1. PH 201 Dr. Cecilia Vogel Lecture

2. REVIEW  Projectiles  Dropping  Upward throw  Range OUTLINE  Newtons Laws  Force, mass, inertia  action, reaction forces

3. 3 rd Law Reaction on What?  The “action” FORCE and the “reaction” FORCE don’t act ON the same thing.  If the action force is Earth’s gravity pulling on ME,  then the reaction force is me pulling on the Earth.  If the action force is your behind pushing down on the chair,  then the reaction force is the chair pushing up on your behind (keeping you from falling)

4. Forces  You may have heard of the four fundamental forces:  Gravity  electromagnetic  strong, and  weak  All we study in 201  gravity  several forces that are the result of electromagnetic interactions of many atoms and/or molecules:  normal force, tension, compression, friction, drag

5. Force Units   F = ma helps us determine the SI unit of force:  unit(Force) = unit(mass)*unit(acceleration)  unit(Force) = (kg)(m/s 2 )  Force is measured in units of  This unit is also called the Newton,  abbreviated N

6. Gravity near Earth’s Surface  If an object is allowed to fall under the influence of gravity only,  we know it will accelerate at 9.8m/s 2 downward.  How big a force is needed to create such an acceleration?  A larger force is needed for a larger mass.  2 nd law with 1 force in 1-D: so F grav = weight = mg (down)

7. Gravity examples  What is the force of gravity on a 1-g object?  F grav = mg = (0.001 kg)(9.8 m/s 2 )  weight = 0.0098 N (down)  Is this the gravitational force on it, if it is sitting on the desk?  Is this the gravitational force on it, if it is falling to the floor?  In either situation, is its acceleration 9.8 m/s 2 ? YES Only when falling freely!

8. Normal Force  normal force is  just big enough to prevent one surface moving into the other.  Always, perpendicular to the surface.  Note a bathroom scale does not measure weight, it measures the normal force. When you are standing still on a scale, it measures F N, which often – but not always! - equals your weight.

9. Fooling the Scale – Case 1 A 110-kg man stands on a scale. He grabs a chain hanging from the ceiling, so that the scale will read only 95 kg. What is the tension in the chain? Use a free-body diagram to help solve this problem. weight T FNFN If the scale reads 95 kg, that means F N = (95kg)(9.8m/s 2 ) = 931 N

10. Fooling the Scale – Case 2 A 110-kg man stands on a scale. He and the scale are on an elevator, which is accelerating downward. The scale reads only 95 kg again. What is the acceleration of the elevator? Use a free-body diagram to help solve this problem. What is our object? the man What are all the forces acting on the man? gravity & normal force from scale weight FNFN  VEL & ACCEL do NOT belong in FBD nor  F

11. Fooling the Scale – Case 2 What is the acceleration of the elevator? weight FNFN Now can we apply 2 nd law?

12. PAL on your own Ride an elevator: If the elevator is accelerating downward, the normal force on your feet will be less than your weight. weight FNFN If the elevator is accelerating upward, the normal force on your feet will be more than your weight. weight FNFN Going up, slowing down Going down, speeding up Going up, speeding up Going down, slowing down

13. Fooling the Scale – Case 3 A 110-kg man stands on a scale. He and the scale are on a cart that is rolling down an incline. The scale reads only 95 kg again. What is the angle of the incline from horizontal? Use a free-body diagram to help solve this problem. What is our object? the man What are all the forces acting on the man? gravity & normal force from scale always perpendicular to surface weight N

14. Fooling the Scale – Case 3 What is the angle of the slope? Now can we apply 2 nd law? weight N Useful x- and y-axes are along slope and perpendicular. x y Let’s consider the y-component What forces are in the y-direction?  Normal  one component of gravity

15. Fooling the Scale – Case 3 weight N x y What forces are in the y-direction?  Normal  one component of gravity  this component is given by What is the accel in the y-direction? zero mg cos 

16. Springs  If a spring is stretched or compressed, there will be a restoring force.  The force that the spring exerts is opposite the displacement,  and proportional to the size of the displacement. PAL xx  k is called the “spring constant,” depends on the spring’s stiffness. F spring = - k  x F

17. Spring Constant Example  If a 1.0 N force stretches a particular spring by 3.0 mm, how much will that spring stretch with a 1.0 kg-weight hanging from it vertically? k = 0.333 N/mm Given: F 1 = 1.0 N, so F spring,1 = -1.0N,  x 1 = 3.0mm F 2 = -9.8 N, so F spring,2 = 9.8 N Use:but need k. First, find k: Want  x 2 =? So:  x 2 = -29.4 mm

18. Tension  If you pull on a string (or rope, or chain, …), and it doesn’t break  the string exerts a tension force.  How big is the tension force?  just big enough to prevent motion.  What direction is the tension force?  often it is up, the force to hold something up. Not always!!  Always, along the string.