Unit 3 Test - Energy of Objects in Motion

Energy and Its Forms

• Energy: Measurement of an object’s ability to do work.

• Work: Applying a force to move an object a certain distance.

  • Work done involves a transfer of energy between objects.

  • Unit of energy and work is the Joule (J).

  • 1 Joule = 1 Newton-meter.

Work

• Work can only be done on a system by an external force, not something inside the system itself.

• The amount of work done correlates with the change in energy of the system.

  • When a force accelerates an object over a distance, work is positive.

  • When a force opposes motion, work is negative.

Positive vs. Negative Work

• If an object moves in the same direction as the force, energy increases (Work is positive).

• If an object moves in the opposite direction of the force, it results in a decrease in energy (Work is negative).

• If an object does not move while a force is applied, no work is done.

Types of Energy

Mechanical Energy

• Mechanical Energy: Energy due to an object's motion and position; comprises kinetic energy and potential energy.

Non-Mechanical Energy

• Non-Mechanical Energy: Energy not linked to motion or position, including electrical, chemical, thermal, and sound energies.

Kinetic and Potential Energy

Energy of Motion

• For an object to move, it must utilize its kinetic energy or receive energy from an external source.

• Kinetic Energy (KE) depends on mass and velocity:

  • KE ∝ mass (m) and velocity (v).

  • More mass = more KE; higher velocity = more KE.

Mass and Velocity Impact

• Two objects with the same velocity but different masses have different kinetic energies; heavier objects possess more KE.

• Velocity is a vector quantity, meaning it has direction, while speed is a scalar quantity.

Gravitational Potential Energy

• Potential Energy (PE): Energy stored due to position.

• Gravitational Potential Energy (GPE) depends on height, mass, and gravity: GPE = mgh.

  • Mass, gravitational acceleration, and height affect the potential energy; all directly proportional.

  • Example: Elevating a heavier object results in greater GPE.

Elastic Potential Energy

• Elastic Potential Energy: Energy stored in elastic materials when stretched or compressed.

  • Factors include material stretchiness and the distance of deformation:

    • More stretch or compression leads to more stored energy.

Conservation of Energy

• Conservation of Energy Principle: Energy cannot be created or destroyed, only transformed.

  • Total Energy in a system remains constant unless influenced by external forces.

  • Potential and kinetic energy can transform into each other, but their sum remains constant:

    • Initial Total Energy = Final Total Energy (TEi = TEf).

Types of Energy Resources

Renewable Energy Resources

• Can replenish over time, e.g., solar, wind, and hydropower.

Non-Renewable Energy Resources

• Limited supply that cannot replenish quickly, e.g., fossil fuels like coal and oil.

Summary of Key Formulas

• Kinetic Energy: KE = 1/2 mv^2

• Gravitational Potential Energy: GPE = mgh

• Elastic Potential Energy: EPE = 1/2 kx^2, where k is the spring constant and x is the distance stretched or compressed.

Practice Questions

1. Identify the unit for energy and work. Answer: Joule

2. Explain positive vs. negative work. Example Scenarios:

   • Rolling wagon vs. trying to stop it.

   • Kicking a soccer ball into a net.

Conservation of Energy Word Problems

1. Pendulum Problem: A pendulum is released from a height of 5 meters. What is the potential energy at the start and what is the kinetic energy at the lowest point?

   • Solution: Potential Energy (PE) at the top = mgh = mg(5). At the lowest point, all PE converts to KE, so KE = PE_initial.

2. Roller Coaster Problem: A roller coaster car starts at rest at a height of 40 meters. What speed does it reach at the bottom?

   • Solution: Use conservation of energy: PE_initial = KE_final. mgh = 1/2 mv^2, solve for v.

Elastic Potential Energy Word Problems

1. Spring Compression: A spring is compressed 0.2 m and has a spring constant of 500 N/m. What is the elastic potential energy stored in the spring?

   • Solution: Use EPE = 1/2 kx^2. EPE = 1/2 (500)(0.2)^2 = 10 J.

2. Sling Shot Problem: A slingshot stretches by 0.3 m, with a spring constant of 1000 N/m. How much energy is stored when the slingshot is pulled back?

   • Solution: EPE = 1/2 kx^2 = 1/2 (1000)(0.3)^2 = 45 J.

Gravitational Potential Energy Word Problems

1. Hiking Problem: A person weighing 70 kg climbs to a height of 10 meters. Calculate the gravitational potential energy gained.

   • Solution: GPE = mgh = (70)(9.8)(10) = 6860 J.

2. Water Tower Problem: Water in a tank at a height of 15 meters has a mass of 1000 kg. What is the potential energy of the water?

   • Solution: GPE = mgh = (1000)(9.8)(15) = 147000 J.

Kinetic Energy Word Problems

1. Car Problem: A car with a mass of 1200 kg is traveling at a speed of 30 m/s. Calculate its kinetic energy.

   • Solution: KE = 1/2 mv^2 = 1/2 (1200)(30)^2 = 540000 J.

2. Sports Ball Problem: A soccer ball with a mass of 0.5 kg is kicked and reaches a speed of 20 m/s. What is its kinetic energy?

   • Solution: KE = 1/2 mv^2 = 1/2 (0.5)(20)^2 = 100 J.