a body of mass 2kg initially at rest is moved by a horizontal force of 0.5 N on a smooth table. obtain the work done by the force in 8 sec and show that this equals the change in kinetic energy of the body.
Answers
Explanation:
refer to the attachment
Given :
- Mass of the body = 2 kg
- Initial Velocity = 0 m/s
- Force = 0.5 N
- Time = 8 second
To Find :
- We have to find the work done and show that the work done is equals to the change in kinetic energy of the body.
Solution :
★ Finding the acceleration of the body :
→ Force = mass × acceleration
→ acceleration = Force ÷ mass
→ acceleration = 0.5 N ÷ 2 kg
→ acceleration = 0.25 m/s²
- Hence,the acceleration of the body is 0.25 m/s².
★ Let's calculate the final velocity of the body by using first equation of motion :
- v = u + at
[Where, a = acceleration, v = final velocity , u = initial velocity , t = time ]
Plug in the given values in above formula :
→ v = 0 + 0.25 × 8
→ v = 0.25 × 8
→ v = 2 m/s
- Hence,the final velocity of the body is 2 m/s.
★ Now, we have to find the distance travelled by the object by using second equation of motion :
- s = ut + ½ at²
[ Where, s = distance travelled, u = initial velocity, v = final velocity , a = acceleration, t = time interval ]
Plug in the given values in above formula :
→ s = 0 × 8 + ½ × 0.25 × (8)²
→ s = ½ × 0.25 × 8 × 8
→ s = 2 × 4
→ s = 8 m
- Hence,the distance travelled by the object is 8 m.
★ Calculating the work done of the body :
→ Work done = Force × displacement
→ Work done = 0.5 × 8
→ Work done = 4 joules
- Hence,the work done of the body is 4 J.
★ Finding the change in kinetic energy :
→ kinetic energy = ½ m (v² - u²)
→ kinetic energy = ½ × 2(2² - 0²)
→ kinetic energy = 4 joules
- Hence,the change kinetic energy of the body is 4 J.