Rocket accelaation at the start of fuel burn

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The discussion revolves around calculating the acceleration of a rocket at the start of fuel burn while correcting its trajectory towards Mars. The rocket has a mass of 420 kg and burns 5 kg of solid fuel in 13 seconds, with an exhaust velocity of 3650 km/hr. Participants emphasize using the momentum conservation principle and the formula F = dp/dt = vdm/dt to determine the net force and resulting acceleration. The calculated net force is approximately 389.96 N, leading to an acceleration of about 0.93 m/s² when divided by the rocket's initial mass. The conversation highlights the importance of understanding how acceleration changes during the fuel burn.
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Hi Guys this is the problem I am stuck at:

The solid fuel of a 420.0 kg rocket traveling at 18100.0 km/hr is ignited to correct the rocket trajectory in mid-flight to Mars. 5.00 kg of fuel is burnt in 13.0 s. If the exhaust velocity of the fuel, relative to the rocket, is 3650.00 km/hr, what is the acceleration of the rocket (in m/s2) at the start of this burn?

I tried momentum conservation and unable to end up with correct accl of Rocket.

Thanks a lot
 
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nag said:
Hi Guys this is the problem I am stuck at:

The solid fuel of a 420.0 kg rocket traveling at 18100.0 km/hr is ignited to correct the rocket trajectory in mid-flight to Mars. 5.00 kg of fuel is burnt in 13.0 s. If the exhaust velocity of the fuel, relative to the rocket, is 3650.00 km/hr, what is the acceleration of the rocket (in m/s2) at the start of this burn?

I tried momentum conservation and unable to end up with correct accl of Rocket.
Use F = dp/dt = vdm/dt.

The rate of change of momentum of the rocket exhaust gives you the net force on the rocket. So you should be able to determine the acceleration at the beginning of the burn. Why is it (slightly) different at the beginning than at the end of the burn?

AM
 
Thanks for the help. It is obvious that backward thrust imposes forward force on rocket. In this case as the fuel start to burn I guess rocket gains a little acceleration. Please correct me If I am wrong or missing any.
 
Andrew Mason said:
Use F = dp/dt = vdm/dt.

The rate of change of momentum of the rocket exhaust gives you the net force on the rocket. So you should be able to determine the acceleration at the beginning of the burn. Why is it (slightly) different at the beginning than at the end of the burn?

AM
Thanks for the help. It is obvious that backward thrust imposes forward force on rocket. In this case as the fuel start to burn I guess rocket gains a little acceleration. Please correct me If I am wrong or missing any.
 
Andrew Mason said:
Use F = dp/dt = vdm/dt.

The rate of change of momentum of the rocket exhaust gives you the net force on the rocket. So you should be able to determine the acceleration at the beginning of the burn. Why is it (slightly) different at the beginning than at the end of the burn?

AM
Hi,

I followed your reply and net force on rocket = (1013.89 m/s)(5/13)kg/s = 389.96N

Since F=ma => a = 389.96 / 420(the initial mass)

Is this right way of doing. Thanks.
 
nag said:
Hi,

I followed your reply and net force on rocket = (1013.89 m/s)(5/13)kg/s = 389.96N

Since F=ma => a = 389.96 / 420(the initial mass)

Is this right way of doing. Thanks.
Looks right.

AM
 

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