3.3 Work Done and Power

• Power is defined as the rate at which work is done or energy is transferred.
• Arrange the steps to calculate Work Done when the force and displacement are at an angle:

  1️⃣ Identify the force (F) and displacement (d)

  2️⃣ Determine the angle (θ) between the force and displacement

  3️⃣ Calculate the cosine of the angle

  4️⃣ Multiply the force, displacement, and cosine value
• What is the formula for Power?

  $Power =$$\frac{Work\ Done}{Time}$
• Power measures how quickly work is performed.


  True
• What are the units of Power, Work Done, and Time, respectively?

  Watt, Joule, Second
• 1 Watt is equal to 1 Joule of work done per second.


  True
• What is the unit for work done?

  Joule
• Match the scenario with the correct angle:

  Force in the direction of displacement ↔️ $\theta =$$0^{\circ}$

  Force against displacement ↔️ $\theta =$$180^{\circ}$

  Force at an angle ↔️ $\theta =$$\text{variable}$
• When lifting a 50 kg object 2 m in 1 second, the power is 1000
• In the first example, what is the power when the work done is 1000 J over 1 second?

  1000 W
• Steps to calculate power given work done and time

  1️⃣ Calculate the work done using the work formula

  2️⃣ Divide the work done by the time
• The cosine function ensures that only the force component acting in the direction of movement contributes to the work done.
• What is the unit for measuring Work Done?

  Joule (J)
• Work Done is a measure of energy and is measured in Joules.


  True
• When the force is applied in the same direction as the displacement, the angle $\theta$ is 0 degrees.
• What is the work done when a force of -20 N acts over a displacement of 10 m with an angle of 180°?

  $- 200\text{ J}$
• Match the parameter in the work done formula with its symbol:

  Force ↔️ F

  Displacement ↔️ d

  Angle ↔️ $\theta$
• When pushing a box with a force of 50 N over a displacement of 5 m at an angle of $0^{\circ}$, the work done is 250
• What is the formula for calculating power?

  Power = \frac{Work\ Done}{Time}</latex>
• What is the power when lifting a 50 kg object 2 m in 1 second?

  1000 W
• What is the key to calculating power accurately?

  Understanding units
• Match the concept with its definition:

  Work Done ↔️ Energy transferred by a force over a distance

  Power ↔️ Rate at which work is done or energy is transferred
• The unit of Work Done is Watts (W).

  False
• The standard unit for Power is the Watt.
• What is the relationship between a Joule and a Newton-meter?

  1 Joule = 1 Newton-meter
• Power is defined as the rate at which work is done or energy is transferred. It measures how quickly work is performed
• Match the variable with its symbol and unit:

  Power ↔️ $P$, Watt (W)

  Work Done ↔️ $W$, Joule (J)

  Time ↔️ $t$, Second (s)
• 1 Joule is equal to 1 Newton-meter.

  True
• When the force is applied opposite to the displacement, $\theta =$$180^{\circ}$ and $\cos(180^{\circ}) =$$- 1$.


  True
• Understanding the units and applying the formulas correctly is crucial for determining power in different scenarios.


  True
• The work done is 200 J over 5 seconds, so the power is 40 W
• What is the formula for Work Done when considering force, displacement, and the angle between them?

  $W =$$F \times d \times \cos(\theta)$
• What is the formula for calculating power using work done and time?

  $P =$$\frac{W}{t}$
• What is the unit for measuring Power?

  Watt (W)
• Steps to apply the Work Done formula in different scenarios

  1️⃣ Identify the force, displacement, and angle

  2️⃣ Convert the angle to radians if necessary

  3️⃣ Use the formula $W =$$F \times d \times \cos(\theta)$

  4️⃣ Calculate the Work Done
• What is the Work Done when a frictional force of -20 N acts on an object over 10 m at 180 degrees?

  -200 J
• When pulling a sled at a $30^{\circ}$ angle, the approximate value of $\cos(30^{\circ})$ is 0.866
• What is the unit of force in the work done formula?

  Newtons (N)
• What is the value of $\cos(0^{\circ})$?


  1
• Match the parameter in the power formula with its symbol:

  Power ↔️ P

  Work Done ↔️ W

  Time ↔️ t