Conservation of Energy, Momentum

In summary, the problem involves a bullet with mass m and speed v passing through a pendulum bob with mass M and emerging with a speed of v/2. The pendulum bob is suspended by a rigid rod of length l and negligible mass, and the question asks for the minimum speed vp for the bob to reach the top of the arc at point A. The speed of the bullet just before hitting the bob and the magnitude of the force in the rod just after the bullet emerges are also requested. The solution involves finding the centripetal force required to keep the bob on the string, which is equal to mv^2/r + mg, and then using this to solve for the minimum speed and the speed of the bullet. The magnitude
  • #1
abpandanguyen
33
0

Homework Statement


A bullet of mass m = .010 kg and speed v passes completely through a pendulum bob of mass M = 1.2 kg. The bullet emerges with a speed of v/2. The pendulum bob is suspended by a rigid rod of length l = 0.50 m and negligible mass that can pivot about the center point.


What minimum speed vp must the pendulum bob have to just make it to the top of the arc at point A (top of the circle, pendulum starting at the bottom)?

What is the speed of the bullet just before hitting the pendulum bob for the situation described in part a?

What is the magnitude of the force in the rod just after the bullet emerges?



Homework Equations



Fr = mv2/r

The Attempt at a Solution


I solved for parts a and b already, and I also got C (answer is 58.8N), but I'm having trouble understanding why this number is the answer. At the bottom of the circle would the magnitude of the force in the rod be:

Fr + mg?

that gets the answer, but aren't these forces going in different directions at the bottom of the circle?
 
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  • #2
Fr = mv2/r is the centripetal force required to keep the bob on the string. Since tension must provide this centripetal force and counteract gravity, T=mv^2/r + mg.
 
  • #3
ideasrule said:
Fr = mv2/r is the centripetal force required to keep the bob on the string. Since tension must provide this centripetal force and counteract gravity, T=mv^2/r + mg.

if it was counteracting gravity, doesn't that mean it would be - mg? I don't think I'm quite understanding here.
 

Related to Conservation of Energy, Momentum

What is conservation of energy?

Conservation of energy is a fundamental principle in physics which states that energy cannot be created or destroyed, but can only be transformed from one form to another.

What is conservation of momentum?

Conservation of momentum is a fundamental principle in physics which states that the total momentum of a closed system (where no external forces act) remains constant over time.

Why is conservation of energy important?

Conservation of energy is important because it allows us to predict and understand the behavior of physical systems, from the movement of objects to the flow of electricity. It also plays a crucial role in many practical applications, such as energy production and conservation.

How do we apply conservation of energy and momentum in real life?

Conservation of energy and momentum are applied in many areas of our daily lives, such as in the design of efficient engines and transportation systems, the production of electricity, and the understanding of natural phenomena like collisions and explosions.

What happens when conservation of energy or momentum is violated?

If conservation of energy or momentum is violated, it means that there is an external force or energy source acting on the system. This can lead to unexpected and unpredictable behavior, and can have consequences such as energy waste or system failure.

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