| Problem statement Solution video |
DISCUSSION THREAD
Any questions?? Please ask/answer questions regarding this homework problem through the “Leave a Comment” link above.
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?
Can we assume the angle of the cannon is the same as angle theta? Is knowing the angle of the cannon necessary to solving this question?
The angle of the cannon is not relevant to the questions that are answered.
I think so
What value of g should be used here?
The usual for this set of British units.
For this problem, I found it useful to create two separate systems – one containing both the cart (with attached cannon) and the cannonball, and another with the cannonball removed. This second system allows for analysis to find the average force over the given time interval.
Would I need to convert the given mg and Mg into just the mass value? In that case, would the units be slug?
Yes, M and m would be in slugs.
Should we take the point in time when the cannon+cart+cannon ball are all stationary as time 1, with time 2 after the cannon ball has rebounded?
That would be a good plan.