Unit 3 Forces Newtons Laws of Motion Newtons
- Slides: 32
Unit 3 Forces & Newton’s Laws of Motion
Newton’s 1 st Law of Motion
Facts about Force • • Unit is the NEWTON(N) Is by definition a push or a pull Can exist during physical contact (Tension, Friction, Applied Force) Can exist with NO physical contact, called FIELD FORCES ( gravitational, electric, etc)
Newton’s First Law – The Law of Inertia INERTIA – a quantity of matter, also called MASS. Italian for “LAZY”. Unit for MASS = kilogram. Weight or Force due to Gravity is how your MASS is effected by gravity. NOTE: MASS and WEIGHT are NOT the same thing. MASS never changes When an object moves to a different planet. What is the weight of an 85. 3 -kg person on earth? On Mars (g=3. 2 m/s/s)?
Newton’s First Law An object in motion remains in motion in a straight line and at a constant speed OR an object at rest remains at rest, UNLESS acted upon by an EXTERNAL (unbalanced) Force. There are TWO conditions here and one constraint. Condition #1 – The object CAN move but must be at a CONSTANT SPEED Condition #2 – The object is at REST Constraint – As long as the forces are BALANCED!!!!! And if all the forces are balanced the SUM of all the forces is ZERO. The bottom line: There is NO ACCELERATION in this case AND the object must be at EQILIBRIUM ( All the forces cancel out).
Free Body Diagrams A pictorial representation of forces complete with labels. FN • Weight(mg) – Always drawn from the center, straight down • Force Normal(FN) – A surface force always drawn perpendicular to a surface. • Tension(T or FT) – force in ropes and always drawn AWAY from object. • Friction(Ff)- Always drawn opposing the motion.
Free Body Diagrams Ff FN mg
Newton’s First Law – The Law of “EQUILIBRIUM” Since the Fnet = 0, a system moving at a constant speed or at rest MUST be at “EQUILIBRIUM”. TIPS for solving problems • Draw a FBD • Resolve anything into COMPONENTS • Write equations of equilibrium • Solve for unknowns
Example A 10 -kg box is being pulled across the table to the right at a constant speed with a force of 50 N. a) Calculate the Force of Friction a) Calculate the Force Normal FN Fa Ff mg
Example Suppose the same box is now pulled at an angle of 30 degrees above the horizontal. a) Calculate the Force of Friction a) Calculate the Force Normal Fa FN Fay 30 Ff Fax mg
Example A cafe sign with a mass of 65. 5 kg is being held up by 2 cables as shown in the picture to the left. Calculate the tension in each of the ropes. T 2 sin 35 T 2 cos 35 T 1 sin 19 T 1 cos 19 mg 750 N T 1 = 650 N
Newton’s 2 nd Law of Motion
Newton’s 2 nd Law "The acceleration of an object is directly proportional to the NET FORCE AND inversely proportional to the mass. " Acceleration is directly proportional to the NET Force. DIRECTLY = They do the same thing. If the force increases, the acceleration increases. If the force decreases, the acceleration decreases. Acceleration is inversely proportional to the mass. INVERSELY = They do the opposite. If the mass decreases, the acceleration will increase. If the mass increases, the acceleration will decrease.
Newton’s 2 nd Law N. S. L. works based on these direct and inverse relationships. As 2 of the variable change, ONE of them must remain constant. If the force is constant, the acceleration and mass change as shown above. If we add a second dog pulling with 100 N just like the first dog, we could pull the sled with twice the acceleration, provided the mass of the sled was constant.
Putting it all together 3 N 10 kg Magnitude of FNET= 7 N Direction = RIGHT Acceleration = 0. 70 m/s/s
Tips Draw a free body diagram 2. Break vectors into components if needed 3. Find the NET force by adding and subtracting forces that are on the same axis as the acceleration. 4. Set net force equal to “ma” this is called writing an EQUATION OF MOTION. NOTE: To avoid negative numbers, always subtract the smaller forces from the larger one. 1.
Example An elevator with a mass of 2000 kg rises with an acceleration of 1. 0 m/s/s. What is the tension in the supporting cable? Equation of Motion T mg 21, 600 N
Example A 50 N applied force drags an 8. 16 kg log to the right across a horizontal surface. What is the acceleration of the log if the force of friction is 40. 0 N? Fn a 50 N 40 N mg 1. 23 m/s/s
Example A sled is being accelerated to the right at a rate of 1. 5 m/s/s by a rope at a 33 degree angle above the + x. Calculate the Frictional Force if the mass of the sled is 66 kg and the tension in the rope is 150 N. FN T Tsinq q Tcosq Ff mg 26. 8 N
Newton’s 3 rd Law of Motion
Newton’s Third Law “For every action there is an EQUAL and OPPOSITE reaction. � This law focuses on action/reaction pairs (forces) � They NEVER cancel out All you do is SWITCH the wording! • PERSON on WALL • WALL on PERSON
Newton’s 3 rd Law This figure shows the force during a collision between a truck and a train. You can clearly see the forces are EQUAL and OPPOSITE. To help you understand the law better, look at this situation from the point of view of Newton’s Second Law. There is a balance between the mass and acceleration. One object usually has a LARGE MASS and a SMALL ACCELERATION, while the other has a SMALL MASS (comparatively) and a LARGE ACCELERATION.
Examples Action: HAMMER HITS NAIL Reaction: NAIL HITS HAMMER Action: Earth pulls on YOU Reaction: YOU pull on the earth
Friction & Inclined Planes
TWO types of Friction � Static – Friction that keeps an object at rest and prevents it from moving � Kinetic – Friction that acts during motion
Force of Friction � The Force of Friction is directly related to the Force Normal. � Mostly due to the fact that BOTH are surface forces The coefficient of friction is a unitless constant that is specific to the material type and usually less than one. Note: Friction ONLY depends on the MATERIALS sliding against each other, NOT on surface area.
Friction and Newton’s 1 st Law If the coefficient of kinetic friction between a 35 -kg crate and the floor is 0. 30, what horizontal force is required to move the crate to the right at a constant speed across the floor? Fn Fa Ff mg 102. 9 N
Friction and Newton’s 2 nd Law Suppose the same 35 kg crate was not moving at a constant speed, but rather accelerating at 0. 70 m/s/s. Calculate the applied force. The coefficient of kinetic friction is still 0. 30. Fn Fa Ff mg 127. 4 N
Inclines Ff FN q q q mg q Tips • Rotate Axis • Break weight into components • Write equations of motion or equilibrium • Solve
Friction & Inclines A person pushes a 30 -kg shopping cart up a 10 degree incline with a force of 85 N. Calculate the coefficient of friction if the cart is pushed at a constant speed. Fa Fn q Ff mg q 0. 117
Example A 5 -kg block sits on a 30 degree incline. It is attached to string that is thread over a pulley mounted at the top of the incline. A 7. 5 -kg block hangs from the string. � a) Calculate the tension in the string if the acceleration of the system is 1. 2 m/s/s � b) Calculate the coefficient of kinetic friction. T FN m 2 gcos 30 30 T m 2 g m 1 m 2 gsin 30 m 1 g Ff 30
Example 64. 5 N 0. 80 N
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