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Workdone In Raising a Box Formula

Work done when raising a box is the measure of energy expended to lift the box against the force of gravity over a certain vertical distance. The workdone in raising a 10 kg box vertically through a height of 5 meters against the force of gravity on Earth.
authorImageMurtaza Mushtaq10 Sept, 2023
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Workdone In Raising a Box Formula

Definition And Formula Of Workdone In Raising a Box

Workdone In Rasing a Box is a fundamental concept in physics that describes the energy transferred when a force acts on an object and causes it to move a certain distance. To calculate the work done by a constant force, you can use the following formula: Let's go through the process step by step with full details: Scenario : You are lifting a box vertically against the force of gravity. Key Information:
  1. Mass of the box  (m : You need to know the mass of the box. Let's say it's 10 kilograms (kg).
  2. Height of the lift  (h : You need to know the vertical distance you are lifting the box. Let's say it's 5 meters (m).
  3. Acceleration due to gravity  (g : The standard value for this is approximately  9.81 \, \text{m/s}^2  on Earth's surface.

Steps to Calculate Workdone In Raising a Box :

  1. Calculate the Force of Gravity :
- The force of gravity  (F  acting on the box is given by Newton's second law:  F = m g . - In this case,  m  is the mass of the box (10 kg), and  g  is the acceleration due to gravity (approximately  9.81m/s^2 . - So,  F= 10 * 9.81 \,m/s^2 \approx 98.1 N

Also Check - Unit, Dimension & Vector

  1. Calculate the Work Done :
- Work done  (W  is given by the formula:  W = Fdcos , where  F  is the force,  d  is the displacement, and \ theta  is the angle between the force and displacement vectors. In this case, \ = 0 because you are lifting vertically. - So,  W = Fhcosθ - Since cos0 = 1 , the equation simplifies to  W = F* h . - Now, plug in the values: W = 98.1 * 5  = 490.5 J .

Also Check - Work, Energy & Power Formula

Interpretation : The workdone in raising a 10 kg box vertically through a height of 5 meters against the force of gravity on Earth is approximately 490.5 joules (J). This represents the energy transfer from you to the box as you lift it. The positive value indicates that you are doing work on the box by applying an upward force to overcome gravity.

Examples

Here are ten examples of Workdone In Raising a Box in various situations to help you understand the concept better:
  1. Lifting a Backpack :
- Scenario: Lifting a 5 kg backpack vertically from the ground to a table that is 1 meter high. - Work Done  (W  = Force  (F  × Distance  (d -  F  = Weight of the backpack =  m \cdot g  = 5 kg × 9.81 m/s² ≈ 49.05 N -  W  = 49.05 N × 1 m = 49.05 J - Interpretation: You do 49.05 joules of work lifting the backpack.

Also Check - Thermodynamics formula

  1. Pushing a Car :
- Scenario: Pushing a 1000 kg car horizontally for a distance of 10 meters with a force of 500 N. - Work Done  (W  = Force  (F  × Distance  (d  × cos(θ) -  W  = 500 N × 10 m × cos(0°) = 5000 J - Interpretation: You do 5000 joules of work pushing the car.
  1. Pulling a Sled Uphill :
- Scenario: Pulling a 50 kg sled up a hill inclined at 30 degrees to the horizontal for a distance of 15 meters with a force of 150 N. - Work Done  (W  = Force  (F  × Distance  (d  × cos(θ) -  W  = 150 N × 15 m × cos(30°) ≈ 1950 J - Interpretation: You do approximately 1950 joules of work pulling the sled uphill.
  1. Climbing Stairs :
- Scenario: Climbing a flight of stairs that is 4 meters high with a weight of 70 kg. - Work Done  (W  = Force  (F  × Distance  (d -  F  = Weight of the person =  m \cdot g  = 70 kg × 9.81 m/s² ≈ 686.7 N -  W  = 686.7 N × 4 m = 2746.8 J - Interpretation: You do 2746.8 joules of work climbing the stairs.
  1. Lifting a Bucket from a Well :
- Scenario: Lifting a 20 kg bucket vertically from a well that is 10 meters deep. - Work Done  (W  = Force  (F  × Distance  (d -  F  = Weight of the bucket =  m \cdot g  = 20 kg × 9.81 m/s² ≈ 196.2 N -  W  = 196.2 N × 10 m = 1962 J - Interpretation: You do 1962 joules of work lifting the bucket.
  1. Rowing a Boat :
- Scenario: Rowing a boat horizontally for a distance of 500 meters with an average force of 150 N. - Work Done  (W  = Force  (F  × Distance  (d  × cos(θ) -  W  = 150 N × 500 m × cos(0°) = 75,000 J - Interpretation: You do 75,000 joules of work rowing the boat.
  1. Pulling a Loaded Cart on a Ramp :
- Scenario: Pulling a 200 kg cart up a 30-degree inclined ramp for a distance of 8 meters with a force of 500 N. - Work Done  (W  = Force  (F  × Distance  (d  × cos(θ) -  W  = 500 N × 8 m × cos(30°) ≈ 3464 J - Interpretation: You do approximately 3464 joules of work pulling the cart up the ramp.
  1. Lifting a Kettlebell :
- Scenario: Lifting a 16 kg kettlebell vertically from the floor to a height of 1.5 meters. - Work Done  (W  = Force  (F  × Distance  (d -  F  = Weight of the kettlebell =  m \cdot g  = 16 kg × 9.81 m/s² ≈ 157.0 N -  W  = 157.0 N × 1.5 m = 235.5 J - Interpretation: You do 235.5 joules of work lifting the kettlebell.
  1. Pushing a Lawnmower :
- Scenario: Pushing a lawnmower horizontally across a lawn for a distance of 20 meters with a force of 80 N. - Work Done  (W  = Force  (F  × Distance  (d  × cos(θ) -  W  = 80 N × 20 m × cos(0°) = 1600 J - Interpretation: You do 1600 joules of work pushing the lawnmower.
  1. Lifting a Book :
- Scenario: Lifting a 1 kg book vertically from a desk that is 0.5 meters high. - Work Done  (W  = Force  (F  × Distance  (d -  F  = Weight of the book =  m \cdot g  = 1 kg × 9.81 m/s² ≈ 9.81 N -  W  = 9.81 N × 0.5 m = 4.905 J - Interpretation: You do 4.905 joules of work lifting the book. These examples demonstrate how to calculate the work done in various everyday scenarios, taking into account factors such as force, distance, and the angle between the force and displacement vectors.

Workdone In Raising a Box Formula FAQs

What is work done when raising a box? 

Work done when raising a box is the measure of energy expended to lift the box against the force of gravity over a certain vertical distance.

Why is lifting a box considered work? 

Lifting a box is considered work because it involves applying a force (against gravity) to move the box a certain height, transferring energy in the process.

Is the work done in raising a box affected by its weight? 

Yes, the work done is affected by the weight of the box. Heavier boxes require more work to lift because the force required to overcome gravity is greater.

What happens to the work done if you raise the box higher?

If you raise the box to a greater height, you will do more work. Work is directly proportional to the height or vertical distance over which the box is lifted.
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