Lab 6 Work & Conservation of Energy PHY250L
Lab Report Format Expectations
Utilize college level grammar and formatting when answering text based questions.
Report all equations in a proper mathematical format, with the correct signs and symbols.
Submissions with incomplete or improperly formatted responses may be rejected.
Pre-Lab Questions
1. In this lab, you will conduct three experiments that will demonstrate the concepts of work,
potential energy and kinetic energy. Briefly explain those three concepts and their mathematical
definitions.
- Work is defined as the force applied to an object multiplied by the displacement in the
direction of the force, and its equation is W=F⋅d⋅cos(θ).
Where F is the force applied, d is the displacement, and θ is the angle between the force
and displacement.
- Potential Energy (U): Energy stored due to the position of an object. In the gravitational case,
its equation is U=mgh.
Where m is the object’s mass, g is the acceleration due to the gravity, and h is the
object’s height.
- Kinetic Energy (K) is the energy associated with an object's motion, and its equation is
K=1/2mv^2.
Where v is the object's velocity.
,Lab 6 Work & Conservation of Energy PHY250L
2. Both kinetic and potential energy are part of the thrill of roller coasters. Refer to Figure 6,
below.
Figure 6: Different points in a roller coaster’s
motion.
a. Describe the kinetic and potential energy at each point of the roller coaster path.
Point A: Maximum potential energy, as it is at the highest height. Kinetic energy is
minimal (if not zero).
Point B: Part of the potential energy was converted into kinetic energy. The cart is
accelerating.
Point C: Minimum potential energy, maximum kinetic energy (highest speed of the cart).
Point D: Kinetic energy is being converted back into potential energy as the cart rises
again.
b. What happens to the rollercoaster’s kinetic energy between Points B and C?
What happens to its potential energy between these points?
Kinetic energy increases because potential energy is being converted. Potential energy
decreases as the cart moves downwards.
c. Why is it important for Point A to be higher than Point C?
To ensure that the initial potential energy is sufficient for the cart to complete the entire
journey without needing an additional energy source.
, Lab 6 Work & Conservation of Energy PHY250L
d. What causes the roller coaster train to lose energy over its trip?
The energy is dissipated due to air resistance and friction between the tracks and the
cart's wheels, converting part of the mechanical energy into heat.
EXPERIMENT 1: WORK DONE BY A SPRING
Introduction Questions
1. In Experiment 1, you will stretch a spring at varying distances and calculate the work required to
do so. The force associated with compressing or stretching a spring is variable and is quantified
by F = kx, where k is the spring constant and x is the displacement.
Given the graph of the force versus displacement graph for a spring in Figure 5, derive an
equation for the amount of work done by the spring. Do not simply state a final equation. Show
the mathematical steps you will take to derive this equation. You must show all work for credit.
- The accumulated work should follow the equation W = ½ kx^2, while the incremental work can
be analyzed by looking at the small increases in W as x increases.
Figure 5: Force versus displacement of a spring.
Lab Report Format Expectations
Utilize college level grammar and formatting when answering text based questions.
Report all equations in a proper mathematical format, with the correct signs and symbols.
Submissions with incomplete or improperly formatted responses may be rejected.
Pre-Lab Questions
1. In this lab, you will conduct three experiments that will demonstrate the concepts of work,
potential energy and kinetic energy. Briefly explain those three concepts and their mathematical
definitions.
- Work is defined as the force applied to an object multiplied by the displacement in the
direction of the force, and its equation is W=F⋅d⋅cos(θ).
Where F is the force applied, d is the displacement, and θ is the angle between the force
and displacement.
- Potential Energy (U): Energy stored due to the position of an object. In the gravitational case,
its equation is U=mgh.
Where m is the object’s mass, g is the acceleration due to the gravity, and h is the
object’s height.
- Kinetic Energy (K) is the energy associated with an object's motion, and its equation is
K=1/2mv^2.
Where v is the object's velocity.
,Lab 6 Work & Conservation of Energy PHY250L
2. Both kinetic and potential energy are part of the thrill of roller coasters. Refer to Figure 6,
below.
Figure 6: Different points in a roller coaster’s
motion.
a. Describe the kinetic and potential energy at each point of the roller coaster path.
Point A: Maximum potential energy, as it is at the highest height. Kinetic energy is
minimal (if not zero).
Point B: Part of the potential energy was converted into kinetic energy. The cart is
accelerating.
Point C: Minimum potential energy, maximum kinetic energy (highest speed of the cart).
Point D: Kinetic energy is being converted back into potential energy as the cart rises
again.
b. What happens to the rollercoaster’s kinetic energy between Points B and C?
What happens to its potential energy between these points?
Kinetic energy increases because potential energy is being converted. Potential energy
decreases as the cart moves downwards.
c. Why is it important for Point A to be higher than Point C?
To ensure that the initial potential energy is sufficient for the cart to complete the entire
journey without needing an additional energy source.
, Lab 6 Work & Conservation of Energy PHY250L
d. What causes the roller coaster train to lose energy over its trip?
The energy is dissipated due to air resistance and friction between the tracks and the
cart's wheels, converting part of the mechanical energy into heat.
EXPERIMENT 1: WORK DONE BY A SPRING
Introduction Questions
1. In Experiment 1, you will stretch a spring at varying distances and calculate the work required to
do so. The force associated with compressing or stretching a spring is variable and is quantified
by F = kx, where k is the spring constant and x is the displacement.
Given the graph of the force versus displacement graph for a spring in Figure 5, derive an
equation for the amount of work done by the spring. Do not simply state a final equation. Show
the mathematical steps you will take to derive this equation. You must show all work for credit.
- The accumulated work should follow the equation W = ½ kx^2, while the incremental work can
be analyzed by looking at the small increases in W as x increases.
Figure 5: Force versus displacement of a spring.
