A body of mass 10 kg initially at rest acquires velocity of 10 ms⁻¹. What is the work done?
Velocity is a vector quantity that describes the rate of change of an object’s position with respect to time. It includes both speed and direction, distinguishing it from scalar speed. Measured in meters per second, velocity is a key parameter in motion analysis and fundamental to understanding dynamics.
Chapter 5 of Class 11 Physics discusses Work Energy and Power. Work involves the transfer of energy when a force moves an object. Energy exists in forms like kinetic and potential and can transform between them. Power measures how quickly work is done and these concepts are crucial in understanding mechanics.
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To calculate the work done on the body, we can use the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy.
Step 1: Calculate the initial kinetic energy (K.E.₁)
Since the body is initially at rest, its initial kinetic energy is:
K.E.₁ = (1/2) m v₁²
K.E.₁ = (1/2) × 10 kg × (0 m/s)²
K.E.₁ = 0 J
Step 2: Final kinetic energy K.E.₂
When the body has achieved a velocity of 10 m/s, the final kinetic energy is:
K.E.₂ = (1/2) m v₂²
K.E.₂ = (1/2) × 10 kg × (10 m/s)²
K.E.₂ = (1/2) × 10 × 100
K.E.₂ = 500 J
Step 3: Work done (W)
The work done equals the change in kinetic energy
W = K.E.₂ – K.E.₁
W = 500 J – 0 J
W = 500 J
Final Answer:
Work done is 500 J.
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