AP/IB Physics Lab

Work-Energy Theorem and Experimental Design

Introduction

     The Work-Energy Theorem states that the work done on a body by an external force is related to the resulting change in kinetic (K) and/or potential (U) energy.

                                                          Work = K + U

When a spring is disturbed from its equilibrium position, it's potential energy is determined by

                                                              Us = 1/2k x2

where k is the force constant (N/m) and x is the displacement from equilibrium.

     When a spring is compressed, it's stored energy can be converted to kinetic energy, which in turn can be converted to gravitational potential energy. This lab will determine the force constant of a spring using the Work-Energy Theorem.

Materials: Jump-up Toy, meter stick, balance

Procedures and Analysis

     Design an experiment that will allow you to accurately determine the force constant (k) of the spring in the jump-up toy. Be sure to consider significant figures in all measurements. Show all data tables and calculations. Consider several trials to validate your results. Indicate the sources of error.

Second Method

Physics Lab

Work-Energy Theorem : Spring Constant-k

Objective: Determine k of a spring using energy conservation

Materials: meter stick, jump-up toy

Procedures:

1. Determine the mass of the jump-up toy.

2. Measure the distance the spring will compress on the jump-up toy.

3. Compress the spring until the toy locks.

4. Estimate the height the toy jumps for five trials. Determine an average.

Analysis (Show all calculations and units throughout.)

1. From the height (s) of the toy, determine the Vy component of velocity. Let g = 9.8 m/s2.

2. Calculate the increase in gravitational potential energy of the toy.

3. Calculate the kinetic energy of the toy immediately upon lift-off.

4. Using the equations of the Work-Energy Theorem, determine the spring constant, k, of the toy's spring using the (a) gravitational potential energy and (b) kinetic energy.

5. Compare your answers for k in 4ab with others in the class.

6. How could the toy be made to go higher?

Another Possible:

Physics Lab

Hooke's Law & Spring Constants (k)

Objective: Determine relationship between Force and Distance (x) for a spring, and the Force Constant (k) of a Spring.

Materials: spring, slotted masses, meter stick, unknown mass

Methods

1. Sketch set up

2. Record starting position of spring (xo = 0 cm).

3. Add 50 or 100 g mass to extend the spring (x); record mass and x.

4. Repeat for 4 more trials.

5. Place an unknown mass on the spring and record the position (x), then find its actual mass.

Analysis

1. Plot a graph of Force (in Newtons) vs. distance (in meters).

2. Find the slope of the line. What are the units and what does the slope represent? Place your slope value on the front board.

3. Using your graph, determine the weight of your unknown object from its x. Calculate its mass (F/g). Determine a % error.

4. Compare your force constant with 2 other springs by comparing slopes. Draw a conclusion about the force constant k and the "stretch" of a spring.

5. Write an equation relating Force (F), distance ( x), and the force constant of a spring (k). State Hooke's Law in a sentence.