A force F= (x2+3x–5) N acts on a 5 kg body along
x-axis as a result of which the body gets displaced
from x=0 to x=3 m. The work done by the force
will be-
(1) 35 J
(2) 15 J
(3) 7.5 J
(4) 70 J
Answers
Answer:
Given that,
Force F=7−2x+3x
2
We know that,
F=
dx
dw
dw=Fdx
Now, the work done is
∫dw=
0
∫
5
F⋅dx
∫dw=
0
∫
5
(7−2x+3x
2
)dx
W=[7x−
2
2x
2
+
3
3x
3
]
0
5
W=35−25+125
W=135J
Hence, the work done is 135 J
The correct answer to the above question is (3), that is 7.5J
Given: F = (x² + 3x - 5) N
Displacement form x = 0 to x= 3
To find: Work done by the force.
Solution:
Work done by the force is defined as the product of the force applied on the body and the displacement of the body. Its SI unit is Joule.
Since the force is not constant, we will use integration.
Work done = Force × displacement
= ∫(x² + 3x - 5).dx ( x =0 to x = 3)
= x³/3 + 3x²/2 - 5x ( x = 0 to x = 3)
= (3³/3 + 3×3²/2 - 5×3) - ( 0³/3 - 3×0²/2 - 5×0)
= ( 9 + 13.5 - 15) - 0
= 7.5J
Therefore, the work done by the force will be 7.5J.