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Sagot :
Answer:
Explanation:
Initial momentum is 1.5e6(3) = 4.5e6 kg•m/s
An impulse results in a change of momentum
The tug applied impulse is 12000(10) = 120000 N•s or 0.12e6 kg•m/s
The remaining momentum is 4.5e6 - 0.12e6 = 4.38e6 kg•m/s
The barge velocity is now 4.38e6 / 1.5e6 = 2.92 m/s
The tug applies 0.012e6 N•s of impulse each second.
The initial barge momentum will be zero in
t = 4.5e6 / 0.012e6 = 375 s or 6 minutes and 15 seconds
To stop the barge in one minute(60 s), the tug would have to apply
4.5e6 / 60 = 75000 N•s /s or 75 000 N
The force would a tugboat needed to apply to stop it in one minute will be 7500 N.It is obtained as the ratio of the impulse and the time period.
What is force?
Force is defined as the push or pulls applied to the body. Sometimes it is used to change the shape, size, and direction of the body.
The given data in the problem is;
m is the mass of the loaded barge =1 500 000 kg
u is the velocity of the bardge= 3 m/s
E is the opposing force = 12 000 N
t is the time period = 10 sec
v is the final velocity
The initial momentum of the badge is;
[tex]\rm P_I = m_iv_i \\\\ \rm P_I = 1500000 \times 3 \\\\ \rm P_I = 45 \times 10^6[/tex]
From thew Newtons second law the impulsive force is equal to the change in the momentum.
The impulse is found as;
[tex]\rm I = F \times t \\\\ \rm I = 12000 \times 10 \\\\ I=120000\ Ns[/tex]
The final momentum is found as;
[tex]\rm I= \triangle p\\\\ I= P_f-P_i \\\\ P_f = p_i-I \\\\ P_f=4.5 \times 10^6 -1.5 \times 10^6\\\\ P_f=2.92 \ m/sec[/tex]
As given the barge is at rest the initial badge momentum is zero;
As we know;
[tex]\rm I=F \times t \\\\ t = \frac{I}{f} \\\\ t= \frac{4.5 \times 10^6}{0.02 \times 10^6} \\\\ t= 375 \ sec[/tex]
The conversion of the minute and second is as;
[tex]\rm 1 \ min = 60\ sec \\\\ 1 sec = \frac{1}{60} min \\\\ 375 \ sec = \frac{375 }{60} \\\\ t = 6 \min \ and \ 15 second[/tex]
The force would a tugboat need to apply to stop it in one minute will be found as;
[tex]\rm I =F \times t \\\\ F = \frac{I}{t}\\\\ F = \frac{4.5 \times 10^6 }{60} \\\\ F= 75000 N[/tex]
Hence force would a tugboat needed to apply to stop it in one minute will be 7500 N.
To learn more about the force refer to the link;
https://brainly.com/question/26115859
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