What is the work done to increase the velocity of a car from 40 km/hr to 60 km/hr if the mass of the car is 1000 kg ? Does the work done by the force have a negative or a positive magnitude ?
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Given :
Initial velocity = 40 km/hr
Final velocity = 60 km/hr
Mass of car = 100 kg
To Find :
Work done by the force
Solution :
❒ As per work - kinetic energy theorem,
- Work done = ∆k
» ∆k denotes change in kinetic energy
Kinetic energy of body of mass m moving at a speed of v is given by, k = 1/2 mv²
➙ W = 1/2 m (v² - u²)
- v denotes final velocity
- u denotes initial velocity
First of all we need to convert unit of time into m/s. We know that, 1 km/hr = 5/18 m/s
• 40 km/hr = 40 × 5/18 = 11.11 m/s
• 60 km/hr = 60 × 5/18 = 16.67 m/s
By substituting the given values;
➙ W = 1000/2 (16.67² - 11.11²)
➙ W = 500 (277.88 - 123.43)
➙ W = 500 × 154.45
➙ W = 77225 J = 77.2 kJ
❒ Work done by force has a positive magnitude as velocity is increasing with time.
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