali ÖVGÜN

Physics 111 Lecture 6 Work-Energy -Power Dr.Ali ÖVGÜN EMU Physics Department www.aovgun.com Why Energy? q Why do we need a concept o energy? q The energy approach to describing motion is particularly useul