A horizontal spring attached to a wall has a force constant of 890 N/m. A block of mass 1.40 kg is attached to the spring and oscillates freely on a horizontal, frictionless surface as in the figure below. The initial goal of this problem is to find the velocity at the equilibrium point after the block is released. (a) KE,-0 (b) wwww (a) What objects constitute the system, and through what forces do they interact? (b) What are the two points of interest? (c) Find the energy stored in the spring when the mass is stretched 5.00 cm from equilibrium and again when the mass passes through equilibrium after being released from rest. x = 5.06 X = 0 (d) Write the conservation of energy equation for this situation and solve it for the speed of the mass as it passes equilibrium. (Do this on paper. Your instructor may ask you to turn in this work.) (e) Substitute to obtain a numerical value.

A horizontal spring attached to a wall has a force constant of 890 N/m. A block of mass 1.40 kg is attached to the spring and oscillates freely on a horizontal, frictionless surface as in the figure below. The initial goal of this problem is to find the velocity at the equilibrium point after the block is released. (a) KE,-0 (b) wwww (a) What objects constitute the system, and through what forces do they interact? (b) What are the two points of interest? (c) Find the energy stored in the spring when the mass is stretched 5.00 cm from equilibrium and again when the mass passes through equilibrium after being released from rest. x = 5.06 X = 0 (d) Write the conservation of energy equation for this situation and solve it for the speed of the mass as it passes equilibrium. (Do this on paper. Your instructor may ask you to turn in this work.) (e) Substitute to obtain a numerical value.

Name: **Physics Problem: Oscillating Block and Spring System**A horizontal
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Description: **Physics Problem: Oscillating Block and Spring System**A horizontal spring attached to a wall has a force constant of 890 N/m. A block of mass 1.40 kg is attached to the spring and oscillates freely on a horizontal, frictionless surface. The initia

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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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.

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Question

**Physics Problem: Oscillating Block and Spring System**

A horizontal spring attached to a wall has a force constant of 890 N/m. A block of mass 1.40 kg is attached to the spring and oscillates freely on a horizontal, frictionless surface. The initial goal of this problem is to determine the velocity at the equilibrium point after the block is released.

**Illustrations and Description:**
1. **Diagram (a):** Spring is compressed (x = 0).
- Energy stored in spring: \( E_s = \frac{1}{2} kx^2 \).
2. **Diagram (b):** Spring at equilibrium (x = 0).
- Potential energy is zero: \( E_s = 0 \).
3. **Diagram (c):** Spring is stretched (x = 0).
- Kinetic energy: \( E_k = \frac{1}{2} mv^2 \).

**Questions:**

(a) **Identify System Objects and Forces of Interaction:**
*What objects constitute the system, and through what forces do they interact?*

(b) **Points of Interest:**
*What are the two points of interest?*

(c) **Energy Stored in the Spring:**
*Calculate the energy when the mass is stretched 5.00 cm from equilibrium and when it passes through equilibrium after being released from rest.*

- \( x = 5.00 \): Stored energy: \(\ \_\_\_\_ \ \text{J} \)
- \( x = 0 \): Stored energy: \(\ \_\_\_\_ \ \text{J} \)

(d) **Conservation of Energy Equation:**
*Write and solve the energy equation for the speed of the mass as it passes equilibrium. (Do this on paper. Your instructor may ask you to turn in this work.)*

(e) **Numerical Solution:**
*Substitute values to obtain a numerical speed: \(\_\_\_\_ \ \text{m/s} \)*

**Note:** Diagrams represent different states of the spring's compression and extension relative to equilibrium, highlighting the transformation between potential and kinetic energy within the system.

(d) Write the conservation of energy equation for this situation and solve it for the speed of the mass as it passes equilibrium. (Do this on paper. Your instructor may ask you to turn in this work.)

(e) Substitute to obtain a numerical value.
_____ m/s

(f) What is the speed at the halfway point?
_____ m/s

(g) Why isn’t it half the speed at equilibrium? (Do this on paper. Your instructor may ask you to turn in this work.)

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