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The ball launcher in a pinball machine has a spring that has a force constant of 1.23 N/cm. The surface on which the ball moves is in- clined 15.6◦ with respect to the horizontal. If the spring is initially compressed 3.58 cm, find the launching speed of a 0.19 kg ball when the plunger is released. The acceleration due to gravity is 9.8 m/s2 . Friction and the mass of the plunger are negligible.

The ball launcher in a pinball machine has a spring that has a force constant of 1.23 N/cm. The surface on which the ball moves is in- clined 15.6◦ with respect to the horizontal. If the spring is initially compressed 3.58 cm, find the launching speed of a 0.19 kg ball when the plunger is released. The acceleration due to gravity is 9.8 m/s2 . Friction and the mass of the plunger are negligible.

College Physics
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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The ball launcher in a pinball machine has a spring that has a force constant of 1.23 N/cm. The surface on which the ball moves is in- clined 15.6◦ with respect to the horizontal.

If the spring is initially compressed 3.58 cm, find the launching speed of a 0.19 kg ball when the plunger is released. The acceleration due to gravity is 9.8 m/s2 . Friction and the mass of the plunger are negligible.

### Transcription for Educational Context #### Description of System and Diagram The diagram illustrates a setup for analyzing the motion of an object on an inclined plane with a spring mechanism. 1. **Setup Overview**: - The system consists of a hand holding a spring-loaded launcher on a 15.6° inclined plane. - The launcher is used to propel a spherical object (indicated in dark gray) along the incline. 2. **Detailed Components**: - **Spring**: - The spring constant is provided as \(1.23 \, \text{N/cm}\). - Initially, the spring is compressed by \(3.58 \, \text{cm}\). - **Projectile Motion**: - The object starts from rest, indicated by \(v_0 = 0\). - Upon release, the object moves up the incline with velocity \(v\). 3. **Inclined Plane**: - The plane is at an angle of \(15.6°\) relative to the horizontal, demonstrating the effect of gravitational and frictional forces on the motion. #### Interpretation This setup is typically used in physics to study concepts such as: - Kinetic and potential energy conversion. - Hooke's Law related to spring force and spring constant. - Motion on an inclined plane including components of gravitational force along the incline. Understanding these principles is crucial for analyzing projectile motion and energy transformation in systems.
Transcribed Image Text:### Transcription for Educational Context #### Description of System and Diagram The diagram illustrates a setup for analyzing the motion of an object on an inclined plane with a spring mechanism. 1. **Setup Overview**: - The system consists of a hand holding a spring-loaded launcher on a 15.6° inclined plane. - The launcher is used to propel a spherical object (indicated in dark gray) along the incline. 2. **Detailed Components**: - **Spring**: - The spring constant is provided as \(1.23 \, \text{N/cm}\). - Initially, the spring is compressed by \(3.58 \, \text{cm}\). - **Projectile Motion**: - The object starts from rest, indicated by \(v_0 = 0\). - Upon release, the object moves up the incline with velocity \(v\). 3. **Inclined Plane**: - The plane is at an angle of \(15.6°\) relative to the horizontal, demonstrating the effect of gravitational and frictional forces on the motion. #### Interpretation This setup is typically used in physics to study concepts such as: - Kinetic and potential energy conversion. - Hooke's Law related to spring force and spring constant. - Motion on an inclined plane including components of gravitational force along the incline. Understanding these principles is crucial for analyzing projectile motion and energy transformation in systems.
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