Forces and Newton’s Laws Dynamics Forces and Newton’s Laws

Force: Any push or pull The SI unit of force is Newtons (N) = (kg Force: Any push or pull The SI unit of force is Newtons (N) = (kg*m/s2) There are four fundamental forces that make up all of the forces in the universe: 1) Gravitational Force - exists between masses 2) Electromagnetic Force - exists between charges 3) Strong Nuclear Force - binds quarks (which make protons, neutrons) 4) Weak Nuclear Force - acts on fermions (e.g. electrons); governs subatomic decay and initiates nuclear fusion

Force of friction, generally resists motion Description Fapp Applied force Ff Force of friction, generally resists motion Fg Force of gravity, weight FN Normal force, perpendicular to surface T Tension, force along a rope or string FE Elastic force FAir Air friction

Newton’s Laws of Motion Newton’s 1st Law

Newton’s 1st Law “An object in motion will stay in motion and an object at rest will stay at rest, unless an outside force is applied to it.” This is also referred to as the Law of Inertia. Inertia: The tendency of an object to remain at a constant velocity.

Imagine that you are racing around a track on a go- kart Imagine that you are racing around a track on a go- kart. List three times when you notice your inertia. 1) 2) 3)

Another way of thinking of Newton’s 1st Law is that if there is no net force on an object then it will stay at a constant velocity. An object with no net force is said to be in equilibrium, so equilibrium implies constant velocity. Remember, if it is not moving then it has a constant velocity of zero!!!

Ex. Imagine a book sitting on a table Ex. Imagine a book sitting on a table. There is a force of gravity pulling down on the book, but there is also a supporting (normal) force pushing up on the book. It stays at rest – constant velocity – because the forces are balanced (i.e. no net force).

Ex. If I drop the book from 2 m, there is only a downwards, gravitational force acting on it. Now that the forces on it are unbalanced, what does the book do? It ACCELERATES!!!!

Newton’s Laws of Motion Newton’s 2nd Law

ΣF or Fnet = ma Newton’s 2nd Law “If a body is acted upon by an unbalanced force, it will accelerate.” Stated as a formula: ΣF or Fnet = ma Note that the units for force are kgm/s2 or N

Ex. A 5.0 kg block is pushed to the right along a frictionless track with a force of 10.0 N. What is its acceleration?

Ex. A 650 kg car accelerates at 4. 0 m/s2 south Ex. A 650 kg car accelerates at 4.0 m/s2 south. What is the net force acting on it?

Since Fnet can be determined using acceleration then you will sometimes be required to use kinematics in solving force problems. Ex: A 1500 kg ice cream truck accelerates from rest to a top speed of 45 km/h in 8.0 s. What was the net force acting on the truck?

Finding Fnet To find Fnet when two forces work together simply add them. Ex. Stan and Kyle are pushing a 75 kg Cartman along a frictionless ice rink. Stan pushes with 55 N and Kyle pushes with 45 N. Find Cartman’s acceleration.

Fnet = Winners – Losers Finding Fnet To find Fnet when many forces act on an object: Fnet = Winners – Losers Ex. The Batmobile exerts a force of 8.50x103 N east, while friction pulls back on it with a force of 1500 N. If it has a mass of 1250 kg, what is its acceleration?

Free Body Diagrams

Free body diagrams show the magnitude and direction of ALL of the forces acting on an object. Generally we represent the object as a box with the force arrows coming out from the centre, in the direction they are acting. Remember that the size of the arrow indicates its relative magnitude.

1. A book is at rest on a table top. Draw the forces acting on the book.

2. A girl is suspended motionless from a bar which hangs from the ceiling by two ropes.

3. An egg is free-falling from a nest in a tree. Neglect air resistance. Diagram the forces acting on the egg as it is falling.

4. A plane flies at a constant velocity (Note: there will be an applied force generated by the engines as well as a lift force provided by the wings).

5. A rightward force is applied to a book in order to move it across a desk with a rightward acceleration. Consider frictional forces. Neglect air resistance. Diagram the forces acting on the book.

6. A rightward force is applied to a book in order to move it across a desk at constant velocity. Consider frictional forces. Neglect air resistance. Diagram the forces acting on the book.

7. A college student rests a backpack upon his shoulder 7. A college student rests a backpack upon his shoulder. The pack is suspended motionless by one strap from one shoulder. Diagram the vertical forces acting on the backpack.

8. A skydiver is descending with a constant velocity 8. A skydiver is descending with a constant velocity. Consider air resistance. Diagram the forces acting upon the skydiver.

10. A football is moving upwards towards its peak after having been booted by the punter. Diagram the forces acting upon the football as it rises upward towards its peak.

Adding Forces On a free body diagram, forces acting in the chosen positive direction are added together and those in the negative direction are subtracted. Forces can only be added/subtracted this way in one dimension. ΣFy = 10 N – 10 N ΣF=ma = 0 N 5 N = 10 kg (ax) ΣFx = 20 N – 15 N ax = 0.5 m/s2 = 5 N [right]