What is the solution for the gravitational pull on earth?
1 answer:
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Answer:
The velocity of the bullet is
Explanation:
The free body diagram of this question is shown on the first uploaded image
Since we are told that the bullet got lodged in the rod we are going to look at the bullet and rod combined as a system
And this also means that the collision is inelastic since the both object stuck together
examining this question we can deduce that the pivot on the rotational axis also exerts an external force on the system (the rod + the bullet)
These eternal force does not cause rotation but hold the rod along the horizontal plane hence the these is no external which mean that the angular momentum is conserved
Generally angular momentum is mathematically represented as
This positive because the bullet misses the axis to the right (Which means it would be moving in a counter clock- wise direction around the axis)
Before the collision
And b is the minimum distance of approach as shown on the diagram
According to trigonometry
Now the total angular momentum before collision is
Generally moment of inertia is mathematically represented as
Where m is the mass and r is the distance to the axis of rotation
After collision since the bullet and the rod combined and became a system
their moment of inertia would be the same and is mathematically given as
Assuming that it was
Now as the system rotates due the force of the bullet and the fact that the plane is fixed about the vertical axis at an angular speed of
The final momentum is mathematically represented as
Since Angular momentum is conserved
Making the subject of the formula gives
