| Problem statement Solution video |
DISCUSSION THREAD
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HINTS:
STEP 1 - FBD: Draw a SINGLE free body diagram (FBD) of the system of cart + cannon + cannonball.
STEP 2 - Kinetics: Write down the impulse/momentum equation in the horizontal direction (x-direction) for the the system of cart + cannon + cannonball. Based on the above FBD, is the momentum conserved in the x-direction for that system?
STEP 3 - Kinematics
STEP 4 - Solve. Solve for the velocity of the cart + cannon.
QUESTION: The above analysis allows you to find the answer to the first part of the problem. Unfortunately, it is not useful for the find the answer to the second part of the problem where you want to find the force on the cart/cannon. What do you need to change in the analysis to find this force?
Is the velocity V_p relative to the cart or the ground?
The absolute velocity. That seen by a fixed observer.
Since gravity is acting on the cannonball and there shouldn't be a reaction force, should we then assume that linear moment is not conserved in that direction since net forces aren't zero?
Agreed. For a system of the cannon/cart/ball, the net force in the vertical direction is not zero, and therefore, linear momentum is not conserved in the y-direction. For that same system, though, linear momentum in the horizontal direction is conserved.
Is the cart stationary before or after the cannonball is launched (but before collision with cart wall)?
The cart/cannon are stationary before the cannon is fired.
Is it acceptable if this problem was solved assuming that after the cannon fires but before the cannonball collided with the wall that the velocity of the cart was zero? This was not clearly specified in the problem statement.
The problem clearly states that the velocity of the cart/cannon BEFORE the cannon fires is at rest: "A cannonball P of mass m is fired toward a steel barrier on a stationary cart".
Once the cannon is fired, both the cannon ball and the cart/cannon move. Therefore, it would be erroneous to say that the cart/cannon does not move until the ball hits the wall.
since the cart is already moving before the collision, and the momentum must be conserved, can we say that the velocity of the cart after the collision is equal and opposite to the velocity of the cart before the collision, so effectively the change in velocity is twice the final velocity of the cart?
Is the initial state being used in the momentum equation supposed to be before the ball is fired, in which the velocity of the ball, cannon, and cart are all zero?
You are free to choose your initial state. The choice of the time before the firing of the canon makes the most sense as you know the states of velocities at that time.
Do I need to more than two states to evaluate the problem? Currently I have the first state as before firing, the second state as when P hits the wall, and the third state as the instant illustrated.
I believe that for part (a), only one state is needed. We are trying to figure out momentum relations, and in the x direction, momentum is conserved, so we just need too look at mass and velocity.
If horizontal momentum is conserved, and force is a time derivate of momentum, shouldn't the net horizontal force be zero?
If i use the equation F*t = delta p, is the delta p the change in momentum of the system or the change in momentum of an object
don't overcomplicate this problem. only one version of the same equation is needed for either part of the question.