November 2 2016 Hookes Laws Hi Waverly High
November 2, 2016 Hooke’s Laws Hi, Waverly High School Physics Students! My name is Robert Hooke and today you are going to hear about my astounding Law!
1. What is Hooke’s Law? 2. How is it calculated? 3. What does k represent? How is it calculated? 4. What does the slope of a force versus distance graph represent?
Hooke’s Law Hooke's Law gives the relationship between the force applied to an unstretched spring and the amount the spring is stretched when the force is applied.
Hooke’s Law Illustration
Hooke’s Law Mathematically Force (Fs) = spring constant (k)×distance (d) Force to stretch the spring Relationship between the Force and the distance Distance the spring will move when the force is applied
Spring Constant 1. Spring Constant (k) = F / d The spring constant will depend on how strong the spring is! 2. Anything that stretches has a spring constant! a) b) c) d) Springs Rubber bands Elastic Skin
The following data was collected during Professor Slinky-Dog’s Experiment: Graphed on the y-axis Force added to the spring (Newtons): Extension Distance of the Spring (centimeters): 0 1 2 3 4 5 0. 0 1. 5 3. 0 4. 5 6. 0 7. 5 Graphed on the x-axis
Find the Slope of this line
Slope of the Graph Slope = rise / run Slope = y 2 -y 1 / x 2 -x 1 Slope = 5 – 0 / 7. 5 – 0 Slope = 0. 7 Newtons / Centimeter
What does the Slope mean? Slope = 0. 7 Newtons per centimeter This means that it will take 0. 7 Newtons of FORCE to extend the spring a distance of 1 centimeter! The Slope is the Spring Constant (k) for this spring used in the Slinky-Dog Experiment!
Example #1 a The largest ruby in the world may be found in New York City. If the ruby is attached to a spring with a spring constant of 2 x 102 N/m so that the spring is stretched 15. 8 cm then what is the gravitational force pulling the spring down? Given: k =2 x 102 N/m d = 15. 8 cm Fs = kd Find: Force (Fs) Solution: Fs = (2 x 102 N/m)(15. 8 cm x 1 meter/100 cm) = 31. 6 N
Example #1 b: What is the mass of the ruby in kilograms? Given: Force of gravity = Weight = mg g = 9. 81 m/s 2 F = 31. 6 N Find: mass Solution: m = Fg / g = (31. 6 kg m/s 2) / (9. 81 m/s 2) = 3. 22 kilograms Newtons’ secret identity!
Example #2 a: Mauna Kea on the island of Hawaii stands 10, 200 meters from base to summit. If you have an elastic cord with a spring constant of 3. 20 x 10 -2 N/m, what force is needed to stretch it to 1. 20 x 104 meters? Given: k = 3. 20 x 10 -2 N/m d = 1. 20 x 104 meters Fs = kd Find: Force on the spring Solution: Fs = kd = (3. 20 x 10 -2 N/m)(1. 20 x 104 meters) = 384 N
Example #2 b: What is the mass in kilogram? Given: F = 384 N weight = mg g = 9. 81 m/s 2 Find: mass Solution: 384 N = m(9. 81 m/s 2) m = 39. 1 kg
Example #3: La Gran Piedra in Cuba is the tallest rock on the Earth! Suppose a spring, with a constant of 25 N/m is placed at the top, how much mass is needed to move the spring a distance of 348 meters? Given: k = 25 N/m d = 348 m Fs = kd Fg = mg g =9. 81 m/s 2 Find: mass Solution: Fs = (25 N/m)(348 m) = 8700 N m = Fg / g = (8700 kg m/s 2) / (9. 81 m/s 2) = 886. 9 kg Newtons’ secret identity!
Assignment: (due today) Hooke’s Law Problem Set #1 • • Hints: Mass must be in KILOGRAMS! Distance must be in METERS! Force must be in Newtons! Force is Weight and Weight is Force!
- Slides: 19