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Newton’s 2 nd Law

Newton’s 2 nd Law. As we learned before, balanced forces mean constant velocity So if an object accelerates, there MUST be an UNbalanced force acting on it in the direction of the acceleration.

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Newton’s 2 nd Law

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  1. Newton’s 2nd Law • As we learned before, balanced forces mean constant velocity • So if an object accelerates, there MUST be an UNbalanced force acting on it in the direction of the acceleration. • Example: hitting a hockey puck (accel = unbalanced force), as opposed to a hockey puck sliding on the ice (no accel = no unbalanced force) Constant velocity Accel

  2. What makes sense? • We know that unbalanced force produces acceleration • How are force and acceleration related? • What else would be related to acceleration? • How is force related to acceleration? • How is mass related to acceleration?

  3. Newton’s 2nd Law • The acceleration produced by a net force on an object is directly proportional to the magnitude of the net force, is in the same direction as the net force,and is inversely proportional to the mass of the object.

  4. Newton’s 2nd Law: the easy way Fnet = mass × accelerationor Fnet = ma

  5. Newton’s 2nd Law: the slightly harder way Fnet = mass × accelerationor Fnet = ma Where net force vector and acceleration vectors are in the same direction

  6. Example: I push on an 8 kg cart with 10N force F = ma, so a = 10/8 = 1.25m/s2 WRONG! Need to include all forces Fnet = ma, so a = 8/8 = 1 m/s2 Newton’s 2nd Law: the Force Fnet = ma Make sure you use net force! Ffr =2N 10N 8kg Fnet = 8N

  7. Units Fnet = m a kg ms2 N kg m s2 = • Force is in N, so a Newton (N) is just a much simpler name for kg•m/s2

  8. Back to “Weight” • Weight is just a force that always uses the acceleration of gravity (on earth, 9.8 m/s2). Force = mass × acceleration so Weight = Fg = mass × 9.8 m/s2 • The acceleration due to gravity is often written “g”. So weight is often written as “m g”

  9. Examples • Practice Problem #1: A 5 kg object is accelerating at 2 m/s2. What is the net force acting on it? • Answer: Fnet = ma = (5 kg)(2 m/s2) = 10 N • Practice Problem #2: A 2000 N force is exerted on a 500 kg car. What will the car’s acceleration be? • Answer: 2000 N = (500 kg)(a), a = 4 m/s2 10N 5kg A = 2m/s2 2000N 500kg A = 4m/s2

  10. Example: Foamcrete • Foamcrete is a solid paving material soft enough to collapse under the weight of an airliner. • Suppose a 747 with a mass of 1.75 x 105 kg and an initial speed of 26.8 m/s is slowed to a stop in 3s. What is the magnitude of the slowing force exerted by the Foamcrete on the plane? • m = 1.75 x 105; a = 26.8/3 = 8.9 m/s2, so f = ma = 1.56 x 106N

  11. (magnitude) (direction) Newton’s 3rd Law For every action force, there is an equal and opposite reaction force.

  12. Newton’s 3rd Law • ALL forces come in pairs (NO exceptions!) • You cannot exert a force on something without that object exerting an equal force back against you!

  13. Examples of Force Pairs • Jumping off of the ground – Action: you push down on the ground Reaction: the ground pushes you up!! • Hitting a nail with a hammer – Action: hammer exerts force on the nail Reaction: nail exerts force back on the hammer

  14. Practice Problem • Identify at least 6 action/reaction force pairs in this diagram: Ugly Truck Moving Co. A B

  15. Different from Newton’s 1st and 2nd! • With Newton’s 1st (and eventually 2nd) Laws, we only talk about the forces on a single object. • For N3L, we are now talking about the interaction between TWO objects.

  16. Horse and Cart Problem Problem: If the force of the cart on the horse (Fc-h) is just as strong as the force of the horse on the cart (Fh-c), how can the horse move the cart? Fh-c Fc-h

  17. Horse and Cart Solution • Think about each object separately! • The force diagram for the cart: • The force diagram for the horse: FN Fh-c Ff FG FN Fc-h Ff FAPPLIED FG

  18. Horse and Cart Solution • Answer: the horse can move because the force from the ground (forward) on the horse is even bigger than the force from the cart (backward)!!! • IMPORTANT!!! - The “equal and opposite” forces don’t cancel each other out, because they are acting on different objects!

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