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Dr WLS, PhD in physics and engineering
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Experience:  Online tutor since '94 in science, math & general topics
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Customer Question

A stationary, but moveable 450-kg cannon is fired, and the 12-kg cannonball moves off to the right with a velocity of 20.0 m/s What is the cannon's velocity (both magnitude and direction) due to the kickback from the firing?
Submitted: 11 years ago.
Category: Homework
Expert:  Dr WLS replied 11 years ago.
Are you sure you copied the cannonball speed corectly? 20 m/s seems to be a very slow speed for a cannonball. You should double check that number. Maybe this was a Revolutionary War cannon.

Because of the law of conservation of momemtum, which applies here because the cannon is free to move,

(Vkickback) x (Mcannon)
= (Vcannonball) x (Mcannonball)

Vkickback = 12/450 x Vcannonball

That would be 0.533 m/s if your 20 m/s velocity of the cannonball is correct, but you should recheck that number you were given
Dr WLS, PhD in physics and engineering
Category: Homework
Satisfied Customers: 483
Experience: Online tutor since '94 in science, math & general topics
Dr WLS and 3 other Homework Specialists are ready to help you
Expert:  xarqi replied 11 years ago.
One small comment:
The magnitude of the cannon has been given correctly above.

However, the law of conservation of momentum states that there
is no net change in momentum in a system over time. That is,
the sum of the momenta is zero.

In a two body system, this means that:
Vk x Mk = -Vc x Mc

The negative sign shows us that the direction of the cannon is
the reverse of that of the cannonball.

Thus the velocity of the cannon should be given as -0.53 m/s.
Note that only two figures of precision are justified given the
uncertainty implicit in the stated mass of the cannonball.
Expert:  Dr WLS replied 11 years ago.
With respect to xarqi's comments:
(1) Since some of the input data were given to three significant figures, I felt there was no harm in doing the same with the answer. I agree that if the true mass was rounded to 12 kg from 12.49 or 11.50 kg, less precision in the answer would be appropriate.
(2) I do not have the benefit, which Xarqi claims to have, of being sure the original problem correctly stated the cannonball velocity. Misprints happen. Cannonball velocities, even in the 18th century, were in a 120-250 m/s range. I felt it was my duty to warn the student of a possible misprint or transcription error with the 20 m/s figure. Such a cannonball could travel no more than 40 meters. A 20 m/s muzzle velocity might be appropriate for a toy, but not a 450 kg cannon firing 12 kg cannonballs. A catapult can do better than 20 m/s.
(3) Xarqi is correct in stating that the cannonball and cannon have opposite-directed velocities, to maintain a net momentum of zero.
Expert:  xarqi replied 11 years ago.
One must used the least precise measurement as a gauge
of precision in an answer, not the most precise.

I inadvertantly omitted a word and should have said:
"The magnitude of the cannon velocity has been given
correctly above", referring to the accurate answer already given.

I quite agree that the figures given in the question are
suspicious and should be verified.
Customer: replied 11 years ago.
Reply to xarqi's Post: Thank you for your response, the question is right. I did accept the answer from Dr. WLS

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