Respuesta :
Answer:
a) [tex]F_H=776.952\ N[/tex]
b) [tex]F_g=706.32\ N[/tex]
c) [tex]v=5.4249\ m.s^{-1}[/tex]
d) [tex]KE=1059.48\ J[/tex]
Explanation:
Given:
- mass of the astronaut, [tex]m=72\ kg[/tex]
- vertical displacement of the astronaut, [tex]h=15\ m[/tex]
- acceleration of the astronaut while the lift, [tex]a=\frac{g}{10} =0.981\ m.s^{-2}[/tex]
a)
Now the force of lift by the helicopter:
Here the lift force is the resultant of the force of gravity being overcome by the force of helicopter.
[tex]F_H-F_g=m.a[/tex]
where:
- [tex]F_H=[/tex] force by the helicopter
- [tex]F_g=[/tex] force of gravity
[tex]F_H=72\times 0.981+72\times9.81[/tex]
[tex]F_H=776.952\ N[/tex]
b)
The gravitational force on the astronaut:
[tex]F_g=m.g[/tex]
[tex]F_g=72\times 9.81[/tex]
[tex]F_g=706.32\ N[/tex]
d)
Since the astronaut has been picked from an ocean we assume her initial velocity to be zero, [tex]u=0\ m.s^{-1}[/tex]
using equation of motion:
[tex]v^2=u^2+2a.h[/tex]
[tex]v^2=0^2+2\times 0.981\times 15[/tex]
[tex]v=5.4249\ m.s^{-1}[/tex]
c)
Hence the kinetic energy:
[tex]KE=\frac{1}{2} m.v^2[/tex]
[tex]KE=0.5\times 72\times 5.4249^2[/tex]
[tex]KE=1059.48\ J[/tex]
Answer:
Explanation:
mass of helicopter, m = 72 kg
height, h = 15 m
acceleration, a = g/10
(a) Work done by the force
Work, W = force due to helicopter x distance
W = m x ( g + a) x h
W = 72 ( 9.8 + 0.98) x 15
W = 11642.4 J
(b) Work done by the gravitational force
W = - m x g x h
W = - 72 x 9.8 x 15
W = - 10584 J
(c) Kinetic energy = total Work done
K = 11642.4 - 10584
K = 1058.4 J
(d) Let the speed is v.
K = 0.5 x m v²
1058.4 = 0.5 x 72 x v²
v = 5.42 m/s
Now the force of lift by the helicopter:
where:
force by the helicopter
force of gravity
b)
The gravitational force on the astronaut:
d)
Since the astronaut has been picked from an ocean we assume her initial velocity to be zero,
using equation of motion:
c)
Hence the kinetic energy:
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