   Chapter 5, Problem 68AP

Chapter
Section
Textbook Problem

A toy gun uses a spring to project a 5.3-g soft rubber sphere horizontally. The spring constant is 8.0 N/m, the barrel of the gun is 15 cm long, and a constant frictional force of 0.032 N exists between barrel and projectile. With what speed does the projectile leave the barrel if the spring was compressed 5.0 cm for this launch?

To determine
The speed of the projectile when it leaves the projectile.

Explanation

Given Info:

The mass of rubber sphere is 5.3g .

The spring constant is 8.0N/m .

The length of the barrel is 15.0cm .

The frictional force between the barrel and projectile is 0.032N .

The length that the spring is compressed for launch is 5.0cm .

According to Work-Energy theorem,

Wnc=(KEf+PEg,f+PEs,f)(KEi+PEg,i+PEs,i)

Since, the work done by the non conservative force is in the opposite of the action,

Thus,

Wnc=(fkcos180°)s

• s is the length of barrel
• fk is the frictional force

Thus,

(fkcos180°)s=(12mvf2+0+0)(0+0+12kxi2)

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started 