SPH 4C Unit 2 Mechanical Systems Forces and Free Body Diagrams Learning Goal: I can consistently identify and draw Free Body Diagrams for given real world situations. There are 4 fundamental forces Gravity attraction between objects that have mass. Strong nuclear force that keeps atomic nuclei together. Weak nuclear responsible for making things radioactive. Electromagnetic combination of electrical force between particles at rest and magnetic field created when particles are moving. What is Force? Definition: The symbol for force is The units for force is Types of Force: Free Body Diagrams a vector diagram showing all the forces acting on an object helps visualize and analyze the situation called a free body diagram because it takes the object away from its surroundings Steps for Drawing a Free Body Diagram 1. Draw the compass points. 2. Draw a dot to represent the object. 3. From that point, draw a force vector to represent each force acting on the object. Make sure to label each vector! Common Forces to Draw force due to gravity normal force force of friction Applied force
Examples Draw a FBD for the following situations: 1) A car travelling with uniform velocity. 2) A car travelling with non uniform velocity. 3) A falling apple. 4) A box on a slope. 5) 6)
Newton's 3 Laws of Motion Learning Goal: I can explain Newton's 3 Laws of Motion and apply them to real world applications. Newton's First Law (Law of Inertia) An object at rest will continue at rest until a force is applied to it. An object which is moving will continue moving until a force is applied to it. Inertia The ability of an object to resist changing its motion. Newton's First Law in easier terms: Newton's Second Law F u = m a Any unbalanced force causes an object to accelerate. Example: What is the acceleration when an unbalanced force of 50 N [E] is applied to a 40 kg person. Example: A student is bowling with her friends. She gives a 7.0 kg bowling ball an acceleration of 5.0 m/s 2 [forward]. Calculate the net force on the ball.
Example: A driver and his motorcycle have a combined mass of 280 kg. They accelerate from 7.0 m/s [E] to 34 m/s [E] in 4.2 seconds. What is the net force on the driver and the motorcycle? Example: Determine the missing quantities. 1) 2) Newton's Third Law Newton's Third Law states that Example: A cart has a chamber inside it where there is a spring that launches a ball horizontally (see diagram). If the cart is 1.2 kg, the ball is 0.07 kg and the spring exerts a 2 N force on the ball, answer the following: A) Identify 3 action reaction pairs of forces when the spring is released. B) Draw a FBD of the ball and calculate its acceleration while the spring is pushing on it.
"Real Life" Applications: Tires: Jet Engines:
Normal and Frictional Forces Learning Goal: I can determine the Normal force acting on an object and calculate the corresponding Frictional Force. Definition: A frictional force When drawing the vector representing friction The coefficient of friction is Why is F N the important force? Types of Friction
Example: A 100 kg crate is pushed across the floor. Determine the following: A) What is the minimum force required to start moving the crate if the coefficient of static friction is 0.6? B) What is the minimum force required to continue moving the crate once it is in motion if the coefficient of kinetic friction is 0.4? C) What applied force is required to accelerate the crate at 2 m/s 2? D) If you push down on the crate with 100 N of force, demonstrate how the force of friction changes. E) If you life up on the crate with 100 N of force, demonstrate how the force of friction changes.
Simple Machines Learning Goal: I can identify the different types of simple machines and explain effort and load forces. A Machine is There are two families of Machines: 1) The Lever Family 2) The Inclined Plane Family The Lever Family Definitions: A Lever is a rigid bar that can rotate around a support called a fulcrum. A Fulcrum is a fixed support around which lever can rotate. An Effort Force is a force applied to one part of a lever to move a load. A Load Force is the force exerted by the load. An Effort Arm is the distance between the fulcrum and the effort force. A Load Arm is the distance between the fulcrum and the load.
First Class Lever A First Class Lever has the fulcrum between the load and the effort force. Some examples... Second Class Lever A second class lever has the load between the fulcrum and the effort force. Some examples... Third Class Levers A third class lever has the effort force between the fulcrum and the load force. Some examples... Real World Applciations
The Inclined Plane Family Definitions: An Inclined Plane is a ramp. A Wedge is a double inclined plane. A Screw is an inclined planed wrapped around a central shaft. A Compound Machine is a machine made up of two or more simple machines. Examples: 1) The ramp. 2) The axe. 3) The car jack.
Torque and Levers Learning Goal: I can explain the concept of torque and calculate it for real world applications. Calculating Torque Formula: Example: A 30 cm long wrench is rotated counter clockwise by a 100 N force. Determine the torque on the nut. Calculating Force Acting on Levers Formula: First Class Lever Second Class Lever Third Class Lever
Example: Determine the missing value for the following.
Mechanical Advantage and Efficiency Learning Goal: I can identify mechanical advantage for a given real world situation and calculate the resulting efficiency. Definitions: Actual Mechanical Advantage: The ratio of the load force to effort force. ie. Ideal Mechanical Advantage: The ratio of the effort arm (length) to the load arm (length). ie. Comparing Actual Mechanical Advantage (AMA) to Ideal Mechanical Advantage (IMA) For static equilibrium (no motion on the machine) the AMA and IMA are equal. When the components of a machine move, IMA is always greater than AMA because... Example: Assume that the forearm mass is 2.0 kg concentrated at the midpoint of the forarm as show in the diagram. The effort force of the triceps to hold the forearm static is 100 N. Determine the following: A. The magnitude of the load force of the forearm due to its own mass. B. The AMA of the arm. C. The magnitude of the load force of the forearm when holding a 5 kg ball. D. The AMA when holding the ball from part C. 20 cm 4.1 cm Fulcrum
Efficiency of Machines Percent Efficiency: is the ratio of the AMA to IMA of a machine. Formula: Example: A 50 N cart is pulled up a 7.5 m ramp with an effort force of 25 N parallel to the ramp, raising the cart 1.5 m above the initial level. Determine the following: A. The IMA. B. The AMA. C. The percent efficiency of the ramp.