Respuesta :
Answer:
Explanation:
The mass of the boat is 3100kg.
Initial position of boat is r1= (2,0,3)m
And initial velocity of boat is 1.9m/s
New position r2=(8,0,0)m
Jill Force =(180,0,360)N
Jack force=(-420,0,210)N
a. Jack work
Work is given as the dot product of force and displacement
W=F•d
The displacement is ∆r
∆r=r2-r1
∆r=(8,0,0)-(2,0,3)
∆r=(6,0,-3)
The force exerted by Jack is Fj=(-420,0,210)
Then,
W=F•∆r
W=(-420 i + 0 j + 210 k)•(6 i +0j - 3 k)
Then, i.i=j.j=k.k=1
Also, i.j=j.i=k.i=i.k=j.k=k.j=0
Using this principle
Then,
W=(-420 × 6) +(0×0)+(210×-3)
W=-2520-630
W=3150J.
The workdone by Jack is 3150J
2. Work done by jill
Using the same principle and they have the same displacement
∆r=(6,0,-3)
Therefore
W=F•∆r
W=(180 i + 0 j + 360 k)•(6 i +0j - 3 k)
Then, i.i=j.j=k.k=1
Also, i.j=j.i=k.i=i.k=j.k=k.j=0
Using this principle
Then,
W=(180× 6) +(0×0)+(360×-3)
W=1080-1080
W=0J.
The workdone by Jill is 0J, she did no work
This show that Jill apply her force perpendicular to the displacement.
Because W=0 if and only if the displacement is zero or it is perpendicular to the applied force
3. I think we can still calculate the final velocity of the boat since we are given the mass
Using conservation of energy principle
∆K.E=W
K.E=1/2mv²
Total work is 0+3150=3150J
Then,
0.5M(Vf²-Vi²) =W
(Vf²-Vi²)=W/0.5M
Given than M=3100kg and Vi=1.9m/s
Vf²-Vi²=3150/(0.5×3100)
Vf²-1.9²=2.03
Vf²=2.03+1.9²
Vf²=5.6423
Vf=√5.6423
Vf=2.38m/s.
Answer:
A) WJack = - 3150 J
B) WJill = 0 J
Explanation:
M= 3100kg and initial speed (u) = 1.9m/s
Now, we know that work done = Force x displacement.
So in this question,
A) Work done by Jack(W) = F x Δr
From the question, force applied by Jack equals (-420, 0, 210)N
Also, since the boat moves from initial position of (2, 0, 3)m to final position of (8, 0, 0)m, thus the displacement (Δr) = (8, 0, 0)m - (2, 0, 3)m = (6,0, -3)m
Thus work done by Jack(W) =
(-420, 0, 210)N x (6,0, -3)m=
( - 420 x 6) + (0) +( 210 x (-3)) =
- 3150J
B) Force applied by Jill = (180, 0, 360)N
Using the same principle, work done by Jill = (180, 0, 360)N x (6,0, -3)m =
(180 x 6) + (0) +( 360 x (-3)) = 0J
