HOOKE’S LAW
THEORY
The amount of force it takes to stretch a spring is proportional to two things: the displacement of the end of the spring from its equilibrium position and the spring constant, k.
PROCEDURE
1. Read the mass of the spring on the triple-beam balance and record it on the data page.
2. Suspend the spring from a support and set up a meter stick next to it, vertically. Read the value of the meter stick next to the bottom end of the spring. Record this value as xo on the data page
3. Hang a 100-gram mass from the bottom of the spring and read the value of the meter stick next to the bottom end of the spring. Record this as New Position on the data sheet.
4. Repeat procedure 2 using 200 , 300, 400 and 500 grams.
Calculations
1. Calculate the weight of each mass in Newtons.
2. Calculate the displacements x – xo for each mass.
3. Plot a graph of weight (Newtons) vs displacement (meters) Calculate the slope of the graph.
4. Show that the slope of the graph is the spring constant k.
HOOKE’S LAW DATA PAGE
x0 ______cm
Hanging Mass
(kg) /Weight
(Newtons) /New Position, x
(cm) /Displacement
x – x00.100
0.200
0.300
0.400
0.500
Plot a graph of weight (Newtons) vs displacement (meters). From the slope, calculate the spring constant, k (N/m).
Simple Harmonic Motion
Oscillating Spring
THEORY
The period of a oscillation of a mass hanging from a spring is given by the formula:
T = 2pÖ(m/k) where m is the mass attached to the spring and k is the spring constant. From this it can be seen that T2 a m.
In this lab activity we will hang several different masses from a spring and measure the period of the mass-spring system for each mass. We will plot T2 vs. m and see if it is in fact a straight line. The slope will allow us to calculate the spring constant k.
PROCEDURE
1. Read the mass of the spring on the triple-beam balance and record it on the data page. Also record 1/3 of the mass of the spring. This will be added to the value of the hanging mass, since part of the spring is oscillating and therefore adds to the inertia of the vibrating system.
2. Suspend the spring from a support and hang the 100-gram mass from the bottom of the spring. Pull the mass down from the equilibrium position by about 2 cm to set the system oscillating. With the photogate timer in pulse mode, obtain the period of the system and record it on the data page. Repeat for a total of three runs.
3. Repeat procedure 2 using 200 , 300, and 400 grams.
Calculations
4. Calculate the averages of the periods.
5. Plot a graph of T2 vs m. Calculate the slope of the graph
6. Show that the slope of the graph is 4p2k and solve for k from the slope.
7. Find the percent difference between this value of k and that found in the previous activity.
OSCILLATING SPRING
Mass of spring (kg) ______
1/3 Mass of spring (kg) ______
Hanging Mass
+ 1/3 Mspring (kg) / 0.100+ 1/3 Mspring
= / 0.200
+ 1/3 Mspring
= / 0.300
+ 1/3 Mspring
= / 0.400
+ 1/3 Mspring
=
T1 (sec)
T2 (sec)
T3 (sec)
Taverage
(Taverage)2
Pendulum
THEORY
As long as the amplitude is not large, the motion of a pendulum is nearly simple harmonic motion. The period of oscillation of a small mass hanging from a string is given by the formula:
T = 2pÖ(l/g) , where l is the length of the and g is gravitational acceleration. From this it can be seen that T2 a l.
In this lab activity we will hang a mass from a string and vary the length. We will measure the period for each length and plot a graph of T2 vs l and see if it is in fact a straight line. From the slope we will be able to find g, and compare it to the known value.
PROCEDURE
1. Set up a pendulum with a length of approximately 25 cm. Measure the length from the pivot point to the center of the mass. Record the actual value to four significant figures
2. Pull the mass about 2 cm from the equilibrium position and release it. With the photogate timer in pendulum mode, obtain the period of the system and record it on the data page. Repeat for a total of three runs.
3. Repeat procedure 2 for four more lengths, up to about 125 cm.
Calculations
1. Calculate the averages of the periods.
2. Plot a graph of T2 vs l. Calculate the slope of the graph
4. Show that the slope of the graph is 4p2g and solve for g from the slope.
5. Calculate the percent error of the value, taking the accepted value to be 980 cm/s2.
Pendulum
Length (cm) / 25 / 50 / 75 / 100 / 125T1
T2
T3
Taverage
(Taverage)2