Dynamics. Newton s Second Law of Motion

Transcription

1 Dynamics Newton s Second Law of Motion

2 Do Now 1. Write down the algebraic equation representing the 2d Law of Motion. 2. What effect the change in one of the variables in the equation will have on the acceleration? a. m=constant Double the net force ->acceleration Half the net force-> acceleration b. Fnet = constant Double the net force-> acceleration Half the net force-> acceleration m F net a

3 Equilibrium Objects at equilibrium (the forces acting upon the object are balanced, net force = 0) do not accelerate.

4 Net Force Causes Acceleration If an object is not at rest and is not moving at a constant velocity then there is a net force that causes change in motion, or accelerated motion. Acceleration = Change in Velocity/ Time Interval

5 Acceleration and Net Force Acceleration depends on net force. To increase the acceleration of an object, you must increase the net force on the object. If you double the net force, the acceleration doubles. Acceleration is directly proportional to the net force. Acceleration Net Force

6 Mass Resists Acceleration If you apply the same force to an empty and loaded shopping cart, the loaded shopping cart will accelerate slower.

7 Acceleration and Mass For the same force, the acceleration produced is inversely proportional to the mass. acceleration 1 mass If you apply force to twice as much mass the acceleration is twice smaller. If you triple the mass, the acceleration is three times smaller.

8 Newton s Second Law of Motion The acceleration produced by a net force on an object is directly proportional to the magnitude of the net force, and inversely proportional to the mass of the object. F net acceleration mass a F net m F net ma

9 Direction of Acceleration Acceleration has the same direction as the net force. (Think of pulling an imaginary rope to change the motion of the object).

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15 Practice Problems 1. Two forces, F1 =12 N and F2=2N, are applied to a block on a frictionless horizontal surface. If the magnitude of the block s acceleration is 2.0 m/s/s, what is the mass of the block? F1 F2

16 Do Now A 25-newton northward force and a 35-newton southward force act concurrently on a 15-kg object on a frictionless surface. What is the magnitude of the object s acceleration.

17 3. A net force of 10 N accelerates an object at 5 m/s/s. What net force would be required to accelerate the same object at 1.0 m/s/s?

18 Questions How does acceleration depend on the net force? How does acceleration depend on the mass of the object? According to the Second Law of Motion, a = F m Does the direction of acceleration depend on the net force?

19 Do Now Calculate the acceleration of a 100 kg cart when the net force on it 50 N. F a m 50N a 100kg a = 0.5 m/s/s

20 Free Fall Explained Consider the free-falling motion of a 1000-kg baby elephant and a 1-kg overgrown mouse.

21 Acceleration of Gravity This ratio (F net /m) is sometimes called the gravitational field strength and is expressed as 9.8 N/kg (for a location upon Earth's surface). Because the 9.8 N/kg gravitational field at Earth's surface causes a 9.8 m/s/s acceleration of any object placed there, we often call this ratio the acceleration of gravity.

22 Free-body diagrams for four situations are shown below. For each situation, determine the net force acting upon the object.

23 Free-body diagrams for four situations are shown below. The net force is known for each situation. However, the magnitudes of a few of the individual forces are not known. Analyze each situation individually and determine the magnitude of the unknown forces.

24 2d Law of Motion. Practice Problems 1. Determine the accelerations that result when a 12-N net force is applied to a 3-kg object and then to a 6-kg object. 2. A net force of 15 N is exerted on an encyclopedia to cause it to accelerate at a rate of 5 m/s 2. Determine the mass of the encyclopedia.

25 3. Suppose that a sled is accelerating at a rate of 2 m/s 2. If the net force is tripled and the mass is doubled, then what is the new acceleration of the sled? 4. Suppose that a sled is accelerating at a rate of 2 m/s 2. If the net force is tripled and the mass is halved, then what is the new acceleration of the sled?

26 5. A force of F newtons causes mass m of m kilograms to accelerate at 24 m/s 2. What acceleration will occur under the following conditions: a) The force is doubled to 2F newtons, and the mass remains the same. b) The force is F newtons and the mass is tripled.

27 6. Calculate the acceleration of a kg jumbo jet just before takeoff when the thrust for each of four engines is N. 7. Calculate the horizontal force that must be applied to a 1-kg puck to make it accelerate on a horizontal friction-free with the same acceleration it would have if it would be dropped and fell freely. a=g=10 m/s/s

28 8. a. Calculate the acceleration it you push with a 20-N horizontal force on a 2 kg block on a horizontal friction-free air table. b. What acceleration occurs if the friction force is 4 N?

29 Newton s Second Law of Motion Force and Acceleration Review Questions. 6.1 Forces Cause Acceleration 1. When a hockey puck is struck with a hockey stick, an unbalanced force acts on the puck and the puck accelerates. 2. d. unbalanced 3. net force 4. increases 5. c. A net force on an object causes acceleration. 6. A net force acts on both carts. The net force on the cart that accelerates faster, is 3 times greater than the other force (masses of the cars are equal).

30 6.2 Mass Resists Acceleration 7. If the force is constant, the increase in mass will result in decrease in acceleration. 8. When one quantity increases, the other quantity decreases. 9. b. acceleration ~ 1/mass

31 6.3 Newton s Second Law. 10. a. mass b. force d. acceleration 11. a. acceleration is directly proportion to the net force. b. the direction of acceleration is the same as net force. c. the acceleration is inversely proportional to mass 12. m/s 2 kg 13. True 14. d. 200 N 15. d. halving the mass 16. The object accelerates at the same rate. 17. a. F a m

32 32. free fall 6.6 Free Fall Explained. 33. They both strike the ground at the same time if there is no air resistance. 34. gravity 35. a. They all fall with the same acceleration. b. The net force acting on them is their weight. c. Their weight to mass ratios are always the same. d. Their acceleration is g, the acceleration due to gravity.