A horizontal block-spring system with the block on a frictionless surface has total mechanical energy E = 46.9 J and maximum displacement from equilibrium of 0.227 m. (a) What is the spring constant? 1820.3 N/m (b) What is the kinetic energy of the system at the equilibrium point? 46.9 J (c) If the maximum speed of the block is 3.45 m/s, what is its mass? 7.88 kg (d) What is the speed of the block when its displacement is 0.160 m? m/s (e) Find the kinetic energy of the block at x = 0.160 m. (f) Find the potential energy stored in the spring when x = 0.160 m. (g) Suppose the same system is released from rest at x = 0.227 m on a rough surface so that it loses 12.1 J by the time it reaches its first turning point (after passing equilibrium at x = 0). What is its position at that instant?

A horizontal block-spring system with the block on a frictionless surface has total mechanical energy E = 46.9 J and maximum displacement from equilibrium of 0.227 m. (a) What is the spring constant? 1820.3 N/m (b) What is the kinetic energy of the system at the equilibrium point? 46.9 J (c) If the maximum speed of the block is 3.45 m/s, what is its mass? 7.88 kg (d) What is the speed of the block when its displacement is 0.160 m? m/s (e) Find the kinetic energy of the block at x = 0.160 m. (f) Find the potential energy stored in the spring when x = 0.160 m. (g) Suppose the same system is released from rest at x = 0.227 m on a rough surface so that it loses 12.1 J by the time it reaches its first turning point (after passing equilibrium at x = 0). What is its position at that instant?

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

Spring Potential Energy

The potential energy is the energy possessed by a body by virtue of its position or the energy held by the object due to its position relative to other objects, its force like stresses, charge, and other factors affecting the particles of the body. The potential energy is the measure of the net work done by or on the body. The spring potential energy is the potential energy stored due to the deformation of an elastic spring and this elasticity is due to the stretched spring. The elasticity is the ability of a solid-state matter to come back to its equilibrium position or original position after any kind of external force is acted on it. It is also known as Elastic potential energy. The potential energy here is caused due to the displacement of the spring from its equilibrium position to another position and this potential energy is equal to the net work done due to the stretching of the spring. It also resembles the same mechanics of the oscillation of a simple pendulum, where due to the external force, the object moves from its equilibrium position to its maximum ends and the periodic motion continues till it comes back to the equilibrium position to rest. 

Question

### Horizontal Block-Spring System on a Frictionless Surface

A horizontal block-spring system with the block on a frictionless surface has a total mechanical energy \( E = 46.9 \, \text{J} \) and a maximum displacement from equilibrium of \( 0.227 \, \text{m} \).

#### (a) What is the spring constant?
- **Answer:** \( 1820.3 \, \text{N/m} \)

#### (b) What is the kinetic energy of the system at the equilibrium point?
- **Answer:** \( 46.9 \, \text{J} \)

#### (c) If the maximum speed of the block is \( 3.45 \, \text{m/s} \), what is its mass?
- **Answer:** \( 7.88 \, \text{kg} \)

#### (d) What is the speed of the block when its displacement is \( 0.160 \, \text{m} \)?
- **Answer:** (Input required)

#### (e) Find the kinetic energy of the block at \( x = 0.160 \, \text{m} \).
- **Answer:** (Input required)

#### (f) Find the potential energy stored in the spring when \( x = 0.160 \, \text{m} \).
- **Answer:** (Input required)

#### (g) Suppose the same system is released from rest at \( x = 0.227 \, \text{m} \) on a rough surface so that it loses \( 12.1 \, \text{J} \) by the time it reaches its first turning point (after passing equilibrium at \( x = 0 \)). What is its position at that instant?
- **Answer:** (Input required)

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