Physics 111A - Lab Report
Lab 6a1: Work and Energy
Introduction
Work is the transfer of energy from an object via the application of force along a displacement.
Energy, the capacity to do work, exists in multiple forms, with kinetic energy representing the
energy of motion, and gravitational potential energy which is the energy stored due to its height
on Earth. The relationship between work and energy is shown by the work-energy theorem,
which states that the net work done on an object is equal to its change in kinetic energy. This
experiment aims to validate the work-energy theorem by examining how work performed on an
object affects its kinetic energy. By applying a constant force to an object at varied angles and
measuring the resulting displacement and velocity, we can quantify the work done and observe
its impact on the object's energy.
Theoretical Background
Work(W) is defined as the product of the force(F) applied to an object and the displacement (d)
of the object in the direction of the force:
𝑊 = 𝐹 * 𝑑 * 𝑐𝑜𝑠θ
Where theta is the angle between the force vector and the displacement vector(the direction it is
moving). For a constant force applied to motion(theta = 0 degrees), the equation simplifies to:
𝑊 = 𝐹 * 𝑑
Energy is the property of an object or system that enables it to perform work. Kinetic energy(KE)
is the energy associated with an object’s motion and is given by the equation:
2
𝐾𝐸 = 1/2𝑚𝑣
Where m is the mass of the object and v is the velocity.
The Work-Energy Theorem
The work-energy theorem states that there is a direct relationship between the net-work done on
an object and its change in kinetic energy:
𝑊𝑛𝑒𝑡 = Δ𝐾𝐸 = 𝐾𝐸𝑓𝑖𝑛𝑎𝑙 − 𝐾𝐸𝑖𝑛𝑖𝑡𝑖𝑎𝑙
This equation implies that when work is done on an object, it results in a change in the object’s
kinetic energy. In the case of a constant force causing an object to accelerate from rest, the work
done by the force increases the object’s kinetic energy.
When a constant force is applied to an object of mass m causing it to accelerate uniformly, the
acceleration(a) can be found using Newton’s second law:
𝐹=𝑚 *𝑎
, Procedure
The Equipment used in our experiment is:
- Data collection system(computer, PASCO Capstone Software)
- Super Pulley with Clamp
- Elastic Bumper
- Dynamics Track Rod Clamp
- Cart mass(pair)
- String
- Dynamics Track
- Wireless Smart Cart(with hook)
- Dynamics Track end Stop
- Mass and Hanger set
- Digital Protractor
- Tripod Stand
- Balance or Scale
Set Up
Part 1: Work-Energy in a Horizontal Track System with a Constant Force
We started up the data collection software and selected the "Measurement" page on the screen. In
the tools sidebar. Using a scale, we measure the total mass of the cart in grams then converted to
kilograms. Since this part of the experiment involves a horizontal track, we ensure that the
inclined angle is set to 0 degrees. We input these values into the software and record them in our
data table.
We set up the equipment by placing the track on a flat, level surface. The cart is positioned at the
starting point farthest from the hanging mass. We attach a string to the cart, run it over a pulley at
the end of the track, and connect it to a hanging mass to apply a constant force. Before releasing
the cart, we click "Record.” We gently release the cart without applying any additional force,
allowing the hanging mass to pull it along the track. The software automatically records data on
position, velocity, net force, and tension over time as the cart accelerates.
Part 2: Work and Energy in an Inclined Track System with a Constant Force
We use the same cart mass as in Part 1 to maintain consistency in our measurements. We adjust
the track to create an incline and determine the angle using an angle reader. We change the value
for the angle to 5 degrees.
Following the same steps as outlined in Part 1, we set up the equipment with the track now
inclined at five degrees. The cart is placed at the starting point farthest from the hanging mass.
We click "Record" on the software screen and release the cart, allowing it to move up the incline
under the influence of both gravity and the constant force from the hanging mass. The software
records data on position, velocity, net force, and tension over time. We add a coordinate tool on
Lab 6a1: Work and Energy
Introduction
Work is the transfer of energy from an object via the application of force along a displacement.
