a rocket following a parabolic path through the air suddenly explodes into many pieces. what can you say about the motion of this system.
and
If only an external force can change the momentum of the center of mass of an object, how can the internal force of the engine accelerate a car?
-For the first one, I think that the since the center of mass changes, the pieces go off into different directions slower?
I don't know about the second one
Why do you think the momemtum of the system has changed? The cm will follow the same path, ignoring air resistance.
Remember, the explosion was NOT an external force.
On the second, the internal force of the engine is transcribed to an external force through the wheels on the pavement.
For the first question, the motion of the system can be understood by considering the conservation of momentum and the behavior of objects in free fall. When the rocket explodes into many pieces, each piece will continue to follow its own independent trajectory, which will be influenced by gravity.
The initial velocity of each piece will be determined by the velocity and direction of the rocket at the time of explosion. As these pieces are now separate entities, they will no longer move as one system. Instead, they will each experience their own independent parabolic paths.
It's important to note that the velocity and direction of each piece may vary depending on the location and time of the explosion. Some pieces may be propelled in a forward direction, while others might be propelled backward or at various angles. The overall motion of the system will be dependent on the velocities and directions of the individual pieces.
Regarding the second question, it is important to understand that the internal force of the engine does not directly accelerate the car's center of mass. Instead, the internal force generated by the engine causes the car's wheels to exert a force on the ground in the opposite direction. According to Newton's third law of motion, the ground then exerts an equal and opposite force on the car, resulting in a forward acceleration.
The force from the engine causes the wheels to push against the ground, creating a forward frictional force. This force helps propel the car forward by allowing the tires to grip the road surface. The friction force between the wheels and the ground generates a reaction force that acts on the car's center of mass, resulting in its acceleration.
In summary, while only external forces can directly change the momentum of an object's center of mass, the internal force from the engine of a car indirectly accelerates the car by generating a frictional force between the wheels and the ground, resulting in a reaction force that acts on the center of mass.