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When an object is moved from one place to another, this displacement of an object means work is done on the object. The displacement caused in the object is done by any other outside force like gravitational force, electromagnetic force, strong force and weak force. Gravity is a force that attracts any object with mass towards the earth. Although gravitational force is the weakest force in nature, it is of primary importance which keeps the universe together by keeping interaction between elements or objects.
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Key terms: Gravity, Force, Work Done, Mass, Object, Gravitational Force
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Work Done
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When an object is displaced with the help of an external force it is called work done. When the external force applied to the object is gravitational force it is called work done by gravity.
For example, if a ball is thrown in the air with a force it will always come down towards the earth. Here, the two objects are the ball and the earth and the force between them which is pulling the ball down is gravity.
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Gravity
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A gravitational force is the most prevalent force present on earth. A gravitational force can be defined as the force which attracts any two objects with a mass towards each other.
Gravitational force is always present in between the two objects even though they are at a far distance from each other. It can be still calculated.
The gravity constant value is 6.67 X 10-11 Nm2 kg-2 and it is independent of the nature and size of bodies.
Gravity
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Formula
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- The formula to calculate gravitational force is;
Where
F = force of gravity
G = gravitational constant
m1 = mass of the object
m2 = mass of another object
r2 = distance between two objects
- To calculate the work done by gravity the formula is,
W = m* g*h
Where,
W = work done by gravity
m = mass of the object
g = gravity
h= height of the object from its original position
- When the angle is made, work done by gravity is calculated by;
W = m*g*h*cos θ
Where,
m = mass of the object
g = gravity
h = height of the object
θ = angle of the object when it falls
- Work done = Force x Displacement
W = F X S
Things to Remember
- Gravity is a constant force in nature. Therefore, for a certain displacement work done by gravity is constant.
- The universal constant of gravitation ‘G’ is numerically equal to the force of attraction between two particles of unit mass each separated by unit distance.
- The value of ‘G’ is 6.67 X 10-11 Nm2 kg-2 and it is independent of size and distance between two objects.
- Work done is zero if displacement is perpendicular to the force i.e.; θ = 90o
- Work done is positive when the angle between force and displacement is acute i.e.; θ < 90o
- Work done is negative when the angle between force and displacement is obtuse i.e.; θ > 90o
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Sample Questions
Ques. A body of 75 kg falls from the terrace of a building 85 m high. Calculate the work done by gravitational force. (1 mark)
Ans. Given: m = 75 kg; h = 85 m; g = 9.8 m/s2
The body falls under the action of the force of gravity, to calculate the work done,
Work done (W) = m*g*h
W = 75 * 9.8 * 85
W = 62475 J.
Ques. A pencil falls from a table. It calculates the work done by the force of gravity. Consider that the mass of the pencil is 10 grams and the height of the table is 60 cm. (1 mark)
Ans. Given: mass (m) = 10 g = 0.01 kg
Gravity (g) = 9.8 m/s2
Height (h) = 60 cm = 0.6 m.
Formula: (W) = m*g*h
W = 0.01 kg x 9.8 m/s2 x 0.6 m
W = 0.06 J.
Therefore the work done by the force of gravity is 0.06 J.
Ques. A 15 kg box falls at angle 25o from a height of 10 m. Determine the work done by gravity. (2 marks)
Ans. Given: Mass (m) = 10 kg
Angle (θ) = 25o
The work done by gravity formula is given by,
W = m*g*h* cos θ
W = 15 × 9.8 × 10× cos 25o
W = 15 × 9.8 × 10×0.9063
W = 1332 J
Therefore, work done by gravity is 1332 J.
Ques. A boy drags a 10 kg box across the friction-less surface. He applies a force of 30 N at an angle of 30o to the horizontal for 6m. Determine the work done by gravity. (2 marks)
Ans. Given: Mass (m) = 10 kg,
Force (F) = 30 N,
Angle (θ) = 30o
Displacement (s) = 6m
The work done by gravity formula is,
W = m*g*h *cos θ
W = 10 x 9.8 x 6 × cos 30o
W = 10 x 9.8 x 6 × 0.866
The work done by gravity is 509.208 J.
Ques. Calculate the work done in lifting a 12 kg suitcase from floor level up to a luggage rack 2.0 m above the floor. (1 mark)
Ans. Given: Mass (m) = 12kg
Height (h) = 2.0 m
Calculation: Work done (W) = m*g*h
W = 12 x 9.8 x 2.0
W = 235.2 kgm2s-2
W = 240 J
Ques. The work done against gravity in taking 10kg mass at 1m height in 1s will be (in J). Choose the correct option. (2 marks)
(A) 49
(B) 196
(C) 98
(D) None
Ans. Given: Mass (m) of an object = 10kg
Height (h) at which it is placed = 1m
Acceleration due to gravity (g) = 9.8m/s2
Work done (W) = 10 × 9.8 × 1
W=10×9.8×1
W=98kgm2s2
W = 98 J.
Work done is a scalar quantity. It depends on initial and final position instead of the path followed.
Option C is the correct option.
Ques. Calculate the work done by force of gravity, when an object of 10kg falls from a height of 10m. (g = 10 m/s2) (1 mark)
Ans. Given: mass (m) = 10kg
Height (h) = 10m
Gravity (g) = 10m/s2
Formula: W = m*g*h
Calculation: W = 10*10*10
W = 1000 kgm2/s2
W = 1000 J
Ques. Determine the work done by gravity if a 9 kg drum is thrown from a height of 10 m at an angle of 25°. (2 marks)
Ans. Given: Mass (m) = 9 kg,
Height (h) = 10m and
θ = 25°.
Work done by gravity = m*g*h* cos θ
W = 9 × 9.8 × 10 × cos25°
W = 9 × 9.8 × 10 × 0.9063
W = 799.35 J
Ques. Determine the work done by gravity if a box of 100 kg is thrown from a height of 23 m. (1 mark)
Ans. Given: m = 100 kg,
h = 23 m
Work done by gravity = m*g*h
W = 100 × 9.8 × 23 J
W = 22540 J
Ques. The work done by gravity on a stone having a mass of 2kg during the 5th second of its vertical fall from rest is; (3 marks)
(a)864 J
(b)864.36 J
(c)648.36 J
(d)486.36 J
Ans. Given: m = 2kg, u = 0, n = 5
Work done by gravity will be mgΔh
Distance travelled in 5th second will be
Δh = 0.5 x 9.8 x (10—1)
Δh = 44.1m
Now, the work done by gravity will be
W = mgΔh
W = 2 x 9.8 x 44.1
W = 864.36 J
Therefore correct option is (2) 864.36 J
Ques. Case (1) A man walks 2 m carrying a mass of 15 kg on his hands. 6.
Case (2) He walks the same distance pulling the rope behind him. The rope goes over a pulley, and a mass of 15 kg hangs at its other end. In which case is the work done greater? (5 marks)
Ans. Case (i): Mass (m) = 15 kg = 15 kg
Displacement (s) = 2 m
Work done (W) = F*s* cos θ
Where, θ=Angle between force and displacement
W = m x g x cos θ
W = 15 × 2 × 9.8 cos90o
W = 0
Case (ii): Mass (m) = 15 kg
Displacement (s) = 2 m
Here, the direction of the force applied on the rope and the direction of the displacement of the rope are the same.
Therefore, the angle between them, θ = 0o
As, cos0o = 1
Work done (W) = F x s x cos θ = mgs
W = 15 × 9.8 × 2
W = 294
Thus, work done in the second case is greater.
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