Respuesta :
Answer:
a) The work done on the astronaut by the force from the helicopter is [tex]W_{h}=16087.68\ J[/tex].
b) The work done on the astronaut by the gravitational force is [tex]W_{g}=-15082.2\ J[/tex] .
Explanation:
We are told that the mass of the astronaut is [tex]m=81\ kg[/tex], the displacement is [tex]\Delta x=19\ m[/tex], the acceleration of the astronaut is [tex]|\vec{a}|=\frac{g}{15}[/tex] and the acceleration of gravity is [tex]g=9.8\ \frac{m}{s^{2}}[/tex] .
We suppose that in the vertical direction the force from the helicopter [tex]F_{h}[/tex] is upwards and the gravitational force [tex]F_{g}[/tex] is downwards. From the sum of forces we can get the value of [tex]F_{h}[/tex]:
[tex]F_{h}-F_{g}=m.a[/tex]
[tex]F_{h}-mg=m.\frac{g}{15}[/tex]
[tex]F_{h}=mg(1+\frac{1}{15})[/tex]
[tex]F_{h}=(\frac{16}{15}).81\ kg.\ 9.8\ \frac{m}{s^{2}}\ \Longrightarrow\ F_{h}=846.72\ N[/tex]
We define work as the product of the force, the displacement of the body and the cosine of the angle [tex]\theta[/tex] between the direction of the force and the displacement of the body:
[tex]W=F.\Delta x.\ cos(\theta)[/tex]
a) The work done on the astronaut by the force from the helicopter
[tex]W_{h}=F_{h}.\Delta x[/tex]
[tex]W_{h}=846.72\ N.\ 19\ m[/tex]
[tex]W_{h}=16087.68\ J[/tex]
b) The work done on the astronaut by the gravitational force
[tex]W_{g}=-F_{g}.\Delta x[/tex]
[tex]W_{g}=-mg\Delta x[/tex]
[tex]W_{g}=-81\ kg.\ 9.8\ \frac{m}{s^{2}}.\ 19\ m[/tex]
[tex]W_{g}=-15082.2\ J[/tex]
Answer:
a) Work done on the astronaut by the force from the helicopter = 16.104 kJ
b) Work done on the astronaut by the gravitational force = -15.082 kJ
Explanation:
mass of the astronaut, m = 81 kg
height, h = 19 m
acceleration of the astronaut, a = g/15
Since the astronaut is lifted up, using the third law of motion:
T - mg = ma
T = mg + ma
T = (81*9.81) + 81*(9.81/15)
T = 847.584 N
Work done on the astronaut by the helicopter
Work done = Tension * height
W = T* h
W = 847.584 * 19
Work done, W = 16104.096 Joules
W = 16.104 kJ
b) Work done on the astronaut by the gravitational force on her
[tex]W = -f_{g} h[/tex]
[tex]f_{g} = mg = 81 * 9.8\\f_{g} = 793.8 N[/tex]
[tex]W = -793.8 * 19\\W =- 15082.2 J[/tex]
W = -15.082 kJ
