Toy Cannon: Calculating the Projectile Speed

In summary, the conversation discusses the use of a toy cannon with a spring to project a 5.30g soft rubber ball. The barrel is compressed 5.00 cm with a k value of 8.00 N/m. The ball moves 15.0 cm through the barrel, with a friction force of 0.0320 N. The question asks for the speed at which the projectile leaves the barrel. The suggested solution involves using mv^2/2 = kx^2/2 - fk(x+d), but it is pointed out that mv^2/2 = kx^2/2 - fk(x) may be more appropriate. After some discussion, it is determined that the answer in the back of
  • #1
Dorothy Weglend
247
2
A toy cannon uses a spring to project a 5.30g soft rubber ball. Spring is compressed 5.00 cm, k=8.00 N/m. Barrel is horizontal.

The ball moves 15.0 cm through the barrel, with friction force of 0.0320 N between thebarrel and the ball. With what speed does the projectile leave the barrel of the cannon?

I thought this problem was simple, but the answer 'in the back' is different from what I am getting, so I thought I would ask for some help.

I use

mv^2/2 = kx^2/2 - fk(x+d)

x = compression of spring, d = distance along the barrel, so

m = 5.32 * 10^-3 m,
k = 8 N/m
x = 0.05 m
k = 8 N/m
fk = 0.032 N
d = 0.15 m

With these figures, I get v = 1.17 m/s.

The answer in the back is 1.40 m/s.

Can anyone see where I am going wrong?

Dorothy
 
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  • #2
Are you sure you are supposed to use ... - fk(x+d)?
if you use mv^2/2 = kx^2/2 - fk(x) instead, it will give a v of 1.40 m/s
I think the problem was trying to help you-it gave you the TOTAL distance the projectile has to travel in the barrel. I tried to make a diagram below, I'm not sure it worked.

Oh, and you meant m=5.30 x 10-3 kg right?

/\/\/ is the compressed spring
X is the projectile...|-0.15m-|
-------------
/\/\-X---->
-------------
 
Last edited:
  • #3
That makes sense. Thanks. Yes, I used 5.30E-3.

Thanks again,
Dorothy
 

Related to Toy Cannon: Calculating the Projectile Speed

What is a "Toy Cannon" and how does it work?

A "Toy Cannon" is a miniature version of a real-life cannon that is used for recreational purposes. It works by using the force of compressed air to propel a small object, such as a foam ball or paper pellet, out of the cannon.

How do you calculate the projectile speed of a "Toy Cannon"?

The formula for calculating projectile speed is: speed = distance / time. To measure the distance, you can use a measuring tape or ruler. To measure the time, you can use a stopwatch or count the seconds.

What factors can affect the projectile speed of a "Toy Cannon"?

The projectile speed of a "Toy Cannon" can be affected by a number of factors, including the amount of force used to compress the air, the weight of the projectile, the angle at which the cannon is fired, and any external factors such as wind or friction.

How accurate are the results when calculating the projectile speed of a "Toy Cannon"?

The accuracy of the results when calculating the projectile speed of a "Toy Cannon" can vary depending on the precision of the measurements and the consistency of the experimental conditions. It is important to repeat the experiment multiple times and take an average to improve accuracy.

What are some potential applications of knowing the projectile speed of a "Toy Cannon"?

Knowing the projectile speed of a "Toy Cannon" can have various applications, such as in the development of toy weapons, educational demonstrations, and recreational activities. It can also be used to teach basic physics principles, such as velocity and acceleration.

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