Lab 08 Prelab Assignment

1. A Hooke’s Law spring of constant k=5 N/m hangs vertically from a rod, and a mass of 200 g is hung from it. How far

does the spring have to stretch to reach equilibrium?

5N/m

200g original equilibrium

d

new equilibrium

200g

2. Consider a Hooke’s Law spring with constant k hanging vertically from a rod. A mass of m is hung from the spring,

stretching the spring to a new equilibrium position, like in question 1. Next the spring is stretched or compressed by an

amount x relative to the new equilibrium position and released:

d d

m x

m | the mass will accelerate upward right after being released |

Draw force diagrams for the hanging mass in both cases. Use N2 to write down a relationship between the weight and the

spring force in case 1, then show that the net force is given by F kx net = when we release the mass in case 2. This fact

means that our hanging spring/mass system behaves exactly like a sideways spring/mass system if we measure

stretch/compression relative to the equilibrium obtained by hanging the mass.

Lab 08: Hooke’s Law Springs

In this course, we assume that all spring are “ideal”, meaning that they follow Hooke’s Law: the force required to stretch

the spring is proportional to the stretch distance (in other words, it takes twice as much force to stretch the spring twice as

far). Stating Hooke’s law in terms of magnitude:

Hooke’s Law: F kx =

In this formula, k (the spring constant) is a measure of the stiffness of the spring, while x is the displacement from the natural

length of the spring.

Spring potential energy is the energy stored in a spring that is compressed or stretched (for example, the spring guns for the

projectile motion lab were storing spring potential energy before you pulled the trigger). Spring potential energy is

computed by the formula:

Spring potential energy: 1 2

s 2

PE kx =

1. Measuring the spring constant:

We showed in the prelab that a vertical spring/mass system has the exact same physics as a horizontal system, provided

we take the equilibrium length to be the length with the mass already attached. It can be difficult to accept, but once we

proved that F kx net = , there is no need to think about gravity for the rest of the lab!

First, we need to find the spring constant, k, for this spring. We will use a force sensor mounted on a rod to measure the

force exerted by the spring as it stretches through a large range of values. Directions will be given in class to help you

calibrate the force sensor and set the motion sensor to record “toward” as the positive direction. The initial position and

force should also be set to zero by “zeroing” the sensors before taking any data.

IMPORTANT NOTE: keep in mind that the position sensors can’t see anything closer than about 15 cm.

Hooke’s Law spring

force sensor |

aluminum mass

position sensor

table top

Remember, we can ignore gravity because this system is completely equivalent to a horizontal spring/mass system with

the shown equilibrium position. When you exert a force downward on the mass, we ignore gravity and say that the force

exerted by the force sensor is equal to your applied force, provided the mass is moved slowly.

Take data on the applied force and position as you slowly move the mass above and below equilibrium by about 20-25

cm. Use Logger Pro to display the data on a Force vs. Position graph. Display the best-fit line on this graph and use it to

find the spring constant. Print and attach the graph.

k = ________________

2. Potential energy and the work done on the spring:

a. Using the spring constant measured in part 1, compute the potential energy stored in the spring at x=20cm.

Make your work clear.

PEspring = __________ J

b. Take force and position data as you slowly push the mass down by 20cm, being careful to never reverse

directions (reversing directions confuses LoggerPro’s integration tool). Make a plot of Force vs. Position. Now

highlight the interval from x=0 to x=20 cm, and use Logger Pro’s integral tool to compute the area under the

curve. The area gives you the total work you did while stretching the spring. Make sure to print and attach your

graphs.

Won the spring = __________ J

Since the work done on the spring should equal the change in potential energy for the spring, these two quantities

should be equal. Compute a percent error to compare them.

% error = _____________ %