Respuesta :
Answer: 0.29 kN
Explanation:
We have the following data:
[tex]W_{E}=800 N[/tex] is the weight of the astronaut on Earth
[tex]g_{E}=9.8 m/s^{2}[/tex] is the free fall acceleration due gravity on Earth (directed downwards)
[tex]g_{Z}=3 m/s^{2}[/tex] is the free fall acceleration due gravity on Zuton (directed downwards)
[tex]a=0.5 m/s^{2}[/tex] is the acceleration of the spaceship at litoff (directed upwards)
We have to find the magnitude of the force [tex]F[/tex] the space ship exerts on the astronaut.
Firstly, we have to know weight has a direct relation with the mass and the acceleration due gravity. In the case of Earth is:
[tex]W_{E}=mg_{E}[/tex] (1)
Where [tex]m[/tex] is the mass of the atronaut.
Isolating [tex]m[/tex]:
[tex]m=\frac{W_{E}}{g_{E}}[/tex] (2)
[tex]m=\frac{800 N}{9.8 m/s^{2}}[/tex] (3)
[tex]m=81.63 kg[/tex] (4)
Now that we know the mass of the astronaut, we can find its weight on Zuton:
[tex]W_{Z}=mg_{Z}[/tex] (5)
[tex]W_{Z}=(81.63 kg)(3 m/s^{2})[/tex] (6)
[tex]W_{Z}=244.89 N[/tex] (7)
Then, we can calculate the force the space ship exerts on the astronaut by the following equation:
[tex]F-W_{Z}=m.a[/tex] (8)
Isolating [tex]F[/tex]:
[tex]F=m.a+W_{Z}[/tex] (9)
[tex]F=(81.63 kg)(0.5 m/s^{2})+244.89 N[/tex] (10)
[tex]F=285.7 N \frac{1 kN}{1000 N}=0.285 kN[/tex] (11)
Finally:
[tex]F=0.285 kN \approx 0.29 kN[/tex]
Force is defined as the product of mass and acceleration. Its unit is Newton. The magnitude of the force of the spaceship on the astronaut will be 0.29 kN.
What is force?
Force is defined as the push or pull applied to the body. Sometimes it is used to change the shape, size, and direction of the body. Force is defined as the product of mass and acceleration. Its unit is Newton.
The given data in the question is
[tex]\rm W_E[/tex] is the weight of the astronaut on Earth= 800 N
[tex]\rm g_e[/tex] is the free-fall acceleration due to gravity on Earth =9.81m/sec²
[tex]\rm g_z[/tex] is the free-fall acceleration due to gravity on Zutons=3m/sec²
a is the acceleration of the spaceship at lift-off =0.5m/sec²
Weight is equal to the product of mass and gravitational acceleration
[tex]\rm W_E=mg_E\\\\\rm m=\frac{\rm W_E}{g_E} \\\\m=\frac{\rm 800}{9.81}\\\\\rm m=81.63 kg[/tex]
Weight of astronaut on Zutons
[tex]\rm W_Z=m_ZG_Z\\\\W_Z=81.36\times3\\\\\rm W_Z=244.89\;N[/tex]
[tex]\rm F-W_Z=ma\\\\\rm F=ma+W_Z\\\\\rm F=81.63\times0.5+244.89\\\\\rm F=285.7\;N=0.285 \;KN[/tex]
F≈29 KN
Hence the magnitude of the force of the spaceship on the astronaut will be 0.29 kN.
To learn more about the force refer to the link;
https://brainly.com/question/26115859
