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# Integrated ConceptsA toy gun uses a spring with a force ISBN: 9781938168000 42

## Solution for problem 63PE Chapter 7

College Physics | 1st Edition

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Problem 63PE

Integrated Concepts

A toy gun uses a spring with a force constant of 300 N/m to propel a 10.0-g steel ball. If the spring is compressed 7.00 cm and friction is negligible: (a) How much force is needed to compress the spring? (b) To what maximum height can the ball be shot? (c) At what angles above the horizontal may a child aim to hit a target 3.00 m away at the same height as the gun? (d) What is the gun’s maximum range on level ground?

Step-by-Step Solution:

Part (a)

Step 1 of 9:

A steel ball is fired using a toy gun. The spring inside the gun is given and the force constant is also provided. Assume that the friction is negligible. We are going to find the force required to compress the spring.

The force constant of the spring The displacement of the spring or Step 2 of 9:

The force required to compress the spring Substituting the values  The force required to compress the ball is -21.0 N

Part (b)

Step 3 of 9:

If the gun is shot vertically, the ball goes in the upward direction. Our aim is to find the maximum height that the ball can go. The expression for the vertical height of a projectile is used to find the maximum height here. Before finding the vertical height, we need to calculate the initial speed of the ball.

Step 4 of 9:

From conservation of energy

The potential energy of the ball by compressed spring = the kinetic energy of the ball Where is the mass of the ball. or  is the initial speed of the ball when it is released

Solving the equation (2) for  Substituting the values  The initial speed of the ball is Step 5 of 9:

The expression for the maximum height of a projectile (ball) Where g is acceleration due to gravity and  , since the ball is shot vertically upward.

Therefore the maximum height is  or The maximum height can be reached by the ball is 7.5 m

Part (c)

Step 6 of 9

Step 7 of 9

##### ISBN: 9781938168000

The full step-by-step solution to problem: 63PE from chapter: 7 was answered by , our top Physics solution expert on 07/07/17, 04:39PM. This full solution covers the following key subjects: spring, gun, height, maximum, ball. This expansive textbook survival guide covers 34 chapters, and 3125 solutions. College Physics was written by and is associated to the ISBN: 9781938168000. Since the solution to 63PE from 7 chapter was answered, more than 1052 students have viewed the full step-by-step answer. The answer to “Integrated ConceptsA toy gun uses a spring with a force constant of 300 N/m to propel a 10.0-g steel ball. If the spring is compressed 7.00 cm and friction is negligible: (a) How much force is needed to compress the spring? (b) To what maximum height can the ball be shot? (c) At what angles above the horizontal may a child aim to hit a target 3.00 m away at the same height as the gun? (d) What is the gun’s maximum range on level ground?” is broken down into a number of easy to follow steps, and 86 words. This textbook survival guide was created for the textbook: College Physics , edition: 1.

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