Breaking the Sound Barrier: Calculating Time and Thrust of a Rocket Launch

In summary, a 25,000-kg rocket with a constant acceleration blasts off vertically from Earth's surface while a 15.0-N instrument hangs from a wire that can support a maximum tension of 35.0 N. The minimum time for the rocket to reach the sound barrier without breaking the inside wire is 25.3 seconds and the maximum vertical thrust of the rocket engines is 5.72 x 10^5 N/s. When the rocket breaks the sound barrier, it is 4170 m above Earth's surface.
  • #1
DKphysics
2
0
A 25,000-kg rocket blasts off vertically from the Earth's surface with a constant acceleration. During the motion considered in the problem, assume that g remains constant. Inside the rocket, a 15.0-N instrument hangs from a wire that can support a maximum tension of 35.0 N.

a) Find the minimum time for this rocket to reach the sound barrier (330 m/s) without breaking the inside wire and the maximum vertical thrust of the rocket engines under these conditions.

b) How far is the rocket above the Earth's surface when it breaks the sound barrier?


I have no idea where to start with this problem. The answers in the back of the book are:
(a) 25.3 seconds; 5.72 x 10^5 N/s
(b) 4170 m
 
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  • #2
Start by drawing a free body diagram of the weight hanging inside the rocket.
 
  • #3
hage567 said:
Start by drawing a free body diagram of the weight hanging inside the rocket.

Okay
 
  • #4
So once you have that, what do you think you can do next?
 
  • #5
A 2.49e4 kg rocket blasts off vertically from the Earth's surface with a constant acceleration. During the motion considered in the problem, assume that g remains constant. Inside the rocket, a 12.4 N instrument hangs from a wire that can support a maximum tension of 36.0 N.

a) Find the minimum time for this rocket to reach the sound barrier (330 m/s) without breaking the inside wire and the maximum vertical thrust of the rocket engines under these conditions.

b) How far is the rocket above the Earth's surface when it breaks the sound barrier?

I have no idea what to do.
 
  • #6
Go to Post #2. Follow steps there.

(It's better not to add new problems to old posts.)
 
  • #7
Are you mocking the other guy by making a name similar to his? I find this either very coincidental, or pretty hilarious...
 

1. How do Newton's Laws apply to everyday life?

Newton's Laws of Motion explain the behavior of objects in everyday life. For example, the first law states that an object at rest will remain at rest unless acted upon by an external force. This can be seen when a book remains on a table until someone picks it up. The second law states that the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass. This can be observed when a heavier object requires more force to move than a lighter object. The third law states that for every action, there is an equal and opposite reaction. This can be seen when you push against a wall and feel the wall pushing back.

2. How do Newton's Laws relate to sports?

Newton's Laws play a significant role in sports. The first law, also known as the law of inertia, explains why a soccer ball will continue to move in a straight line until it is acted upon by a player's foot or a goalkeeper's hands. The second law helps explain why a baseball will travel further when hit with a more massive bat. The third law can be seen when a tennis player hits a ball with a racket, and the ball bounces off in the opposite direction.

3. How does Newton's third law apply to rocket propulsion?

Newton's third law explains the principle of action and reaction, which is crucial in rocket propulsion. The rocket engines push hot gases out in one direction, and in return, the rocket moves in the opposite direction. This is due to the equal and opposite reaction described in the third law. The force of the gases pushing out is greater than the force of gravity, allowing the rocket to lift off.

4. How can Newton's Laws be used to calculate the motion of an object?

Newton's Laws can be used to calculate the motion of an object by using the equations derived from them. The second law, F=ma, can be used to calculate the acceleration of an object when the net force and mass are known. The first law can be used to determine whether an object will remain at rest or continue moving at a constant velocity. And the third law can be used to predict the direction of forces acting on an object.

5. Can Newton's Laws be applied to non-inertial reference frames?

Newton's Laws are only valid in inertial reference frames, which are frames of reference that are not accelerating. In non-inertial reference frames, such as a rotating frame or an accelerating car, additional forces called fictitious forces must be taken into account. These forces are not real but are necessary to explain the motion of objects in these frames. Therefore, Newton's Laws can be applied to non-inertial frames with the inclusion of fictitious forces.

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