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You pull upward on a stuffed suitcase with a force of 105N , and it accelerates upward at 0.710m/s2, what is the wieght and mass of the suitcase?


Suppose the suitcase is on a rocket. The rocket launches with an acceleration of 29.0m/s2, What is the apparent weight of an 86-kg astronaut aboard this rocket?

Verified Answer :

faiqraees

I will assume the value of gravitational acceleration is 10m/s^-2 towards the centre of Earth.

\(F_{Resultant} =F_{Pull}-F_{Weight}\)
\(Mass_{R}* Acceleration_{R}=105-(Mass_{Weight}* Acceleration_{Weight})\)\(Mass_{R}*0.71 =105-(Mass_{W}*10)\)
Assuming mass remains constant
\(0.71M =105-10M\)
\(10.71M =105\)
\(M =9.8kg\)
\(W=Mg\)
\(W=9.8*10\)
\(W=98N\)

\(W_{Apparent}=Mass*(Acceleration_{Weight}+Acceleration_{Rocket})\)
\(W_{Apparent}=9.8*(10+29)\)
\(W_{Apparent}=9.8*(39)\)
\(W_{Apparent}=382.2N\)

Answer:

a) m_s = 9.981 kg  ,  W_s = 9.9819.81 = 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_sa_s

                                     F_pull - W_s = m_sa_s

Where,                          W_s = m_sg

                                     F_pull - m_sg = m_sa_s

Rearrange,                   F_pull = m_sa_s + m_sg

                                     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 = 9.9819.81 = 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_ag = m_aa_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.

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