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A bullet of mass 10 g leaves a rifle at an initial velocity of 100 m/s and strikes the earth at the same level with a velocity of 500 m/s. The work done in joule overcoming the resistance of air will be
The joule is the SI unit of energy, work, and heat. It is defined as the amount of energy transferred when a force of one newton acts through a distance of one meter. The joule is also used to measure electrical energy, mechanical energy, and thermal energy in various applications.
Class 11 Physics covers Chapter 5, focusing on work, energy and power. This chapter explores fundamental concepts including definitions, calculations and the relationships between work and energy. Students learn about different forms of energy, the work-energy theorem and the principle of conservation of energy in various physical contexts.
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To calculate the work done overcoming the resistance of air, we will need to determine the change in kinetic energy.
Step 1: Write down the formula for work done
The work done by air resistance is equal to the loss in the kinetic energy of the bullet. The formula for kinetic energy is:
K.E. = (1/2) m v²
Where:
– m = mass of the bullet = 10 g = 0.01 kg
– v = velocity of the bullet (initial and final)
Step 2: Calculate the initial and final kinetic energies
Initial velocity, u = 100 m/s
Final velocity, v = 500 m/s
Initial kinetic energy:
K.E.₁ = (1/2) m u²
K.E.₁ = (1/2) × 0.01 × (100)²
K.E.₁ = 0.005 × 10000
K.E.₁ = 50 J
Final kinetic energy:
K.E.₂ = (1/2) m v²
K.E.₂ = (1/2) × 0.01 × (500)²
K.E.₂ = 0.005 × 250000
K.E.₂ = 1250 J
Step 3: Find the work done
The work done in overcoming air resistance is the difference in kinetic energy:
Work done = K.E.₂ − K.E.₁
Work done = 1250 − 50
Work done = 1200 J
The work done in overcoming the resistance of air is 1200 J.
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