A force 2i^+3j^ acts on a body to displace it from(1,2) to (4,1) . if initial velocity of body is 2m/s and mass 10kg find finnal velocity.
Answers
Answer:
√4.6 m/s
Explanation:
Prerequisite knowledge:
- The dot product of two vectors A and B is a scalar quantity
- The dot product of two perpendicular vectors is zero.
Given:
- F=2i+3j
- initial position =A(1,2)=i+2j
- final position =B(4,1)=4i+j
- Initial velocity=2 m/s
- final velocity= v
- mass of the body= 10 kg
Solution:
To solve this problem we have to Work Energy theorem which states that
'Work done by all the forces is equal to the change in kinetic energy of the body'
Its given by the formula
W=ΔKE
=KEf - KEi
In our problem only the force F does work and work done by this force is given by
W=F.s
(where s is the displacement of the body and given by BA)
(BA=position vector of B- position vector of A)
W=F.s
=(2i+3j)(4i+j-(i+2j))
=(2i+3j)(3i-j)
=2*3 + 0 + 0 + 3*(-1)
=6-3
=3 N m
We also know that
W=ΔKE
=1/2*m*(v²-u²)
=1/2*10*(v²-4)
Equating the above two equations as LHS is same
We get
3=1/2*10*(v²-4)
0.6=v²-4
4.6=v²
v=√4.6 m/s
Hope this helps.
Answer work done by all forces is equal to change in kinetic energy
