Impulse on and the distance traveled by a cannonball

• benca
In summary, the problem states that a cannonball fired by a cannon starts at rest. However, the assumption is not sensible and the problem does not provide information about the force acting on the cannonball.
benca
Homework Statement
A cannonball with a mass of 70 kg experiences an impulse of 4.0 x 10^3 N*s for 0.35 s

a) calculate the force acting on the cannonball

b) How long was the barrel of the cannon?. Assume the force is applied only for the period of time that the cannonball is in the cannon.
Relevant Equations
J = Ft
W= Fd
J = mv' - mv
a)
F = J/t
F = 4000 N*s / 0.35 s
F = 11429 N

b) I was going to equate impulse to the change in momentum and solve for v' (final velocity). Then use v' to solve for ΔEk. set ΔEk = Fd and solve for d. (The question never mentioned an angle of inclination, so I thought it would be ok to use W = Fd)

However when I was isolating v' I realized I wasn't sure what v (initial velocity) was. Is it 0 m/s?

I can solve for Δv using J = ΔP = mΔv (right?) But I'm not sure what I could do with that without knowing either the initial or final velocity. Basically, I'm not sure whether I can use 0 m/s for initial velocity or not.

benca said:
Homework Statement: A cannonball with a mass of 70 kg experiences an impulse of 4.0 x 10^3 N*s for 0.35 s

a) calculate the force acting on the cannonball

b) How long was the barrel of the cannon?. Assume the force is applied only for the period of time that the cannonball is in the cannon.
Homework Equations: J = Ft
W= Fd
J = mv' - mv

a)
F = J/t
F = 4000 N*s / 0.35 s
F = 11429 N

b) I was going to equate impulse to the change in momentum and solve for v' (final velocity). Then use v' to solve for ΔEk. set ΔEk = Fd and solve for d. (The question never mentioned an angle of inclination, so I thought it would be ok to use W = Fd)

However when I was isolating v' I realized I wasn't sure what v (initial velocity) was. Is it 0 m/s?

I can solve for Δv using J = ΔP = mΔv (right?) But I'm not sure what I could do with that without knowing either the initial or final velocity. Basically, I'm not sure whether I can use 0 m/s for initial velocity or not.

Where are you getting these problems? This is another very poor question. The problem mentions nothing about constant force. Without assuming constant force the problem is not well posed.

Moreover, it's almost certain that the force would be far from constant. The ball would likely accelerate rapidly and reach close to its maximum speed long before it emerges from the barrel. You can look this up online, if you are interested.

Assuming that a cannonball fired by a cannon starts at rest is perhaps a logical and sensible assumption, don't you think? That should be the least of the issues with this problem.

It's from an adult high school course I'm taking. There are no formal lectures, just small lessons I need to hand in. I don't know about other adult learning centres but I found out that this one is notorious for it's poor material quality, almost every lesson so far has had either outright mistakes or questions that are poorly phrased. (that's me venting)

anyways, I'll assume it starts at 0 m/s, thanks

What is impulse and how does it relate to a cannonball?

Impulse is a measure of the change in momentum of an object. In the case of a cannonball, impulse is the force applied to the cannonball when it is fired from the cannon. This force causes the cannonball to accelerate and gain momentum, ultimately determining the distance it will travel.

What factors affect the impulse and distance traveled by a cannonball?

The impulse and distance traveled by a cannonball are affected by several factors, including the force of the cannon, the mass of the cannonball, the angle at which the cannon is fired, and air resistance. Other factors such as elevation and wind speed may also play a role.

How does the angle at which a cannon is fired affect the distance traveled by a cannonball?

The angle at which a cannon is fired can greatly impact the distance traveled by a cannonball. The optimal angle for maximum distance is typically around 45 degrees, as this angle allows for the most efficient use of the cannon's force and minimizes air resistance. Lower or higher angles will result in a shorter distance traveled.

How does air resistance affect the distance traveled by a cannonball?

Air resistance, also known as drag, can greatly impact the distance traveled by a cannonball. As the cannonball travels through the air, it experiences resistance from the air molecules, which slows it down. This means that the longer the distance traveled, the more air resistance the cannonball will encounter, resulting in a shorter overall distance.

Can the distance traveled by a cannonball be calculated using mathematical equations?

Yes, the distance traveled by a cannonball can be calculated using mathematical equations, such as the projectile motion equations. These equations take into account factors such as initial velocity, angle of launch, and air resistance to determine the distance traveled by the cannonball. However, these calculations may not be entirely accurate due to the unpredictable nature of air resistance and other external factors.

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