Toy Cannon: Calculating the Projectile Speed

[Dorothy Weglend]

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

 

[d843]

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---->
-------------

 

[Dorothy Weglend]

That makes sense. Thanks. Yes, I used 5.30E-3.

Thanks again,
Dorothy