3.2 Work, Energy, and Power

• What does the work-energy theorem state?

  Work equals change in KE
• What is the mathematical formula for work in mechanics?

  $W =$$F \cdot d \cos \theta$
• Match the form of energy with its description:

  Kinetic Energy ↔️ Energy of motion

  Potential Energy ↔️ Stored energy due to position

  Thermal Energy ↔️ Energy from heat
• Work in mechanics quantifies the energy transferred when a force causes an object to move.

  True
• What is power in mechanics defined as?

  Rate of work done
• Match the concept with its description:

  Power ↔️ Rate at which work is done

  Work ↔️ Energy transferred by force

  Energy ↔️ Capacity to do work
• What is the difference between power and work?

  Rate vs. total energy
• What is the formula for the work-energy theorem?

  $W =$$\Delta KE$
• The conservation of energy principle assumes no non-conservative forces act on the system.

  True
• Energy is the capacity to do work.
• What is the definition of power in mechanics?

  Rate of energy transfer
• The unit of power is the watt, which is equivalent to 1 joule per second.


  True
• Power measures the total energy transferred, while work measures the rate of energy transfer.

  False
• What does the work-energy theorem state?

  W = ΔKE
• Steps to calculate the speed of a ball dropped from a height using conservation of energy

  1️⃣ Identify initial conditions: KEi and PEi

  2️⃣ Identify final conditions: KEf and PEf

  3️⃣ Apply the conservation of energy formula

  4️⃣ Solve for the final velocity
• The work done by a constant force is zero when the force is perpendicular to the displacement.


  True
• The unit of work done is the joule
• What is the force-displacement relationship of a spring in the example provided?

  $F(x) =$$kx$
• What is the formula for calculating power using force and velocity?

  $P =$$F \cdot v$
• Work in mechanics is defined as the product of force and displacement in the direction of the force.

  True
• The formula for power in terms of work and time is $P =$$\frac{W}{t}$.
• What is work in mechanics defined as?

  Force times displacement
• Work done by variable forces is calculated using the same formula as work done by constant forces.

  False
• The definition of work in mechanics is the same as its everyday usage.

  False
• The work done on an object is equal to the change in its total energy.
• Match the form of energy with its description:

  Kinetic Energy ↔️ Energy of motion

  Thermal Energy ↔️ Energy from heat

  Chemical Energy ↔️ Energy stored in bonds
• 1 watt is equivalent to 1 joule per second.


  True
• The work-energy theorem states that the net work done on an object is equal to the change in its kinetic energy.
• In the work-energy theorem, W represents the net work done.


  True
• The conservation of energy principle states that the total energy in an isolated system remains constant over time.
• A 500 kg roller coaster starts at 20 m and descends to 5 m. What is its speed at 5 m without friction?

  17.15 m/s
• What are five different forms of energy?

  Kinetic, potential, thermal, electrical, chemical
• The formula for power as the ratio of work done to time taken is $P =$$\frac{W}{t}$, where W is work and t is time.
• A motor lifts a 50 kg box to a height of 10 m in 2 seconds. Calculate the power.

  2452.5 W
• Match the concept with its description:

  Power ↔️ Rate at which work is done

  Work ↔️ Energy transferred by force

  Energy ↔️ Capacity to do work
• The principle of conservation of energy states that energy can neither be created nor destroyed.


  True
• Match the concept with its formula:

  Conservation of Energy ↔️ $KE_{i} +$$PE_{i} =$$KE_{f} +$$PE_{f}$

  Kinetic Energy ↔️ $\frac{1}{2}mv^{2}$

  Potential Energy ↔️ $mgh$
• What is the formula for work done by a variable force?

  $W =$$\int_{x_{i}}^{x_{f}} F(x) \, dx$
• The work done in compressing the spring is 0.02k joules.
• The unit of power is the watt.