*HINTS:*

* STEP 1 - FBD*: Draw a

*SINGLE*free body diagram (FBD) of the system of

*cart + cannon + cannonball*.

*: Write down the impulse/momentum equation in the horizontal direction (x-direction) for the the system of*

**STEP 2 - Kinetics***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 for the velocity of the cart + cannon.*

**Solve.***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?

Any questions?? Please ask/answer questions regarding this homework problem through the "Leave a Comment" link above.

Can we assume the cart is stationary before the cannonball is shot? Also, is it accurate that the cannon is on the cart, so the momentum created by the gunpoweder explosion also applies to it?

Yes, everything is stationary before the cannon is fired. The gunpowder explosion force to which you refer is INTERNAL for the suggested system, and therefore does not influence the momentum of that system.

Does that mean that momentum is conserved in the x direction? If so how would that work for part b?

According to lecture slide 19, it means that there is no net force acting in a given direction. I don't know if it applies to part b. Would it?

TREVOR: You are asking the perfect questions here.

The answer to the first question is "yes", linear momentum in the x-direction for the system of cart+cannon+ball IS conserved because there are no forces in the x-direction for that system.

The hint for the answer to your second question is you need to consider a different FBD for the second part of the question: draw an FBD of the cart+cannon. In this case, momentum is not conserved; however, you still use the impulse/momentum equation to find the (average) force acting on that system.

Does this help?

Yes thank you!

For part b, should I use the linear moment/impulse equation? Or is it easier to find the average Fx using the work-energy equation?

: You should stick with the impulse/momentum equation for the second part. This equation includes "time", and you are given the time delta_t. The work/energy equation will not be useful because that equation involves distance traveled, something that you do not know in this case.sophiekI know we are only required to find the F_x_avg, but in this problem, what is the direction of the force vector?

I meant the force done on the cannon-cart system by P, not the net force.

Technically, we assume an average force but it’s still a vector. And velocities and force are vectors in Impluse-Momentum equation, which will tell you the direction.

Do we need to know the initial velocity of the cannon ball to be able to find the final velocity of the cart? I'm stuck with M*Vcart + m*Vp = m*Vp,initial

Everything is at rest when fired. "Initial" = before firing.