I know i am doing this right but somewhere with the numbers ikeep getting it wro

Question

I know i am doing this right but somewhere with the numbers ikeep getting it wrong A toy gun uses a spring to project a 5.1 g soft rubber sphere horizontally. The springconstant is 13.0 N/m, the barrelof the gun is 12.5 cm long, anda constant frictional force of 0.037 N exists between barrel and projectile.With what speed does the projectile leave the barrel if the springwas compressed5.6 cm for thislaunch? I know i am doing this right but somewhere with the numbers ikeep getting it wrong A toy gun uses a spring to project a 5.1 g soft rubber sphere horizontally. The springconstant is 13.0 N/m, the barrelof the gun is 12.5 cm long, anda constant frictional force of 0.037 N exists between barrel and projectile.With what speed does the projectile leave the barrel if the springwas compressed5.6 cm for thislaunch?

Explanation / Answer

We know that:

Final Energy - Initial Energy = -Work by Non-Conservative forces

We know the initial energy of thesystem is the energy from the spring:

Es = 1/2kx2         wherek is the spring constant and x is the distance it iscompressed Es = 1/2 * 13N/m*(.056m)2 = .020384 J

We also know that the finalenergy is just kinetic energy:

Ke =1/2mV2    where m is the mass of theprojectile and V is the velocity

Finally, we know the work done byfriction is equal to:

W =F*d          whereF is force and d is distance W = 0.037 N * .125 m = .004625J

We can therefore determine thefinal velocity:

1/2mV2 - .020384 J = -.004625 J

V = ((- .004625 J +.020384 J )*2 / .0051kg) = 2.49m/s

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---