# Chapter 11: Shooting a Block up an Incline## Problem DescriptionA block of mass \( m \) is placed in a smooth-bored spring gun at the bottom of the incline so that it compresses the spring by an amount \( x_c \). The spring has a spring constant \( k \). The incline makes an angle \( \theta \) with the horizontal, and the coefficient of kinetic friction between the block and the incline is \( \mu \). The block is released, exits the muzzle of the gun, and slides up an incline a total distance \( L \). ![Figure 1](Link-to-Figure)## Part A**Objective:**Find \( L \), the distance traveled along the incline by the block after it exits the gun. Ignore friction when the block is inside the gun. Also, assume that the uncompressed spring is just at the top of the gun (i.e., the block moves a distance \( x_c \) while inside of the gun). Use \( g \) for the magnitude of acceleration due to gravity.**Question:**Express the distance \( L \) in terms of \( x_c, k, m, g, \mu, \) and \( \theta \).\[L = \](Use the provided input box to enter your solution.)**Submit** your answer when ready.## Figure DescriptionThe figure illustrates a block of mass \( m \) on an incline. The incline forms an angle \( \theta \) with the horizontal. A spring at the bottom is compressed by a distance \( x_c \). Once released, the block travels a distance \( L \) up the incline. The figure shows the block in motion, the initial compression of the spring \( x_c \), and the total distance traveled \( L \) along the inclined surface.[View Available Hint(s)] to assist with the solution process.[Provide Feedback] if you have any suggestions or questions regarding this educational content.

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College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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# Chapter 11: Shooting a Block up an Incline

## Problem Description

A block of mass \( m \) is placed in a smooth-bored spring gun at the bottom of the incline so that it compresses the spring by an amount \( x_c \). The spring has a spring constant \( k \). The incline makes an angle \( \theta \) with the horizontal, and the coefficient of kinetic friction between the block and the incline is \( \mu \). The block is released, exits the muzzle of the gun, and slides up an incline a total distance \( L \). ![Figure 1](Link-to-Figure)

## Part A

**Objective:**

Find \( L \), the distance traveled along the incline by the block after it exits the gun. Ignore friction when the block is inside the gun. Also, assume that the uncompressed spring is just at the top of the gun (i.e., the block moves a distance \( x_c \) while inside of the gun). Use \( g \) for the magnitude of acceleration due to gravity.

**Question:**

Express the distance \( L \) in terms of \( x_c, k, m, g, \mu, \) and \( \theta \).

\[
L =
\]

(Use the provided input box to enter your solution.)

**Submit** your answer when ready.

## Figure Description

The figure illustrates a block of mass \( m \) on an incline. The incline forms an angle \( \theta \) with the horizontal. A spring at the bottom is compressed by a distance \( x_c \). Once released, the block travels a distance \( L \) up the incline. The figure shows the block in motion, the initial compression of the spring \( x_c \), and the total distance traveled \( L \) along the inclined surface.

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