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.