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Work Done By Gravity Formula

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  • Last Updated : 23 Feb, 2022

We witness several examples of gravity working with force in our daily lives. We know that there is continual motion and force in the cosmos in the form of pushes and pulls. Among the countless movements, there are four major elementary forces that are responsible for a wide range of phenomena. Gravitational force, strong force, weak force, and electromagnetic force are the four forces.

Work Done By Gravity

Gravity is a force that draws items to the ground. Forces have the power to work, hence gravity is fundamentally doing the job. When you apply force to an item, the force does the work for you. When you toss a ball, for example, the force given to the ball causes the ball to go a distance and therefore the job is completed. The work is proportional to the force applied and the distance travelled or made as a result; for example, if you throw the ball with less force, the distance covered by the ball will be smaller, proportional to the force applied; similarly, if you throw the ball with a lot of force, the distance covered will be long. When a particle is falling, it is compelled to point in the direction of gravity. The mass, gravitational constant, and height from which the falling body is falling determine the magnitude of the falling body.

The formula for calculating gravity’s work is as follows:

Wg = −mg(∆h)

where,

  • m is the mass of the object,
  • g depicts the acceleration due to gravity
  • h depicts the height from which the said object was dropped.

If θ is the angle made when the object falls down, the formula used is: 

W = mgh cosθ

Sample Problems

Question 1. Determine the work done by gravity if a 9 kg drum is thrown from a height of 10 m at an angle of 25°.

Solution:

Given: m = 9 kg, h = 10m and θ = 25°.

Work done by gravity = mgh cosθ

= 9 × 9.8 × 10 × cos25°

= 9 × 9.8 × 10×0.9063

⇒ Wg = 799.35 J

Question 2. Determine the work done by gravity if a box of 100 kg is thrown from a height of 23 m.

Solution:

Given: m = 100 kg, h = 23 m

Work done by gravity = mgh

= 100 × 9.8 × 23 J

Wg = 22540 J

Question 3. Determine the work done by gravity while a satellite goes around the planet in an orbit with a radius of 100000 km.

Solution:

Since the gravity acts towards the center of the earth only and not around its orbit, the satellite orbiting around the planet would not be affected by the gravitational pull. Thus the work done at any point on the satellite is zero. 

So the work done by gravity while a satellite goes around the planet in an orbit with a radius of 100000 km is 0 J.

Question 4. Two identical cylindrical jars, each with the same level of base, each hold a liquid of density p. The area of either base is A, but the liquid height in one vessel is h1 and the other h2(such that h2<h1). Find the work done by gravity in equalizing liquid levels if the said containers are connected.

Solution:

Work  done  by  gravity =− Change  in  potential  energy

Total work done by gravity (Wg) =W1 + W2

​W1Apg\frac{h_1}{2}(h_1-h)

W2Apg\frac{h_2}{2}(h_2-h)

Thus required value = Apg(\frac{h_1-h_2}{2})^2

Question 5. Determine the work done by gravity if a box of 70 kg is thrown from a height of 3 m.

Solution:

Given: m = 70 kg, h = 3 m

Work done by gravity = mgh

= 70 × 9.8 × 3 J

Wg = 2058 J

Question 6. Determine the work done by gravity if a box of 6 kg is thrown from a height of 13 m.

Solution:

Given: m = 6 kg, h = 13 m

Work done by gravity = mgh

= 6 × 9.8 × 13 J

Wg = 764.4 J

Question 7. Determine the work done by gravity if a box of 60 kg is thrown from a height of 5 m.

Solution:

Given: m = 60 kg, h = 5 m

Work done by gravity = mgh

= 50 × 9.8 × 5 J

Wg = 2450 J

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