Energy, the capacity to do work, exists in multiple forms, with kinetic energy representing the
energy of motion, and gravitational potential energy which is the energy stored due to its height
on Earth. The relationship between work and energy is shown by the work-energy theorem,
which states that the net work done on an object is equal to its change in kinetic energy. This
experiment aims to validate the work-energy theorem by examining how work performed on an
object affects its kinetic energy. By applying a constant force to an object at varied angles and
measuring the resulting displacement and velocity, we can quantify the work done and observe
its impact on the object's energy.
Theoretical Background
Work(W) is defined as the product of the force(F) applied to an object and the displacement (d)
of the object in the direction of the force:
𝑊 = 𝐹 * 𝑑 * 𝑐𝑜𝑠θ
Where theta is the angle between the force vector and the displacement vector(the direction it is
moving). For a constant force applied to motion(theta = 0 degrees), the equation simplifies to:
𝑊 = 𝐹 * 𝑑
Energy is the property of an object or system that enables it to perform work. Kinetic energy(KE)
is the energy associated with an object’s motion and is given by the equation:
2
𝐾𝐸 = 1/2𝑚𝑣
Where m is the mass of the object and v is the velocity.
The Work-Energy Theorem
The work-energy theorem states that there is a direct relationship between the net-work done on
an object and its change in kinetic energy:
𝑊𝑛𝑒𝑡 = Δ𝐾𝐸 = 𝐾𝐸𝑓𝑖𝑛𝑎𝑙 − 𝐾𝐸𝑖𝑛𝑖𝑡𝑖𝑎𝑙
This equation implies that when work is done on an object, it results in a change in the object’s
kinetic energy. In the case of a constant force causing an object to accelerate from rest, the work
done by the force increases the object’s kinetic energy.
When a constant force is applied to an object of mass m causing it to accelerate uniformly, the
acceleration(a) can be found using Newton’s second law:
𝐹=𝑚 *𝑎
, Procedure
The Equipment used in our experiment is:
- Data collection system(computer, PASCO Capstone Software)
- Super Pulley with Clamp
- Elastic Bumper
- Dynamics Track Rod Clamp
- Cart mass(pair)
- String
- Dynamics Track
- Wireless Smart Cart(with hook)
- Dynamics Track end Stop
- Mass and Hanger set
- Digital Protractor
- Tripod Stand
- Balance or Scale
Set Up
Part 1: Work-Energy in a Horizontal Track System with a Constant Force
We started up the data collection software and selected the "Measurement" page on the screen. In
the tools sidebar. Using a scale, we measure the total mass of the cart in grams then converted to
kilograms. Since this part of the experiment involves a horizontal track, we ensure that the
inclined angle is set to 0 degrees. We input these values into the software and record them in our
data table.
We set up the equipment by placing the track on a flat, level surface. The cart is positioned at the
starting point farthest from the hanging mass. We attach a string to the cart, run it over a pulley at
the end of the track, and connect it to a hanging mass to apply a constant force. Before releasing
the cart, we click "Record.” We gently release the cart without applying any additional force,
allowing the hanging mass to pull it along the track. The software automatically records data on
position, velocity, net force, and tension over time as the cart accelerates.
Part 2: Work and Energy in an Inclined Track System with a Constant Force
We use the same cart mass as in Part 1 to maintain consistency in our measurements. We adjust
the track to create an incline and determine the angle using an angle reader. We change the value
for the angle to 5 degrees.
Following the same steps as outlined in Part 1, we set up the equipment with the track now
inclined at five degrees. The cart is placed at the starting point farthest from the hanging mass.
We click "Record" on the software screen and release the cart, allowing it to move up the incline
under the influence of both gravity and the constant force from the hanging mass. The software
records data on position, velocity, net force, and tension over time. We add a coordinate tool on
