**Problem Statement:**A 0.8 kg ball is launched into the air by a spring with \( k = 8000 \, \text{N/m} \) that has been compressed by 0.07 m. How fast is the ball moving when it is 0.5 m above the spring?**Diagram:**The diagram on the right shows a spring at the bottom with a ball placed on top of it. The ball's initial position is compressed on the spring. There is an arrow indicating the ball's trajectory upwards, reaching a point labeled 0.5 m above the spring.**Table for Energy Calculations:**The table is divided into four sections with headings:- \( E_f \) (Final Energy)- \( = \) (Indicating equality between initial and final energy)- \( E_i \) (Initial Energy)- \( + \) (Adding terms)- \( W \) (Work done)Each section is a blank space for completing energy calculations based on the given scenario, incorporating kinetic energy, potential energy, and work done by the spring.

Name: **Problem Statement:**A 0.8 kg ball is launched into the air by a spr
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Description: **Problem Statement:**A 0.8 kg ball is launched into the air by a spring with \( k = 8000 \, \text{N/m} \) that has been compressed by 0.07 m. How fast is the ball moving when it is 0.5 m above the spring?**Diagram:**The diagram on the right shows a

Given: The mass of the ball is m=0.8 kg The spring constant is k=8000 N/m The maximum compression in the spring is x=0.07 m The initial height of the ball from the spring is h=0.5 m it is required to determine the speed of the ball above 0.5 m above the spring.Explanation: There is no external force applied, so the kinetic energy of the ball is transferred to the potential energy of the spring. Spring potential energy= kinetic energy+ gravitational PE From the conservation of energy in the system: 12 kx2=mgh+12mv212 kx2=mg0.5 m+12mv212 kx2=12mg+12mv212mv2=12kx2-mgmv2=kx2-mgv=kx2-mgm at the fully compressed state, the gravitational potential energy of the spring is zero. Here, v is the speed of the ball at height h, k is the spring constant, m is the mass of the object, k is the spring constant, x is the maximum compression, and g is the acceleration due to gravity. Substitute, all known values in the above expression. v=8000 N/m0.07 m2-00.8 kg=49 m/s=7 m/s The final answer: The speed of the ball above 0.5 m above the spring is 7 m/s

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3. A 0.8kg ball is launched into the air by a spring with k = 8000N/m that has been compressed by 0.07m. How fast is the ball moving when it is 0.5m above the spring? L W 0.5m

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ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

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Concept explainers

Simple harmonic motion

Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.

Simple Pendulum

A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.

Oscillation

In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.

Topic Video

Question

**Problem Statement:**

A 0.8 kg ball is launched into the air by a spring with \( k = 8000 \, \text{N/m} \) that has been compressed by 0.07 m. How fast is the ball moving when it is 0.5 m above the spring?

**Diagram:**

The diagram on the right shows a spring at the bottom with a ball placed on top of it. The ball's initial position is compressed on the spring. There is an arrow indicating the ball's trajectory upwards, reaching a point labeled 0.5 m above the spring.

**Table for Energy Calculations:**

The table is divided into four sections with headings:
- \( E_f \) (Final Energy)
- \( = \) (Indicating equality between initial and final energy)
- \( E_i \) (Initial Energy)
- \( + \) (Adding terms)
- \( W \) (Work done)

Each section is a blank space for completing energy calculations based on the given scenario, incorporating kinetic energy, potential energy, and work done by the spring.

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