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Understanding Forces in Mechanics

Learn how to calculate forces and equilibrium with Newton's laws of motion. Practice drawing free-body diagrams and solving for net force, acceleration, and tension in various scenarios.

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Understanding Forces in Mechanics

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  1. Do Now: • 1. What is the formula to calculate weight? • 2. A. Draw the resultant force and calculate it. • B. Calculate the angle. R = 8.6N 7N 7N Θ=54.5° 5N 5N

  2. Aim: How can we calculate forces acting on an object? Free-Body diagrams FN Fapp Ff Fg

  3. FN Fg Free-body diagrams – is a sketch that shows all of the forces acting on an object. Example1: Draw a free-body diagram of the forces acting on a text book sitting on a table. Normal force – contact force exerted by the surface on the object. (always perpendicular to the surface)

  4. Ex2: An .1 kilogram egg is free-falling from a nest in a tree. Neglect air resistance. Fg

  5. Ex3: A 50 newton object is suspended motionless from the ceiling by two ropes. FT FT Fg

  6. A rightward force is applied to a book in order to move it across a desk. Draw the free-body diagram. FN Ff Fapp Fg

  7. Aim: How can we describe objects in equilibrium? • Explain equilibrium in one word. • Determine the normal force of a 35 newton object at rest on a table.

  8. How can we define equilibrium? • Forces are equal in a specific direction. (x-direction & Y-direction) • Resultant force equals zero. (net force = 0N) • Ex: A box has a mass of 10 kg. Calculate the magnitude of the normal force. FN Fg

  9. Equilibrium At rest At constant velocity Fnet = 0 Newtons

  10. A student pushes a 15 newton box across the table with 20 newtons of force at constant velocity. • ***Constant velocity the net force equals zero*** • What does “a 15 newton box mean?” • Sketch a free body diagram. • Determine the frictional force.

  11. A flying bird is gliding (no wingflaps) from a tree to the ground at constant velocity. Consider air resistance. Draw a free-body diagram. Fair fric Fg

  12. A student holds a 4.5 kilogram object from a string. The object is motionless. Calculate the force of tension in the string. FT Fg

  13. Do Now: • 1. List three ways an object can have acceleration. • A 10 Newton force to the left is applied to a box. Also, a 10 Newton force to the right is applied to the same box. The box must be • A) at rest • B) in motion • C) either in motion or at rest

  14. How can we describe Newton’s 1st law?

  15. Introduction to Newton’s laws of Motion • Dynamics – is the branch of mechanics that deals with how the forces acting on an object affect its motion. • An object in dynamic equilibrium moves with constant velocity. That means No NET Force! Net force equals zero.

  16. How can we apply Newton’s first law of motion? • A .5 kilogram mass is hanging from a spring. How can we determine the net force?

  17. How can we describe the two states of equilibrium? Equilibrium Static Equilibrium Dynamic Equilibrium Net force zero, object moving with constant velocity Net force zero, object at rest

  18. How can we describe inertia? • Inertia is the tendency of an object to resist a change in state of motion. • Mass is used to measure inertia. (kilograms) • Inertia and mass are directly proportional. • Example: The more mass an object has the more inertia the object has.

  19. Newton’s first law of motion – An object at rest will remain at rest and an object in motion (constant velocity) will remain in motion unless acted on by an unbalanced force. • Have you ever experienced inertia in an automobile while it is braking to a stop?

  20. Describe the following situation using Newton’s first law. • While riding a skateboard (or bicycle), you fly forward off the board when hitting a curb which abruptly halts the motion of the skateboard. • To dislodge ketchup from the bottom of a ketchup bottle, it is often turned upside down and thrusted downward at high speeds and then abruptly halted.

  21. How can we apply Newton’s 2nd law? • A 6 kilogram box is being pushed with a 25 newton force to the left on a table. The box is moving with constant velocity. • Sketch free body diagram and label all of the forces.

  22. How can we define Newton’s 2nd law? • Newton’s second law states when an unbalanced force acts on an object, the object is accelerated in the same direction of the force. • The net force is NOT zero. NO Equilibrium. • Formula: • Fnet (sum of forces), m (mass), a (acceleration).

  23. Describe the mathematical relationship between acceleration and net force. • Its acceleration is directly proportional to the net force • Describe the mathematical relationship between acceleration and mass. • Its acceleration is inversely proportional to the object’s mass

  24. A 5 kilogram box is pushed with a 20 newton force to the right on a frictionless surface. Determine the acceleration. • A 2 kilogram box at rest accelerates to a speed of 10 meters per second in 2 seconds. Calculate the net force.

  25. How can we determine the net force?

  26. Determine net force using a picture • Example 1: A 2kg block is sitting on a table. A 10 N force is applied to the right and a 45 N force is applied to the left. • A) Determine the net force acting on the block? • B) Calculate the acceleration. F net in the x direction is the difference between the two forces acting in the x direction. to the left

  27. Refer to example 1: • The net force acting on the box is 20 Newtons to the right. • Calculate the acceleration. to the left

  28. A 20 newton force is applied to a 4 kilogram object to the right accelerating it at 4.5 meters per second2. • A) Determine the net force. • B) Calculate the frictional force.

  29. A person pushes a 7.0 kg box on a frictionless surface. The box accelerates 5 m/s2. Calculate the applied force on the box. to the right

  30. How can we use Newton’s 2nd law to solve motion problems? • Define Newton’s 1st law. • Sketch the equilibrium diagram. • Determine the net force on an object when it is moving with constant velocity. • A 3 kilogram chair is being push with a 10-newton force to the right. Sketch a free body diagram.

  31. Cart demonstration • As mass decreases, acceleration _____________. • How would you sketch a graph of acceleration vs. mass?

  32. A 50 newton force is required to accelerate a 3.5 kilogram object at 8.6m/s2 over a level floor. • A) Sketch a free body diagram. • B) Determine the net force • C) Calculate the magnitude of the frictional force acting on the object

  33. A 6.5 kilogram object is accelerating at 8.0 meters per second2. The magnitude of the frictional force is 10 newtons. • A) Sketch a free body diagram. • B) Determine the net force. • C) Calculate the applied force.

  34. **A constant 3,000 newton frictional force is acting on a 1200 kilogram car. The car is brought to rest in 20 seconds. • A) Identify the net force. • B) Calculate the deceleration. • C) Calculate the initial velocity of the car.

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