Newton’s Laws, Forces, and circular motion

1. Newton’s Laws, Forces, and circular motion

2. Newton’s 1st law of motion • The “Law of Inertia” • An object will maintain its original state of motion unless acted upon by an external unbalanced force. An object will maintain a constant velocity (straight-line, uniform rate of motion) unless acted upon by an external unbalanced force.

3. Translation: • All objects at rest will remain at rest until disturbed by an unbalanced force to get it moving. • All objects in motion will move in a straight-line direction at the same rate forever unless a force causes the object to speed up, slow down, or change direction.

4. Newton’s 2nd Law of motion: • The acceleration experienced by an object is proportional to the magnitude of the force (F) causing the acceleration and inversely proportional to the mass of the object being accelerated.

5. Translation: • F = m * a • The greater the mass of the object, the greater the force required to accelerate the object. • The lesser the mass of the object, the lesser the force required to accelerate the object. • If two objects of unequal mass (one greater, one lesser) are affected by the same force, the object with the greater mass experiences a lesser acceleration, the object with the lesser mass experiences the greater acceleration.

6. Newton’s 3rd Law of motion: • “Law of paired forces” • When two objects interact, the force exerted by one object is equal to and opposite the force exerted by the other object.

7. Translation: • “For every action there is an equal but opposite reaction.” • Object 1 pushes or pulls with the same force upon object 2 as object 2 pushes or pulls upon object 1, but in opposite directions.

8. Interactive Game/Video! • http://science.discovery.com/games-and-interactives/newtons-laws-of-motion-interactive.htm

9. What is a force? • Forces are push and pull actions that one object induces upon other objects. • Forces change the state of motion of objects, they make them speed up, slow down, or change direction. • Forces cause acceleration. (Remember, acceleration is a change in direction or velocity).

10. Therefore, forces induce acceleration by changing the state of motion or velocity of objects when they interact. • Forces are vectors, they have both magnitude and direction. They can be positive or negative depending upon direction.

11. Calculating Forces • Because of Newton’s 2nd Law, we know: Force = Mass x Acceleration. • So our units would be in kg*m/s2, because that’s mass*acceleration. That’s too long to look at. So we named the kg x m/s2 unit after the man who discovered the laws of motion: Sir Isaac Newton. • Newtons are always in kg*m/s2. We abbreviate this with an N, when talking about forces.

12. Formulas! • We can put these formulas together to solve for all our problems. • F = m x a • A = (Vf-V0)/T • N=kg(m/s2)

13. Example! • A 3.0 kg ball is accelerated at 1.5 m/s2. Calculate the force acting upon the ball. • F = m*a. • F = 3.0 kg x 1.5 m/s2 • 4.5 kg x m/s2 • 4.5 N. • So the force acting upon the ball is 4.5 N.

14. Balanced and Unbalanced Forces • When two objects interact, their forces are either going to be balanced or unbalanced. • We call the combination of them the “net force.” Net force is the calculation that’s either going to inevitably cause movement or the object to hold still.

15. Balanced Forces • Balanced Forces occur when the forces of two interacting objects that exert upon each other are equal in magnitude and opposite in direction. • For balanced forces, the net force acting upon both objects is zero – the forces equal each other and cancel each other out.

16. Case 1: Opposite Directions • Two objects are tethered together and moving in opposite directions with equal force. Because each object is pulling in the opposite direction with the same magnitude of force, neither object will move – they remain still. Net force would equal 0. Think of this like an tied tug of war game.

17. Case 2: • Two objects are pushing against each other from opposite directions with the same magnitude. Because the objects are pushing equally on each other in opposite direction with equal magnitude of force, neither will move. Net force is 0. This is like a book sitting on a table.

18. If we want to do the math: • Case 1: • Net force acting upon A = -2N + 2N = 0 • Net force acting upon B = 2N + -2N = 0 • Case 2: • Net force acting upon A = 2N +-2N = 0 • Net force acting upon B = -2N+2N = 0

19. Unbalanced Forces • They occur when the forces of two interacting objects that exert upon each other are • Not Equal • Not in Opposite Directions The Net force is the sum of the magnitudes in the direction of the greatest force. The object will move.

20. Case 3: • Two objects tethered together and moving in opposite direction with unequal force. • Object A is pulling to the left with greater force than object B pulling right. Because A has the greater force, both objects will move in A’s direction with the net force. Object B is pulled backwards.

21. Case 4: • Two objects are pushing on each other. • Object A is pushing to the right with greater force, object B is pushing left with less. Because object A has the greater force, both objects will move in A’s direction with the net force. Object B is pushed backwards.

22. Proving with Math! • Case 3: • Net force acting upon A = -4N+2N = -2N • Net force acting upon B = 2N+-4N = -2N • Case 4: • Net force acting upon A = 4N+-2N = 2N • Net force acting upon B = -2N+4N = 2N

23. Uniform Circular Motion and Speed • Some definitions! • Uniform Circular Motion is when an object is rotating or revolving at a constant rate in a circular path. • Rotation is the motion of spinning. • Revolution is the motion of one object moving around another.

25. Radius (r) = half the diameter. • Circumference (C) = total distance around the circle. • C = 2πr • Formula to calculate velocity of moving in uniform circular path:

26. Example! • A merry-go-round has a radius of 6 meters. It rotates 4 times per minute. Calculate the rotation speed of the merry-go-round at its edge. • Remember in our formula “n” is the number of times the object rotates or revolves.

27. Example 2! • A ball on a string is swung in a circle. It completes 2 revolutions per minute. The length of the string is 40 cm. Calculate the speed of the ball moving around in a circle.

28. Blast from the past! • Centripetal acceleration = acceleration experienced by an object moving in a uniform circular path or when direction is changing. • Remember our formula from last unit? • Remember the V is squared. Centripetal acceleration increases exponentially with speed. • The turn radius is in the denominator. That means as your turn radius gets bigger, the centripetal acceleration get smaller, and vice versa.

29. Centripetal force – the force required to keep an object moving in the circular motion or curved path. • Centripetal force is what pushes all the force of things moving in a circle toward the center, and keeps moving in a center. (If it’s too low, stuff goes flying off in a straight line). • Same formula for regular force, EXCEPT: • When we write it, we put the little “c”’s in it so we know it’s for centripetal force: Fc=m*Ac • We use centripetal acceleration in the calculation instead of regular acceleration (Ac = (v)2/r)

30. Example! • A gaucho swings a 2.0 kg bolas in a circle. The length of the rope is connected to the bolas (radius) is 1.3 m. The gaucho swings the bolas 1 rotation per minute, calculate the revolution speed, the centripetal acceleration, and the centripetal force.