FORCE is a vector quantity which can cause an object to change its shape

1. FORCEis a vector quantity which can cause an object to change its shape (ie., become deformed). And, for every force, there is an equal and opposite force!! Check out the equal and opposite forces exerted on the ball and the nose in this photo from the October 3, 2005, issue of Sports Illustrated.

2. NOTES 10 - Topic 2 - Mechanics ------------------------------------------------------------------------------------------------- DYNAMICS - the explanation of motions; ie., WHY objects move; 2.2.2 Describe force as the cause of velocity change and/or deformation; •Force ...a vector quantity; ...can cause an object to change its velocity (ie., increase speed, decrease speed, or change direction); ...can cause an object to change its shape (ie., become deformed); ...usually thought of as a “push” or a “pull”; ...can be measured with a spring scale. • Measurement ofForce ...English unit - pounds; SI unit - Newtons; 1.00 lb = 4.45 N

3. • Types of Forces... ...weight - a measure of the force of gravity exerted on an object; ...tension - the force that arises in any body when it is stretched (electromagnetic); forces exerted on/by springs and ropes; ...normal - the reaction force of two objects in contact, perpendicular to the body exerting the force (electromagnetic); force on you by chair seat; ...drag - force that opposes the motion of an object through a fluid (liquid or gas); force of air on hand held out of moving car; ...upthrust (buoyant) - upward force exerted on an object placed in a fluid (object floats if buoyant force is equal the object’s weight); ...friction - force that opposes the sliding of one object across another (electromagnetic); static friction keeps objects motionless; kinetic friction

4. • Free Body Diagram ...shows all forces acting on an object or a group of objects. Here are 2 examples: FN Ffr Fg Ffr is the force of friction exerted by surface; FN is the “normal force” exerted by a surface on an object on it and is perpendicular to the surface; FN is the force of gravity exerted perpendicular to the surface of the earth;

9. 2.2.3a Resolve forces into components

10. 2.2.3b Determine the resultant force in different situations; • Step 1: Resolve each vector into its x-component and its y-component, being sure to keep the signs (direction) correct; • Step 2: Add all x-components; • Step 3: Add all y-components; • Step 4: Draw the resultant vector R using the sum of x-components and sum of y-components as sides to the triangle; • Step 5: Use Pythagoras’ equation to determine the length of the R as the hypotenuse of the right triangle; • Step 6: Use the tangent function to determine the value of the angle (direction) of the triangle; 4.0 N 30o 6.0 N

11. The first LAW involving Force - • HOOKE’s LAW (Robert Hooke, 1676, English)...The force exerted on or by a spring to compress it or stretch it is directly related to the distance the spring is moved and to the “spring constant” (the elastic property ["stiffness"] of the spring): F = - kx where k is measured in Nm-1; the force is negative because it always points to the equilibrium position;

12. 2.2.4 State Newton’s 1st Law of Motion 2.2.5 Describe examples of Newton’s 1st Law The Law of Inertia - Law #1... ∑F = 0, v = k ...or... 1. When the sum of all forces acting on an object is zero, the object’s velocity remains constant; or... 2. Objects at rest tend to remain at rest and objects in motion tend to remain in motion in the same direction and at the same speed; • Inertia...the property of matter that resists acceleration and is determined by mass; There are many devices in autos which have been invented to lessen the effect of inertia... brakes, seat belts, air bags, padded dashboards, padded seats, headrests, collapsing steering wheels, “crumple zones”; all are designed to decrease the acceleration a person must experience before coming to rest from a high velocity.

14. 2.2.6 State the condition for translational equilibrium 2.2.7 Solve problems involving translational equilibrium When ∑F = 0, v = k, a = 0, or... the object maintains a constant velocity. When the forces are applied to the Center of Mass (CoM), and ∑F = 0, the condition is called Translational Equilibrium. All forces are assumed to be applied to the CoM unless stated otherwise. • Translational Equilibrium A. Static Equilibrium - the object on which the forces are exerted is stationary (motionless); ∑F = 0, v = 0, a = 0; N (Normal force of table) surface of table W (Weight of book; force of gravity) ∑F = 0 N + W = 0 N = -W

15. A. Dynamic Equilibrium - the object on which the forces are exerted is moving at a constant velocity; ∑F = 0, v = k, a = 0 N (Normal force of table) P (pulling force) F (force of friction) surface of table W (Weight of book; force of gravity) ∑F = 0; N + W = 0; so...N = -W; and...P + F = 0; so...F = -P

16. Center of Mass = CoM

18. Center of mass (CoM) used pretty interchangeably with Center of Gravity (CG) If the center of gravity is over the support, it won't fall.

20. • Torque (τ)...a force applied away from the CoM; ...an unbalanced torque causes an object to change its rotational motion; ...the farther away from the CoM the unbalanced force is applied, the greater the torque and the greater the rotational acceleration; ...mathematically, τ = F x r, where F is the unbalanced force and r is the perpendicular distance from the CoM (r ‘s proper name is lever arm) the force is applied; ...Torque is measured in Nm; Remember... Torque is cheap!!

23. Balancing Torques