To satisfy Hook’s law and calculate the spring constant.
Mechanics - hooks law Data studio file
Introduction
Hook’s law is named after the 17th century British physicist Robert Hook. For systems that obey Hook’s law, the extension produced is directly proportional to the load. The purpose of this activity is to use Hook’s Law to determine the spring constant of a spring.
Force applied Extension produced
F Applied x
F = k x
Where x is the distance that the spring has been stretched or compressed away from the equilibrium position, which is the position where the spring would naturally come to rest (m), F is the restoring force exerted by the spring (N), and k is the force constant (or spring constant). The constant has units of force per unit length (N/m). When this formula holds, the behavior of the spring is linear (a graph of a linear relationship) .The negative sign in the Hooks law formula shows that the restoring force always acts in the opposite direction of the x displacement (for compression and extension).
The experiment will be performed for two arrangements, Horizontal and Vertical.
Result and Calculation
Attach the linear fitted graphs of the vertical setups.
Table for the Vertical setup
Spring # Slope of the graph
Silver long
Black short
Big Black long
The actual value for the spring constants:
Silver long: 8 N/m or 5 N/m , Black short 3.4N/m or 6.8 N/m, Big Black long: 3.4N/m or 6.8 N/m
Calculate % errors in the value of the spring constants. List the sources of error also. Discuss your results.
Vertical Setup
a) Spring # 1-Silver long/ Black short/ Big Black long
Run # Mass (g) Extension (cm) Force applied ( N )
Fg=mg
1 20
2 40
3 60
4 80
5 100
Attach the linear fitted graphs of the vertical setups.
Table for the Vertical setup
Spring # Slope of the graph
Silver long
Black short
Big Black long
The actual value for the spring constants:
Silver long: 8 N/m or 5 N/m , Black short 3.4N/m or 6.8 N/m, Big Black long: 3.4N/m or 6.8 N/m
Calculate % errors in the value of the spring constants. List the sources of error also. Discuss your results.
Data Table for spring #2- Black short/ Big Black long
Run # Mass (g) Extension (cm) Force applied ( N )
1 20
2 40
3 60
4 80
5 100
Questions
- In general, what pattern do you notice between the force due to gravity of the masses and the extension of the spring?
- Write an equation that represents the relationship between force and displacement using standard linear equation y = mx + b. Don't forget to include units on all numbers!
- What is the physical meaning of the slope and the vertical intercept of the force- extension graph?
- What would be the displacement of a 100 g mass (for vertical set up)?
Extra Questions
- How far must a spring (spring constant = 35N/m) be pulled in order to exert a force of 63N?
- How far will a spring with rest length 82cm and spring constant 0.50N/m be if it is stretched until it exerts 0.25N?
- A spring has a rest length of 1.30m. When a 20kg mass is hung on it, it stretches to 3.60m. What is its spring constant?
- Draw on the below axis the expected graph for the different springs.
- What would happen to the spring constant if the spring were cut in half?
(Hint: What force would be required to stretch the spring to a length equal to a length before it was cut?)
Discussion and conclusion:
Note:- (Include what is the significance of measuring the spring constants ad refer your result in discussion)