Respuesta :
I will assume the value of gravitational acceleration is 10m/s^-2 towards the centre of Earth.
[tex]F_{Resultant} =F_{Pull}-F_{Weight}[/tex]
[tex]Mass_{R}* Acceleration_{R}=105-(Mass_{Weight}* Acceleration_{Weight})[/tex][tex]Mass_{R}*0.71 =105-(Mass_{W}*10)[/tex]
Assuming mass remains constant
[tex]0.71M =105-10M[/tex]
[tex]10.71M =105[/tex]
[tex]M =9.8kg[/tex]
[tex]W=Mg[/tex]
[tex]W=9.8*10[/tex]
[tex]W=98N[/tex]
[tex]W_{Apparent}=Mass*(Acceleration_{Weight}+Acceleration_{Rocket})[/tex]
[tex]W_{Apparent}=9.8*(10+29)[/tex]
[tex]W_{Apparent}=9.8*(39)[/tex]
[tex]W_{Apparent}=382.2N[/tex]
[tex]F_{Resultant} =F_{Pull}-F_{Weight}[/tex]
[tex]Mass_{R}* Acceleration_{R}=105-(Mass_{Weight}* Acceleration_{Weight})[/tex][tex]Mass_{R}*0.71 =105-(Mass_{W}*10)[/tex]
Assuming mass remains constant
[tex]0.71M =105-10M[/tex]
[tex]10.71M =105[/tex]
[tex]M =9.8kg[/tex]
[tex]W=Mg[/tex]
[tex]W=9.8*10[/tex]
[tex]W=98N[/tex]
[tex]W_{Apparent}=Mass*(Acceleration_{Weight}+Acceleration_{Rocket})[/tex]
[tex]W_{Apparent}=9.8*(10+29)[/tex]
[tex]W_{Apparent}=9.8*(39)[/tex]
[tex]W_{Apparent}=382.2N[/tex]
Answer:
a) m_s = 9.981 kg , W_s = 9.981*9.81 = 97.9 N
b) N = 3337.66 N
Explanation:
Given:
- F_pull = 105 N
- Acceleration of suitcase a_s = 0.710 m/s^2
- Acceleration of rocket a_r = 29.0 m/s^2
- Mass of the astronaut m_a = 86 kg
Find:
- What is the weight and mass of the suitcase?
- What is the apparent weight of an 86-kg astronaut aboard this rocket?
Solution:
- With the help of a free body diagram we can see that two forces act on the suitcase the one which you pulled and weight of the suitcase. Using Newton's second law we can model this as:
F_net = m_s*a_s
F_pull - W_s = m_s*a_s
Where, W_s = m_s*g
F_pull - m_s*g = m_s*a_s
Rearrange, F_pull = m_s*a_s + m_s*g
F_pull = m_s(a_s + g)
m_s = F_pull / (a_s + g)
-Compute: m_s = 105 / (9.81 + 0.71)
m_s = 9.981 kg
Hence, W_s = 9.981*9.81 = 97.9 N
- With the help of a free body diagram we can see that two forces act on the astronaut the normal contact force that the rocket exerts on the astronaut and his own weight. Using Newton's second law we can model this as:
N - m_a*g = m_a*a_r
N = m_a*(a_r + g)
- Compute: N = 86*(29.0 + 9.81)
N = 3337.66 N
- The normal contact force that the rocket exerts on the astronaut will also act on the rocket by the astronaut according to Newton's Third law. So this is the amount of force "weight" felt by the rocket, hence apparent weight.
