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Answers
Answer:
- Work done by body = -160 N
[ Negative sign expresses that body is losing energy ]
Explanation:
Given
- Mass of body, m = 20 kg
- Initial velocity of body, u = 5 m/s
- Final velocity of body, v = 2 m/s
To find
- Work done by the force, W =?
Knowledge required
- Work energy thereom
Work - energy theorem states that the net work done by the forces on object is equal to the change in its Kinetic energy.
→ W = Final KE - Initial KE
→ W = (1/2 m v²) - (1/2 m u²)
[ Where W is work done, m is mass of body, v is final velocity, u is initial velocity ]
Solution
By work energy theorem
→ W = (1/2 m v²) - (1/2 m u²)
→ W = 1/2 m ( v² - u² )
→ W = 1/2 · ( 20 ) · [ (2)² - (5)² ]
→ W = 10 · ( 4 - 25 )
→ W = ( 10 ) · ( -16 )
→ W = -160 N
Therefore,
- The work done by the Body would be 160 N in magnitude, and a negative sign with work shows that body will lose energy.
We can calculate the Work done in two ways:
• Work = Force × Displacement
• Work = Change in Kinetic Energy
Since the displacement and acceleration aren't mentioned in the question, we will use the second way.
Work = ∆K.E.
→ Work = 1/2 (mv² - mu²)
→ Work = 1/2 m(v² - u²)
→ Work = 1/2 (20)(4 - 25)
→ Work = 1/2(20)(-21)