1. PH 201 Dr. Cecilia Vogel Lecture 8

2. REVIEW  Forces  Gravity OUTLINE  Various types of forces  Free Body Diagrams  Centripetal forces  tension and springs

3. Normal Force  normal force is  just big enough to prevent motion.  Always, perpendicular to the surface.  Note a bathroom scale does not measure weight, it measures the normal force. When you are standing still on the scale, it measures F N, which equals your weight.

4. 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

5. 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

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

7. 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

8. 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

9. 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

10. 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 

11. 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

12. 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

13. 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.